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<!DOCTYPE html> <html lang="en" class="no-js"> <head> <meta charset="UTF-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="applicable-device" content="pc,mobile"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="robots" content="max-image-preview:large"> <meta name="access" content="Yes"> <meta name="360-site-verification" content="1268d79b5e96aecf3ff2a7dac04ad990" /> <title>Measurement of charged particle multiplicity distributions in DIS at HERA and its implication to entanglement entropy of partons | The European Physical Journal C </title> <meta name="twitter:site" content="@SpringerLink"/> <meta name="twitter:card" content="summary_large_image"/> <meta name="twitter:image:alt" content="Content cover image"/> <meta name="twitter:title" content="Measurement of charged particle multiplicity distributions in DIS at HERA and its implication to entanglement entropy of partons"/> <meta name="twitter:description" content="The European Physical Journal C - Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy $$\sqrt{s}=319$$ &nbsp;GeV are measured...."/> <meta name="twitter:image" content="https://static-content.springer.com/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig1_HTML.png"/> <meta name="journal_id" content="10052"/> <meta name="dc.title" content="Measurement of charged particle multiplicity distributions in DIS at HERA and its implication to entanglement entropy of partons"/> <meta name="dc.source" content="The European Physical Journal C 2021 81:3"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="Springer"/> <meta name="dc.date" content="2021-03-03"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="2021 The Author(s)"/> <meta name="dc.rights" content="2021 The Author(s)"/> <meta name="dc.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="dc.description" content="Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy $$\sqrt{s}=319$$ &nbsp;GeV are measured. The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of 136&nbsp;&nbsp;pb $$^{-1}$$ . Charged particle multiplicities are measured as a function of photon virtuality $$Q^2$$ , inelasticity y and pseudorapidity $$\eta $$ in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined and the KNO scaling behaviour is investigated. The multiplicity distributions as a function of $$Q^2$$ &nbsp;&nbsp; and the Bjorken variable $$x_{\mathrm{bj}}$$ are converted to the hadron entropy $$S_{\mathrm{hadron}}$$ , and predictions from a quantum entanglement model are tested."/> <meta name="prism.issn" content="1434-6052"/> <meta name="prism.publicationName" content="The European Physical Journal C"/> <meta name="prism.publicationDate" content="2021-03-03"/> <meta name="prism.volume" content="81"/> <meta name="prism.number" content="3"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.startingPage" content="1"/> <meta name="prism.endingPage" content="46"/> <meta name="prism.copyright" content="2021 The Author(s)"/> <meta name="prism.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="prism.url" content="https://link.springer.com/article/10.1140/epjc/s10052-021-08896-1"/> <meta name="prism.doi" content="doi:10.1140/epjc/s10052-021-08896-1"/> <meta name="citation_pdf_url" content="https://link.springer.com/content/pdf/10.1140/epjc/s10052-021-08896-1.pdf"/> <meta name="citation_fulltext_html_url" content="https://link.springer.com/article/10.1140/epjc/s10052-021-08896-1"/> <meta name="citation_journal_title" content="The European Physical Journal C"/> <meta name="citation_journal_abbrev" content="Eur. 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Van"/> <meta name="citation_author_institution" content="Inter-University Institute for High Energies ULB-VUB, Brussels and Universiteit Antwerpen, Antwerp, Belgium"/> <meta name="citation_author" content="Wegener, D."/> <meta name="citation_author_institution" content="Institut für Physik, TU Dortmund, Dortmund, Germany"/> <meta name="citation_author" content="Wünsch, E."/> <meta name="citation_author_institution" content="DESY, Hamburg, Germany"/> <meta name="citation_author" content="Žáček, J."/> <meta name="citation_author_institution" content="Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic"/> <meta name="citation_author" content="Zhang, J."/> <meta name="citation_author_institution" content="Stony Brook University, Stony Brook, USA"/> <meta name="citation_author" content="Zhang, Z."/> <meta name="citation_author_institution" content="LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France"/> <meta name="citation_author" content="Žlebčík, R."/> <meta name="citation_author_institution" content="DESY, Hamburg, Germany"/> <meta name="citation_author" content="Zohrabyan, H."/> <meta name="citation_author_institution" content="Yerevan Physics Institute, Yerevan, Armenia"/> <meta name="citation_author" content="Zomer, F."/> <meta name="citation_author_institution" content="LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France"/> <meta name="format-detection" content="telephone=no"/> <meta name="citation_cover_date" content="2021/03/01"/> <meta property="og:url" content="https://link.springer.com/article/10.1140/epjc/s10052-021-08896-1"/> <meta property="og:type" content="article"/> <meta property="og:site_name" content="SpringerLink"/> <meta property="og:title" content="Measurement of charged particle multiplicity distributions in DIS at HERA and its implication to entanglement entropy of partons - The European Physical Journal C"/> <meta property="og:description" content="Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy $$\sqrt{s}=319$$ s = 319 GeV are measured. The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of 136 pb $$^{-1}$$ - 1 . Charged particle multiplicities are measured as a function of photon virtuality $$Q^2$$ Q 2 , inelasticity y and pseudorapidity $$\eta $$ η in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined and the KNO scaling behaviour is investigated. The multiplicity distributions as a function of $$Q^2$$ Q 2 and the Bjorken variable $$x_{\mathrm{bj}}$$ x bj are converted to the hadron entropy $$S_{\mathrm{hadron}}$$ S hadron , and predictions from a quantum entanglement model are tested."/> <meta property="og:image" content="https://static-content.springer.com/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig1_HTML.png"/> <meta name="format-detection" content="telephone=no"> <link rel="apple-touch-icon" sizes="180x180" href=/oscar-static/img/favicons/darwin/apple-touch-icon-92e819bf8a.png> <link rel="icon" type="image/png" sizes="192x192" href=/oscar-static/img/favicons/darwin/android-chrome-192x192-6f081ca7e5.png> <link rel="icon" type="image/png" sizes="32x32" href=/oscar-static/img/favicons/darwin/favicon-32x32-1435da3e82.png> <link rel="icon" type="image/png" sizes="16x16" href=/oscar-static/img/favicons/darwin/favicon-16x16-ed57f42bd2.png> <link rel="shortcut icon" data-test="shortcut-icon" 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The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of 136 pb\n \n \n \n $$^{-1}$$\n \n . Charged particle multiplicities are measured as a function of photon virtuality \n \n \n \n $$Q^2$$\n \n , inelasticity y and pseudorapidity \n \n \n \n $$\\eta $$\n \n in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined and the KNO scaling behaviour is investigated. 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Boudry</a><sup class="u-js-hide"><a href="#Aff22">22</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-G_-Brandt-Aff40" data-author-popup="auth-G_-Brandt-Aff40" data-author-search="Brandt, G.">G. Brandt</a><sup class="u-js-hide"><a href="#Aff40">40</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-Britzger-Aff20" data-author-popup="auth-D_-Britzger-Aff20" data-author-search="Britzger, D.">D. Britzger</a><sup class="u-js-hide"><a href="#Aff20">20</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Buniatyan-Aff2" data-author-popup="auth-A_-Buniatyan-Aff2" data-author-search="Buniatyan, A.">A. Buniatyan</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-L_-Bystritskaya-Aff18" data-author-popup="auth-L_-Bystritskaya-Aff18" data-author-search="Bystritskaya, L.">L. 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Chekelian</a><sup class="u-js-hide"><a href="#Aff20">20</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Z_-Chen-Aff46" data-author-popup="auth-Z_-Chen-Aff46" data-author-search="Chen, Z.">Z. Chen</a><sup class="u-js-hide"><a href="#Aff46">46</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J__G_-Contreras-Aff17" data-author-popup="auth-J__G_-Contreras-Aff17" data-author-search="Contreras, J. G.">J. G. 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Gal</a><sup class="u-js-hide"><a href="#Aff47">47</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J_-Gayler-Aff10" data-author-popup="auth-J_-Gayler-Aff10" data-author-search="Gayler, J.">J. Gayler</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-L_-Goerlich-Aff6" data-author-popup="auth-L_-Goerlich-Aff6" data-author-search="Goerlich, L.">L. Goerlich</a><sup class="u-js-hide"><a href="#Aff6">6</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-N_-Gogitidze-Aff19" data-author-popup="auth-N_-Gogitidze-Aff19" data-author-search="Gogitidze, N.">N. Gogitidze</a><sup class="u-js-hide"><a href="#Aff19">19</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M_-Gouzevitch-Aff34" data-author-popup="auth-M_-Gouzevitch-Aff34" data-author-search="Gouzevitch, M.">M. Gouzevitch</a><sup class="u-js-hide"><a href="#Aff34">34</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-C_-Grab-Aff32" data-author-popup="auth-C_-Grab-Aff32" data-author-search="Grab, C.">C. Grab</a><sup class="u-js-hide"><a href="#Aff32">32</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Grebenyuk-Aff3" data-author-popup="auth-A_-Grebenyuk-Aff3" data-author-search="Grebenyuk, A.">A. Grebenyuk</a><sup class="u-js-hide"><a href="#Aff3">3</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-T_-Greenshaw-Aff14" data-author-popup="auth-T_-Greenshaw-Aff14" data-author-search="Greenshaw, T.">T. Greenshaw</a><sup class="u-js-hide"><a href="#Aff14">14</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-G_-Grindhammer-Aff20" data-author-popup="auth-G_-Grindhammer-Aff20" data-author-search="Grindhammer, G.">G. Grindhammer</a><sup class="u-js-hide"><a href="#Aff20">20</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-Haidt-Aff10" data-author-popup="auth-D_-Haidt-Aff10" data-author-search="Haidt, D.">D. Haidt</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-R__C__W_-Henderson-Aff13" data-author-popup="auth-R__C__W_-Henderson-Aff13" data-author-search="Henderson, R. C. W.">R. C. W. Henderson</a><sup class="u-js-hide"><a href="#Aff13">13</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J_-Hladk_-Aff24" data-author-popup="auth-J_-Hladk_-Aff24" data-author-search="Hladkỳ, J.">J. Hladkỳ</a><sup class="u-js-hide"><a href="#Aff24">24</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-Hoffmann-Aff16" data-author-popup="auth-D_-Hoffmann-Aff16" data-author-search="Hoffmann, D.">D. Hoffmann</a><sup class="u-js-hide"><a href="#Aff16">16</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-R_-Horisberger-Aff28" data-author-popup="auth-R_-Horisberger-Aff28" data-author-search="Horisberger, R.">R. Horisberger</a><sup class="u-js-hide"><a href="#Aff28">28</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-T_-Hreus-Aff3" data-author-popup="auth-T_-Hreus-Aff3" data-author-search="Hreus, T.">T. Hreus</a><sup class="u-js-hide"><a href="#Aff3">3</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-F_-Huber-Aff12" data-author-popup="auth-F_-Huber-Aff12" data-author-search="Huber, F.">F. Huber</a><sup class="u-js-hide"><a href="#Aff12">12</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M_-Jacquet-Aff21" data-author-popup="auth-M_-Jacquet-Aff21" data-author-search="Jacquet, M.">M. Jacquet</a><sup class="u-js-hide"><a href="#Aff21">21</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-X_-Janssen-Aff3" data-author-popup="auth-X_-Janssen-Aff3" data-author-search="Janssen, X.">X. Janssen</a><sup class="u-js-hide"><a href="#Aff3">3</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A__W_-Jung-Aff43" data-author-popup="auth-A__W_-Jung-Aff43" data-author-search="Jung, A. W.">A. W. Jung</a><sup class="u-js-hide"><a href="#Aff43">43</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-H_-Jung-Aff10" data-author-popup="auth-H_-Jung-Aff10" data-author-search="Jung, H.">H. Jung</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M_-Kapichine-Aff8" data-author-popup="auth-M_-Kapichine-Aff8" data-author-search="Kapichine, M.">M. Kapichine</a><sup class="u-js-hide"><a href="#Aff8">8</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J_-Katzy-Aff10" data-author-popup="auth-J_-Katzy-Aff10" data-author-search="Katzy, J.">J. Katzy</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-C_-Kiesling-Aff20" data-author-popup="auth-C_-Kiesling-Aff20" data-author-search="Kiesling, C.">C. Kiesling</a><sup class="u-js-hide"><a href="#Aff20">20</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M_-Klein-Aff14" data-author-popup="auth-M_-Klein-Aff14" data-author-search="Klein, M.">M. Klein</a><sup class="u-js-hide"><a href="#Aff14">14</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-C_-Kleinwort-Aff10" data-author-popup="auth-C_-Kleinwort-Aff10" data-author-search="Kleinwort, C.">C. Kleinwort</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-R_-Kogler-Aff11" data-author-popup="auth-R_-Kogler-Aff11" data-author-search="Kogler, R.">R. Kogler</a><sup class="u-js-hide"><a href="#Aff11">11</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P_-Kostka-Aff14" data-author-popup="auth-P_-Kostka-Aff14" data-author-search="Kostka, P.">P. Kostka</a><sup class="u-js-hide"><a href="#Aff14">14</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J_-Kretzschmar-Aff14" data-author-popup="auth-J_-Kretzschmar-Aff14" data-author-search="Kretzschmar, J.">J. Kretzschmar</a><sup class="u-js-hide"><a href="#Aff14">14</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-Kr_cker-Aff10" data-author-popup="auth-D_-Kr_cker-Aff10" data-author-search="Krücker, D.">D. Krücker</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-K_-Kr_ger-Aff10" data-author-popup="auth-K_-Kr_ger-Aff10" data-author-search="Krüger, K.">K. Krüger</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M__P__J_-Landon-Aff15" data-author-popup="auth-M__P__J_-Landon-Aff15" data-author-search="Landon, M. P. J.">M. P. J. Landon</a><sup class="u-js-hide"><a href="#Aff15">15</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-W_-Lange-Aff31" data-author-popup="auth-W_-Lange-Aff31" data-author-search="Lange, W.">W. Lange</a><sup class="u-js-hide"><a href="#Aff31">31</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P_-Laycock-Aff14" data-author-popup="auth-P_-Laycock-Aff14" data-author-search="Laycock, P.">P. Laycock</a><sup class="u-js-hide"><a href="#Aff14">14</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Lebedev-Aff19" data-author-popup="auth-A_-Lebedev-Aff19" data-author-search="Lebedev, A.">A. Lebedev</a><sup class="u-js-hide"><a href="#Aff19">19</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-S_-Levonian-Aff10" data-author-popup="auth-S_-Levonian-Aff10" data-author-search="Levonian, S.">S. Levonian</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-K_-Lipka-Aff10" data-author-popup="auth-K_-Lipka-Aff10" data-author-search="Lipka, K.">K. Lipka</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-B_-List-Aff10" data-author-popup="auth-B_-List-Aff10" data-author-search="List, B.">B. List</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J_-List-Aff10" data-author-popup="auth-J_-List-Aff10" data-author-search="List, J.">J. List</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-W_-Li-Aff45" data-author-popup="auth-W_-Li-Aff45" data-author-search="Li, W.">W. Li</a><sup class="u-js-hide"><a href="#Aff45">45</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-B_-Lobodzinski-Aff20" data-author-popup="auth-B_-Lobodzinski-Aff20" data-author-search="Lobodzinski, B.">B. Lobodzinski</a><sup class="u-js-hide"><a href="#Aff20">20</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-E_-Malinovski-Aff19" data-author-popup="auth-E_-Malinovski-Aff19" data-author-search="Malinovski, E.">E. Malinovski</a><sup class="u-js-hide"><a href="#Aff19">19</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-H__U_-Martyn-Aff1" data-author-popup="auth-H__U_-Martyn-Aff1" data-author-search="Martyn, H.-U.">H.-U. Martyn</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-S__J_-Maxfield-Aff14" data-author-popup="auth-S__J_-Maxfield-Aff14" data-author-search="Maxfield, S. J.">S. J. Maxfield</a><sup class="u-js-hide"><a href="#Aff14">14</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Mehta-Aff14" data-author-popup="auth-A_-Mehta-Aff14" data-author-search="Mehta, A.">A. Mehta</a><sup class="u-js-hide"><a href="#Aff14">14</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A__B_-Meyer-Aff10" data-author-popup="auth-A__B_-Meyer-Aff10" data-author-search="Meyer, A. B.">A. B. Meyer</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-H_-Meyer-Aff29" data-author-popup="auth-H_-Meyer-Aff29" data-author-search="Meyer, H.">H. Meyer</a><sup class="u-js-hide"><a href="#Aff29">29</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J_-Meyer-Aff10" data-author-popup="auth-J_-Meyer-Aff10" data-author-search="Meyer, J.">J. Meyer</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-S_-Mikocki-Aff6" data-author-popup="auth-S_-Mikocki-Aff6" data-author-search="Mikocki, S.">S. Mikocki</a><sup class="u-js-hide"><a href="#Aff6">6</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M__M_-Mondal-Aff47" data-author-popup="auth-M__M_-Mondal-Aff47" data-author-search="Mondal, M. M.">M. M. Mondal</a><sup class="u-js-hide"><a href="#Aff47">47</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Morozov-Aff8" data-author-popup="auth-A_-Morozov-Aff8" data-author-search="Morozov, A.">A. Morozov</a><sup class="u-js-hide"><a href="#Aff8">8</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-K_-M_ller-Aff33" data-author-popup="auth-K_-M_ller-Aff33" data-author-search="Müller, K.">K. Müller</a><sup class="u-js-hide"><a href="#Aff33">33</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Th_-Naumann-Aff31" data-author-popup="auth-Th_-Naumann-Aff31" data-author-search="Naumann, Th.">Th. Naumann</a><sup class="u-js-hide"><a href="#Aff31">31</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P__R_-Newman-Aff2" data-author-popup="auth-P__R_-Newman-Aff2" data-author-search="Newman, P. R.">P. R. Newman</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-C_-Niebuhr-Aff10" data-author-popup="auth-C_-Niebuhr-Aff10" data-author-search="Niebuhr, C.">C. Niebuhr</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-G_-Nowak-Aff6" data-author-popup="auth-G_-Nowak-Aff6" data-author-search="Nowak, G.">G. Nowak</a><sup class="u-js-hide"><a href="#Aff6">6</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J__E_-Olsson-Aff10" data-author-popup="auth-J__E_-Olsson-Aff10" data-author-search="Olsson, J. E.">J. E. Olsson</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-Ozerov-Aff28" data-author-popup="auth-D_-Ozerov-Aff28" data-author-search="Ozerov, D.">D. Ozerov</a><sup class="u-js-hide"><a href="#Aff28">28</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-S_-Park-Aff47" data-author-popup="auth-S_-Park-Aff47" data-author-search="Park, S.">S. Park</a><sup class="u-js-hide"><a href="#Aff47">47</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-C_-Pascaud-Aff21" data-author-popup="auth-C_-Pascaud-Aff21" data-author-search="Pascaud, C.">C. Pascaud</a><sup class="u-js-hide"><a href="#Aff21">21</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-G__D_-Patel-Aff14" data-author-popup="auth-G__D_-Patel-Aff14" data-author-search="Patel, G. D.">G. D. Patel</a><sup class="u-js-hide"><a href="#Aff14">14</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-E_-Perez-Aff37" data-author-popup="auth-E_-Perez-Aff37" data-author-search="Perez, E.">E. Perez</a><sup class="u-js-hide"><a href="#Aff37">37</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Petrukhin-Aff34" data-author-popup="auth-A_-Petrukhin-Aff34" data-author-search="Petrukhin, A.">A. Petrukhin</a><sup class="u-js-hide"><a href="#Aff34">34</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-I_-Picuric-Aff23" data-author-popup="auth-I_-Picuric-Aff23" data-author-search="Picuric, I.">I. Picuric</a><sup class="u-js-hide"><a href="#Aff23">23</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-Pitzl-Aff10" data-author-popup="auth-D_-Pitzl-Aff10" data-author-search="Pitzl, D.">D. Pitzl</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-R_-Polifka-Aff25" data-author-popup="auth-R_-Polifka-Aff25" data-author-search="Polifka, R.">R. Polifka</a><sup class="u-js-hide"><a href="#Aff25">25</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-V_-Radescu-Aff44" data-author-popup="auth-V_-Radescu-Aff44" data-author-search="Radescu, V.">V. Radescu</a><sup class="u-js-hide"><a href="#Aff44">44</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-N_-Raicevic-Aff23" data-author-popup="auth-N_-Raicevic-Aff23" data-author-search="Raicevic, N.">N. Raicevic</a><sup class="u-js-hide"><a href="#Aff23">23</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-T_-Ravdandorj-Aff27" data-author-popup="auth-T_-Ravdandorj-Aff27" data-author-search="Ravdandorj, T.">T. Ravdandorj</a><sup class="u-js-hide"><a href="#Aff27">27</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P_-Reimer-Aff24" data-author-popup="auth-P_-Reimer-Aff24" data-author-search="Reimer, P.">P. Reimer</a><sup class="u-js-hide"><a href="#Aff24">24</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-E_-Rizvi-Aff15" data-author-popup="auth-E_-Rizvi-Aff15" data-author-search="Rizvi, E.">E. Rizvi</a><sup class="u-js-hide"><a href="#Aff15">15</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P_-Robmann-Aff33" data-author-popup="auth-P_-Robmann-Aff33" data-author-search="Robmann, P.">P. Robmann</a><sup class="u-js-hide"><a href="#Aff33">33</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-R_-Roosen-Aff3" data-author-popup="auth-R_-Roosen-Aff3" data-author-search="Roosen, R.">R. Roosen</a><sup class="u-js-hide"><a href="#Aff3">3</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Rostovtsev-Aff41" data-author-popup="auth-A_-Rostovtsev-Aff41" data-author-search="Rostovtsev, A.">A. Rostovtsev</a><sup class="u-js-hide"><a href="#Aff41">41</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M_-Rotaru-Aff4" data-author-popup="auth-M_-Rotaru-Aff4" data-author-search="Rotaru, M.">M. Rotaru</a><sup class="u-js-hide"><a href="#Aff4">4</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D__P__C_-Sankey-Aff5" data-author-popup="auth-D__P__C_-Sankey-Aff5" data-author-search="Sankey, D. P. C.">D. P. C. Sankey</a><sup class="u-js-hide"><a href="#Aff5">5</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M_-Sauter-Aff12" data-author-popup="auth-M_-Sauter-Aff12" data-author-search="Sauter, M.">M. Sauter</a><sup class="u-js-hide"><a href="#Aff12">12</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-E_-Sauvan-Aff16-Aff39" data-author-popup="auth-E_-Sauvan-Aff16-Aff39" data-author-search="Sauvan, E.">E. Sauvan</a><sup class="u-js-hide"><a href="#Aff16">16</a>,<a href="#Aff39">39</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-S_-Schmitt-Aff10" data-author-popup="auth-S_-Schmitt-Aff10" data-author-search="Schmitt, S." data-corresp-id="c1">S. Schmitt<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-B__A_-Schmookler-Aff47" data-author-popup="auth-B__A_-Schmookler-Aff47" data-author-search="Schmookler, B. A.">B. A. Schmookler</a><sup class="u-js-hide"><a href="#Aff47">47</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-L_-Schoeffel-Aff9" data-author-popup="auth-L_-Schoeffel-Aff9" data-author-search="Schoeffel, L.">L. Schoeffel</a><sup class="u-js-hide"><a href="#Aff9">9</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Sch_ning-Aff12" data-author-popup="auth-A_-Sch_ning-Aff12" data-author-search="Schöning, A.">A. Schöning</a><sup class="u-js-hide"><a href="#Aff12">12</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-F_-Sefkow-Aff10" data-author-popup="auth-F_-Sefkow-Aff10" data-author-search="Sefkow, F.">F. Sefkow</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-S_-Shushkevich-Aff35" data-author-popup="auth-S_-Shushkevich-Aff35" data-author-search="Shushkevich, S.">S. Shushkevich</a><sup class="u-js-hide"><a href="#Aff35">35</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Y_-Soloviev-Aff19" data-author-popup="auth-Y_-Soloviev-Aff19" data-author-search="Soloviev, Y.">Y. Soloviev</a><sup class="u-js-hide"><a href="#Aff19">19</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P_-Sopicki-Aff6" data-author-popup="auth-P_-Sopicki-Aff6" data-author-search="Sopicki, P.">P. Sopicki</a><sup class="u-js-hide"><a href="#Aff6">6</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-South-Aff10" data-author-popup="auth-D_-South-Aff10" data-author-search="South, D.">D. South</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-V_-Spaskov-Aff8" data-author-popup="auth-V_-Spaskov-Aff8" data-author-search="Spaskov, V.">V. Spaskov</a><sup class="u-js-hide"><a href="#Aff8">8</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Specka-Aff22" data-author-popup="auth-A_-Specka-Aff22" data-author-search="Specka, A.">A. Specka</a><sup class="u-js-hide"><a href="#Aff22">22</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-M_-Steder-Aff10" data-author-popup="auth-M_-Steder-Aff10" data-author-search="Steder, M.">M. Steder</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-B_-Stella-Aff26" data-author-popup="auth-B_-Stella-Aff26" data-author-search="Stella, B.">B. Stella</a><sup class="u-js-hide"><a href="#Aff26">26</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-U_-Straumann-Aff33" data-author-popup="auth-U_-Straumann-Aff33" data-author-search="Straumann, U.">U. Straumann</a><sup class="u-js-hide"><a href="#Aff33">33</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-T_-Sykora-Aff25" data-author-popup="auth-T_-Sykora-Aff25" data-author-search="Sykora, T.">T. Sykora</a><sup class="u-js-hide"><a href="#Aff25">25</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P__D_-Thompson-Aff2" data-author-popup="auth-P__D_-Thompson-Aff2" data-author-search="Thompson, P. D.">P. D. Thompson</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-Traynor-Aff15" data-author-popup="auth-D_-Traynor-Aff15" data-author-search="Traynor, D.">D. Traynor</a><sup class="u-js-hide"><a href="#Aff15">15</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P_-Tru_l-Aff33" data-author-popup="auth-P_-Tru_l-Aff33" data-author-search="Truöl, P.">P. Truöl</a><sup class="u-js-hide"><a href="#Aff33">33</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-B_-Tseepeldorj-Aff27-Aff38" data-author-popup="auth-B_-Tseepeldorj-Aff27-Aff38" data-author-search="Tseepeldorj, B.">B. Tseepeldorj</a><sup class="u-js-hide"><a href="#Aff27">27</a>,<a href="#Aff38">38</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Z_-Tu-Aff42" data-author-popup="auth-Z_-Tu-Aff42" data-author-search="Tu, Z.">Z. Tu</a><sup class="u-js-hide"><a href="#Aff42">42</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-T_-Ullrich-Aff42" data-author-popup="auth-T_-Ullrich-Aff42" data-author-search="Ullrich, T.">T. Ullrich</a><sup class="u-js-hide"><a href="#Aff42">42</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-A_-Valk_rov_-Aff25" data-author-popup="auth-A_-Valk_rov_-Aff25" data-author-search="Valkárová, A.">A. Valkárová</a><sup class="u-js-hide"><a href="#Aff25">25</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-C_-Vall_e-Aff16" data-author-popup="auth-C_-Vall_e-Aff16" data-author-search="Vallée, C.">C. Vallée</a><sup class="u-js-hide"><a href="#Aff16">16</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-P__Van-Mechelen-Aff3" data-author-popup="auth-P__Van-Mechelen-Aff3" data-author-search="Mechelen, P. Van">P. Van Mechelen</a><sup class="u-js-hide"><a href="#Aff3">3</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-D_-Wegener-Aff7" data-author-popup="auth-D_-Wegener-Aff7" data-author-search="Wegener, D.">D. Wegener</a><sup class="u-js-hide"><a href="#Aff7">7</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-E_-W_nsch-Aff10" data-author-popup="auth-E_-W_nsch-Aff10" data-author-search="Wünsch, E.">E. Wünsch</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J_-___ek-Aff25" data-author-popup="auth-J_-___ek-Aff25" data-author-search="Žáček, J.">J. Žáček</a><sup class="u-js-hide"><a href="#Aff25">25</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-J_-Zhang-Aff47" data-author-popup="auth-J_-Zhang-Aff47" data-author-search="Zhang, J.">J. Zhang</a><sup class="u-js-hide"><a href="#Aff47">47</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Z_-Zhang-Aff21" data-author-popup="auth-Z_-Zhang-Aff21" data-author-search="Zhang, Z.">Z. Zhang</a><sup class="u-js-hide"><a href="#Aff21">21</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-R_-_leb__k-Aff10" data-author-popup="auth-R_-_leb__k-Aff10" data-author-search="Žlebčík, R.">R. Žlebčík</a><sup class="u-js-hide"><a href="#Aff10">10</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-H_-Zohrabyan-Aff30" data-author-popup="auth-H_-Zohrabyan-Aff30" data-author-search="Zohrabyan, H.">H. Zohrabyan</a><sup class="u-js-hide"><a href="#Aff30">30</a></sup> & </li><li class="c-article-author-list__show-more" aria-label="Show all 139 authors for this article" title="Show all 139 authors for this article">…</li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-F_-Zomer-Aff21" data-author-popup="auth-F_-Zomer-Aff21" data-author-search="Zomer, F.">F. Zomer</a><sup class="u-js-hide"><a href="#Aff21">21</a></sup> </li></ul><button aria-expanded="false" class="c-article-author-list__button"><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-down-medium"></use></svg><span>Show authors</span></button> <div data-test="article-metrics"> <ul class="app-article-metrics-bar u-list-reset"> <li class="app-article-metrics-bar__item"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-accesses-medium"></use> </svg>2191 <span class="app-article-metrics-bar__label">Accesses</span></p> </li> <li class="app-article-metrics-bar__item"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-altmetric-medium"></use> </svg>76 <span class="app-article-metrics-bar__label">Altmetric</span></p> </li> <li class="app-article-metrics-bar__item"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon app-article-metrics-bar__icon--mentions" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-mentions-medium"></use> </svg>11 <span class="app-article-metrics-bar__label">Mentions</span></p> </li> <li class="app-article-metrics-bar__item app-article-metrics-bar__item--metrics"> <p class="app-article-metrics-bar__details"><a href="/article/10.1140/epjc/s10052-021-08896-1/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Explore all metrics <svg class="u-icon app-article-metrics-bar__arrow-icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-arrow-right-medium"></use> </svg></a></p> </li> </ul> </div> <div class="u-mt-32"> </div> </header> </div> <div data-article-body="true" data-track-component="article body" class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV are measured. The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of 136 pb<span class="mathjax-tex">$^{-1}$</span>. Charged particle multiplicities are measured as a function of photon virtuality <span class="mathjax-tex">$Q^2$</span>, inelasticity <i>y</i> and pseudorapidity <span class="mathjax-tex">$\eta $</span> in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined and the KNO scaling behaviour is investigated. The multiplicity distributions as a function of <span class="mathjax-tex">$Q^2$</span> and the Bjorken variable <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> are converted to the hadron entropy <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span>, and predictions from a quantum entanglement model are tested.</p></div></div></section> <div data-test="cobranding-download"> </div> <section aria-labelledby="inline-recommendations" data-title="Inline Recommendations" class="c-article-recommendations" data-track-component="inline-recommendations"> <h3 class="c-article-recommendations-title" id="inline-recommendations">Similar content being viewed by others</h3> <div class="c-article-recommendations-list"> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1007%2FJHEP01%282018%29045/MediaObjects/13130_2018_7411_Figa_HTML.gif" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1007/JHEP01(2018)045?fromPaywallRec=false" data-track="select_recommendations_1" data-track-context="inline recommendations" data-track-action="click recommendations inline - 1" data-track-label="10.1007/JHEP01(2018)045">Pseudorapidity distributions of charged hadrons in proton-lead collisions at <span class="mathjax-tex">$ \sqrt{s_{\mathrm{NN}}}=5.02 $</span> and 8.16 TeV </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">11 January 2018</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-016-4571-1/MediaObjects/10052_2016_4571_Fig1_HTML.gif" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1140/epjc/s10052-016-4571-1?fromPaywallRec=false" data-track="select_recommendations_2" data-track-context="inline recommendations" data-track-action="click recommendations inline - 2" data-track-label="10.1140/epjc/s10052-016-4571-1">Charged-particle multiplicities in proton–proton collisions at <span class="mathjax-tex">$\sqrt{s} = 0.9$</span> to 8 TeV </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">17 January 2017</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-016-4002-3/MediaObjects/10052_2016_4002_Fig1_HTML.gif" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1140/epjc/s10052-016-4002-3?fromPaywallRec=false" data-track="select_recommendations_3" data-track-context="inline recommendations" data-track-action="click recommendations inline - 3" data-track-label="10.1140/epjc/s10052-016-4002-3">Measurement of the centrality dependence of the charged-particle pseudorapidity distribution in proton–lead collisions at <span class="mathjax-tex">$\sqrt{s_{_\text {NN}}} = 5.02$</span> TeV with the ATLAS detector </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">12 April 2016</span> </div> </div> </article> </div> </div> </section> <script> window.dataLayer = window.dataLayer || []; window.dataLayer.push({ recommendations: { recommender: 'semantic', model: 'specter', policy_id: 'NA', timestamp: 1733971137, embedded_user: 'null' } }); </script> <div class="app-card-service" data-test="article-checklist-banner"> <div> <a class="app-card-service__link" data-track="click_presubmission_checklist" data-track-context="article page top of reading companion" data-track-category="pre-submission-checklist" data-track-action="clicked article page checklist banner test 2 old version" data-track-label="link" href="https://beta.springernature.com/pre-submission?journalId=10052" data-test="article-checklist-banner-link"> <span class="app-card-service__link-text">Use our pre-submission checklist</span> <svg class="app-card-service__link-icon" aria-hidden="true" focusable="false"><use xlink:href="#icon-eds-i-arrow-right-small"></use></svg> </a> <p class="app-card-service__description">Avoid common mistakes on your manuscript.</p> </div> <div class="app-card-service__icon-container"> <svg class="app-card-service__icon" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-clipboard-check-medium"></use> </svg> </div> </div> <div class="main-content"> <section data-title="Introduction"><div class="c-article-section" id="Sec1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec1"><span class="c-article-section__title-number">1 </span>Introduction</h2><div class="c-article-section__content" id="Sec1-content"><p>In the parton model [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J.D. Bjorken, E.A. Paschos, Phys. Rev. 185, 1975 (1969). 
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 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR5" id="ref-link-section-d48852095e2860">5</a>] that quantum entanglement of partons could be an important probe of the underlying mechanism. Measurements of charged particle multiplicities are proposed [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="D.E. Kharzeev, E.M. Levin, Phys. Rev. D 95, 114008 (2017). 
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 " href="#ref-CR9" id="ref-link-section-d48852095e2863_4">9</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="Z. Tu, D.E. Kharzeev, T. Ullrich, Phys. Rev. Lett. 124, 062001 (2020). 
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 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR10" id="ref-link-section-d48852095e2867">10</a>] to be related to the entanglement entropy predicted from the gluon density [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="D.E. Kharzeev, E.M. Levin, Phys. Rev. D 95, 114008 (2017). 
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 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR5" id="ref-link-section-d48852095e2870">5</a>], as an indication of quantum entanglement of partons inside the proton. The entanglement entropy is defined here for the bipartite quantum system consisting of the struck partons and the proton remnants, respectively. It is then determined by the von Neumann entropy [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 11" title="J. Von Neumann, Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932) (English edition: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955)" href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR11" id="ref-link-section-d48852095e2873">11</a>] of either reduced state, for example by that of the struck partons.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-1" data-title="Fig. 1"><figure><figcaption><b id="Fig1" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 1</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/1" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig1_HTML.png?as=webp"><img aria-describedby="Fig1" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig1_HTML.png" alt="figure 1" loading="lazy" width="685" height="661"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-1-desc"><p>Reconstructed momentum transfer <span class="mathjax-tex">$Q^2$</span>, inelasticity <i>y</i>, pseudorapidity <span class="mathjax-tex">$\eta _{_{\mathrm{lab}}}$</span>, and charged particle multiplicity <span class="mathjax-tex">$N_{\mathrm{rec}}$</span> for data (open circle), and the DJANGOH (red line) and the RAPGAP (blue line) MC models. The phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. The photoproduction background simulated from PYTHIA 6.4 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 55" title="T. Sjöstrand, S. Mrenna, P. Skands, JHEP 05, 026 (2006). 
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 . 
 arXiv:hep-ph/0603175
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR55" id="ref-link-section-d48852095e2966">55</a>] is shown for the <span class="mathjax-tex">$Q^2$</span> and <i>y</i> distributions. Error bars indicate the statistical uncertainty of data</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/1" data-track-dest="link:Figure1 Full size image" aria-label="Full size image figure 1" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>Particle multiplicity distributions have previously been measured in deep inelastic scattering (DIS) at HERA [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="ZEUS Collaboration, M. Derrick et al., Z. Phys. C 67, 93 (1995). 
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 . 
 arXiv:0803.3878
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR16" id="ref-link-section-d48852095e3008">16</a>]. In this paper, charged particle multiplicity distributions in positron-proton (<i>ep</i>) DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV are reported using high statistics data collected with the H1 detector. The phase space of the measurement of multiplicity distributions is defined in bins of the virtuality of the photon <span class="mathjax-tex">$5<Q^2<100 ~\mathrm {GeV}^2 $</span>, the inelasticity <i>y</i> variable <span class="mathjax-tex">$0.0375<y<0.6$</span> and the pseudorapidity <span class="mathjax-tex">$\eta $</span> of charged particles, <span class="mathjax-tex">$|\eta _{_{\text {lab}}}|<1.6$</span> in the laboratory frame, and <span class="mathjax-tex">$0<\eta ^{*}<4$</span> in the hadronic centre-of-mass (HCM) frame.<sup><a href="#Fn1"><span class="u-visually-hidden">Footnote </span>1</a></sup> The first and the second moments of the multiplicity distributions, corresponding to the mean and the variance, are measured as a function of the hadronic centre-of-mass energy <i>W</i>, in different bins of <span class="mathjax-tex">$Q^2$</span>. The KNO scaling function [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 17" title="Z. Koba, H.B. Nielsen, P. Olesen, Nucl. Phys. B 40, 317 (1972). 
 https://doi.org/10.1016/0550-3213(72)90551-2
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR17" id="ref-link-section-d48852095e3370">17</a>] is also measured in different <i>W</i> and <span class="mathjax-tex">$Q^2$</span> regions.</p><p>The final-state hadron entropy, <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span>, as a function of the Bjorken variable <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> in different <span class="mathjax-tex">$Q^2$</span> bins is also measured. A relation between the <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> and the initial-state parton entropy, <span class="mathjax-tex">$S_{\mathrm{gluon}}$</span>, due to “parton liberation” [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="A.H. Mueller, Nucl. Phys. B 572, 227 (2000). 
 https://doi.org/10.1016/S0550-3213(99)00502-7
 
 . 
 arXiv:hep-ph/9906322
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR18" id="ref-link-section-d48852095e3516">18</a>] and “local parton-hadron duality (LPHD)” [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 19" title="Y.L. Dokshitzer, V.A. Khoze, S.I. Troyan, J. Phys. G Nucl. Part. Phys. 17, 1585 (1991). 
 https://doi.org/10.1088/0954-3899/17/10/017
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR19" id="ref-link-section-d48852095e3519">19</a>], is described by [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="D.E. Kharzeev, E.M. Levin, Phys. Rev. D 95, 114008 (2017). 
 https://doi.org/10.1103/PhysRevD.95.114008
 
 . 
 arXiv:1702.03489
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR5" id="ref-link-section-d48852095e3522">5</a>]:</p><div id="Equ1" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} S_{\mathrm{hadron}} \!\equiv \! -\sum {P(N)\ln {P(N)}}\!=\!\ln {[xG(x,Q^2)]} \equiv S_{\mathrm{gluon}}.\nonumber \\ \end{aligned}$$</span></div><div class="c-article-equation__number"> (1) </div></div><p>Here, <i>P</i>(<i>N</i>) is the charged particle multiplicity distribution measured in either the current fragmentation region or the target fragmentation region, and the gluon density <span class="mathjax-tex">$xG(x,Q^{2})$</span> is evaluated at <span class="mathjax-tex">$x =$</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span>.</p><p>The measurements are compared to theoretical predictions obtained from simulations including parton showers and hadronisation (RAPGAP [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="H. Jung, Comput. Phys. Commun. 86, 147 (1995). 
 https://doi.org/10.1016/0010-4655(94)00150-Z
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR20" id="ref-link-section-d48852095e3762">20</a>], DJANGOH [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="K. Charchula, G.A. Schuler, H. Spiesberger, Comput. Phys. Commun. 81, 381 (1994). 
 https://doi.org/10.1016/0010-4655(94)90086-8
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR21" id="ref-link-section-d48852095e3765">21</a>] and PYTHIA 8 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 22" title="T. Sjöstrand, S. Ask, J.R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C.O. Rasmussen, P.Z. Skands, Comput. Phys. Commun. 191, 159 (2015). 
 https://doi.org/10.1016/j.cpc.2015.01.024
 
 . 
 arXiv:1410.3012
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR22" id="ref-link-section-d48852095e3768">22</a>]).</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-1"><figure><figcaption class="c-article-table__figcaption"><b id="Tab1" data-test="table-caption">Table 1 Summary of the fiducial kinematic phase space used in this analysis</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/1" aria-label="Full size table 1"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div></div></div></section><section data-title="H1 detector"><div class="c-article-section" id="Sec2-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec2"><span class="c-article-section__title-number">2 </span>H1 detector</h2><div class="c-article-section__content" id="Sec2-content"><p>A full description of the H1 detector can be found elsewhere [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="H1 Collaboration, I. Abt et al., Nucl. Instrum. Meth. A 386, 310 (1997). 
 https://doi.org/10.1016/S0168-9002(96)00893-5
 
 " href="#ref-CR23" id="ref-link-section-d48852095e4324">23</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="H1 Collaboration, I. Abt et al., Nucl. Instrum. Meth. A 386, 348 (1997). 
 https://doi.org/10.1016/S0168-9002(96)00894-7
 
 " href="#ref-CR24" id="ref-link-section-d48852095e4324_1">24</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="H1 SPACAL Group, R.D. Appuhn et al., Nucl. Instrum. Meth. A 386, 397 (1997). 
 https://doi.org/10.1016/S0168-9002(96)01171-0
 
 " href="#ref-CR25" id="ref-link-section-d48852095e4324_2">25</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="D. Pitzl et al., Nucl. Instrum. Meth. A 454, 334 (2000). 
 https://doi.org/10.1016/S0168-9002(00)00488-5
 
 . 
 arXiv:hep-ex/0002044
 
 " href="#ref-CR26" id="ref-link-section-d48852095e4324_3">26</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="B. List, Nucl. Instrum. Meth. A 501, 49 (2001). 
 https://doi.org/10.1016/S0168-9002(02)02009-0
 
 " href="#ref-CR27" id="ref-link-section-d48852095e4324_4">27</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="J. Becker et al., Nucl. Instrum. Meth. A 586, 190 (2008). 
 https://doi.org/10.1016/j.nima.2007.11.024
 
 . 
 arXiv:physics/0701002
 
 " href="#ref-CR28" id="ref-link-section-d48852095e4324_5">28</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="P.J. Laycock, R.C.W. Henderson, S.J. Maxfield, J.V. Morris, G.D. Patel, D.P.C. Sankey, JINST 7, T08003 (2012). 
 https://doi.org/10.1088/1748-0221/7/08/T08003
 
 . 
 arXiv:1206.4068
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR29" id="ref-link-section-d48852095e4327">29</a>] and only the components most relevant for this analysis are briefly mentioned here. The coordinate system of H1 is defined such that the positive <i>z</i> axis is pointing in the proton beam direction (forward direction) and the nominal interaction point is located at <i>z</i> = 0. The polar angle <span class="mathjax-tex">$\theta $</span> is defined with respect to this axis. The pseudorapidity is defined to be <span class="mathjax-tex">$\eta \equiv -\ln {(\tan {(\theta /2)})}$</span>.</p><p>Charged particles are measured in the polar angle range <span class="mathjax-tex">${15}^{\circ }<\theta <{165}^{\circ }$</span> using the central tracking detector (CTD), which is also used to reconstruct the interaction vertex. The CTD comprises two large cylindrical, concentric and coaxial jet chambers (CJCs), and the silicon vertex detector [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 26" title="D. Pitzl et al., Nucl. Instrum. Meth. A 454, 334 (2000). 
 https://doi.org/10.1016/S0168-9002(00)00488-5
 
 . 
 arXiv:hep-ex/0002044
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR26" id="ref-link-section-d48852095e4454">26</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 27" title="B. List, Nucl. Instrum. Meth. A 501, 49 (2001). 
 https://doi.org/10.1016/S0168-9002(02)02009-0
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR27" id="ref-link-section-d48852095e4457">27</a>]. The CTD is operated inside a 1.16 T solenoidal magnetic field. The CJCs are separated by a cylindrical drift chamber which improves the <i>z</i> coordinate reconstruction. A cylindrical multiwire proportional chamber [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 28" title="J. Becker et al., Nucl. Instrum. Meth. A 586, 190 (2008). 
 https://doi.org/10.1016/j.nima.2007.11.024
 
 . 
 arXiv:physics/0701002
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR28" id="ref-link-section-d48852095e4463">28</a>], which is mainly used in the trigger, is situated inside the inner CJC. The trajectories of charged particles are measured with a transverse momentum resolution of <span class="mathjax-tex">$\sigma (p_{T})/p_{T} \approx 0.2\%/\,\text{ GeV }\oplus 1.5\%$</span>. The forward tracking detector (FTD) [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="P.J. Laycock, R.C.W. Henderson, S.J. Maxfield, J.V. Morris, G.D. Patel, D.P.C. Sankey, JINST 7, T08003 (2012). 
 https://doi.org/10.1088/1748-0221/7/08/T08003
 
 . 
 arXiv:1206.4068
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR29" id="ref-link-section-d48852095e4538">29</a>] measures the tracks of charged particles at polar angles <span class="mathjax-tex">${6}^{\circ }<\theta <{25}^{\circ }$</span>. In the region of angular overlap, FTD and short CTD track segments are used to reconstruct combined tracks, extending the detector acceptance for well-reconstructed tracks. Both CTD tracks and combined tracks are linked to hits in the vertex detectors: the central silicon tracker (CST) [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 26" title="D. Pitzl et al., Nucl. Instrum. Meth. A 454, 334 (2000). 
 https://doi.org/10.1016/S0168-9002(00)00488-5
 
 . 
 arXiv:hep-ex/0002044
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR26" id="ref-link-section-d48852095e4585">26</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 27" title="B. List, Nucl. Instrum. Meth. A 501, 49 (2001). 
 https://doi.org/10.1016/S0168-9002(02)02009-0
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR27" id="ref-link-section-d48852095e4588">27</a>], the backward silicon tracker (BST) and the forward silicon tracker (FST). These detectors provide precise spatial coordinate measurements and therefore significantly improve the primary vertex spatial resolution. The CST consists of two layers of double-sided silicon strip detectors surrounding the beam pipe covering an angular range of <span class="mathjax-tex">${30}^{\circ }<\theta <{150}^{\circ }$</span> for tracks passing through both layers. The BST consists of six double wheels of silicon strip detectors measuring the transverse coordinates of charged particles. The FST design is similar to that of the BST and consists of five double wheels of single-sided silicon strip detectors. The lead-scintillating fibre calorimeter (SpaCal) [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 25" title="H1 SPACAL Group, R.D. Appuhn et al., Nucl. Instrum. Meth. A 386, 397 (1997). 
 https://doi.org/10.1016/S0168-9002(96)01171-0
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR25" id="ref-link-section-d48852095e4636">25</a>] covering the region <span class="mathjax-tex">${153}^{\circ }<\theta <{177.5}^{\circ }$</span> has electromagnetic and hadronic sections. The calorimeter is used to measure the scattered positron and the backward hadronic energy flow. The energy resolution for positrons in the electromagnetic section is <span class="mathjax-tex">$\sigma (E)/E \approx 7.1\%/ \sqrt{E/\,\text{ GeV }} \oplus 1\%$</span>, as determined in test beam measurements [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="H1 SPACAL Group, T. Nicholls et al., Nucl. Instrum. Meth. A 374, 149 (1996). 
 https://doi.org/10.1016/0168-9002(95)01443-8
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR30" id="ref-link-section-d48852095e4756">30</a>]. The SpaCal provides energy and time-of-flight information used for triggering purposes. A backward proportional chamber (BPC) in front of the SpaCal is used to improve the angular measurement of the scattered lepton. The liquid argon (LAr) calorimeter [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 31" title="H1 Calorimeter Group, B. Andrieu et al., Nucl. Instrum. Meth. A 336, 460 (1993). 
 https://doi.org/10.1016/0168-9002(93)91257-N
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR31" id="ref-link-section-d48852095e4759">31</a>] covers the range <span class="mathjax-tex">${4}^{\circ }<\theta <{154}^{\circ }$</span> and is used in this analysis in the reconstruction of the hadronic final state. It has an energy resolution of <span class="mathjax-tex">$\sigma (E)/E \approx 50\%/ \sqrt{E/\,\text{ GeV }} \oplus 2\%$</span> for hadronic showers, as obtained from test beam measurements [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="H1 Calorimeter Group, B. Andrieu et al., Nucl. Instrum. Meth. A 336, 499 (1993). 
 https://doi.org/10.1016/0168-9002(93)91258-O
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR32" id="ref-link-section-d48852095e4880">32</a>].</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-2"><figure><figcaption class="c-article-table__figcaption"><b id="Tab2" data-test="table-caption">Table 2 Summary of the systematic uncertainties in this analysis</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/2" aria-label="Full size table 2"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div></div></div></section><section data-title="Theoretical predictions"><div class="c-article-section" id="Sec3-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec3"><span class="c-article-section__title-number">3 </span>Theoretical predictions</h2><div class="c-article-section__content" id="Sec3-content"><p>The DIS process is simulated by different Monte Carlo (MC) event generators, which include the hard scattering process and simulations of higher order QCD correction in form of parton showers and hadronisation. A brief description of the MC event generators is given below:</p><ul class="u-list-style-bullet"> <li> <p>The <b>RAPGAP 3.1</b> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="H. Jung, Comput. Phys. Commun. 86, 147 (1995). 
 https://doi.org/10.1016/0010-4655(94)00150-Z
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR20" id="ref-link-section-d48852095e5564">20</a>] MC event generator matches first order Quantum Chromodynamics (QCD) matrix elements to the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="V.N. Gribov, L.N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972)" href="#ref-CR33" id="ref-link-section-d48852095e5567">33</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="L.N. Lipatov, Sov. J. Nucl. Phys. 20, 94 (1975)" href="#ref-CR34" id="ref-link-section-d48852095e5567_1">34</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="G. Altarelli, G. Parisi, Nucl. Phys. B 126, 298 (1977). 
 https://doi.org/10.1016/0550-3213(77)90384-4
 
 " href="#ref-CR35" id="ref-link-section-d48852095e5567_2">35</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 36" title="Y.L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977)" href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR36" id="ref-link-section-d48852095e5570">36</a>] parton showers with strongly ordered transverse momenta of subsequently emitted partons. The factorisation and renormalisation scales are set to <span class="mathjax-tex">$\mu _{f}=\mu _{r}=\sqrt{Q^2+{\hat{p}}^{2}_{T}}$</span>, where <span class="mathjax-tex">${\hat{p}}_{T}$</span> is the transverse momentum of the outgoing hard parton from the matrix element in the centre-of-mass frame of the hard subsystem. The CTEQ 6L [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 37" title="J. Pumplin, D. Stump, J. Huston, H. Lai, P.M. Nadolsky, W. Tung, JHEP 07, 012 (2002). 
 https://doi.org/10.1088/1126-6708/2002/07/012
 
 . 
 arXiv:hep-ph/0201195
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR37" id="ref-link-section-d48852095e5671">37</a>] leading order parametrisation of the parton density function (PDF) is used.</p> </li> <li> <p>The <b>DJANGOH 1.4</b> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="K. Charchula, G.A. Schuler, H. Spiesberger, Comput. Phys. Commun. 81, 381 (1994). 
 https://doi.org/10.1016/0010-4655(94)90086-8
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR21" id="ref-link-section-d48852095e5683">21</a>] MC event generator uses the Colour Dipole Model (CDM) as implemented in ARIADNE [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 38" title="L. Lönnblad, Comput. Phys. Commun. 71, 15 (1992). 
 https://doi.org/10.1016/0010-4655(92)90068-A
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR38" id="ref-link-section-d48852095e5686">38</a>], which models first order QCD processes and creates dipoles between coloured partons. Gluon emission is treated as radiation from these dipoles, and new dipoles are formed from the emitted gluons from which further radiation is possible. The radiation pattern of the dipoles includes interference effects, thus modelling gluon coherence. The transverse momenta of the emitted partons are not ordered in transverse momentum with respect to rapidity, producing a configuration similar to the Balitsky–Fadin–Kuraev–Lipatov (BFKL) [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="E.A. Kuraev, L.N. Lipatov, V.S. Fadin, Sov. Phys. JETP 44, 443 (1976)" href="#ref-CR39" id="ref-link-section-d48852095e5689">39</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="E.A. Kuraev, L.N. Lipatov, V.S. Fadin, Sov. Phys. JETP 45, 199 (1977)" href="#ref-CR40" id="ref-link-section-d48852095e5689_1">40</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 41" title="I.I. Balitsky, L.N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978)" href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR41" id="ref-link-section-d48852095e5692">41</a>] treatment of parton evolution [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="L. Lönnblad, Z. Phys. C 65, 285 (1995). 
 https://doi.org/10.1007/BF01571885
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR42" id="ref-link-section-d48852095e5696">42</a>]. The CTEQ 6L [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 37" title="J. Pumplin, D. Stump, J. Huston, H. Lai, P.M. Nadolsky, W. Tung, JHEP 07, 012 (2002). 
 https://doi.org/10.1088/1126-6708/2002/07/012
 
 . 
 arXiv:hep-ph/0201195
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR37" id="ref-link-section-d48852095e5699">37</a>] at leading order is used as the PDF.</p> </li> <li> <p>The <b>PYTHIA 8</b> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 22" title="T. Sjöstrand, S. Ask, J.R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C.O. Rasmussen, P.Z. Skands, Comput. Phys. Commun. 191, 159 (2015). 
 https://doi.org/10.1016/j.cpc.2015.01.024
 
 . 
 arXiv:1410.3012
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR22" id="ref-link-section-d48852095e5711">22</a>] MC event generator models the hard collision by LO-pQCD cross sections. In order to enable the PYTHIA 8 program to simulate DIS processes, the <span class="mathjax-tex">$\mathcal{O}(\alpha _s^0)$</span> process together with the DIrect REsummation (DIRE) parton shower [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="S. Höche, S. Prestel, Eur. Phys. J. C 75, 461 (2015). 
 https://doi.org/10.1140/epjc/s10052-015-3684-2
 
 . 
 arXiv:1506.05057
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR43" id="ref-link-section-d48852095e5750">43</a>] is applied. The parton shower recoil is treated such that the kinematic variables of the DIS process (<i>y</i> and <span class="mathjax-tex">$\,\,Q^2$</span>) are unchanged. The PDF CTEQ 5L [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 37" title="J. Pumplin, D. Stump, J. Huston, H. Lai, P.M. Nadolsky, W. Tung, JHEP 07, 012 (2002). 
 https://doi.org/10.1088/1126-6708/2002/07/012
 
 . 
 arXiv:hep-ph/0201195
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR37" id="ref-link-section-d48852095e5786">37</a>] is used.</p> </li> </ul><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-2" data-title="Fig. 2"><figure><figcaption><b id="Fig2" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 2</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/2" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig2_HTML.png?as=webp"><img aria-describedby="Fig2" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig2_HTML.png" alt="figure 2" loading="lazy" width="685" height="710"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-2-desc"><p>Charged particle multiplicity distributions <i>P</i>(<i>N</i>) as a function of the number of particles <i>N</i> at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV ep collisions. Different panels correspond to different <span class="mathjax-tex">$Q^2$</span> and <i>y</i> bins, as indicated by the text in the figure. The phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. Predictions from DJANGOH, RAPGAP and PYTHIA 8 are also shown. The total uncertainty is denoted by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/2" data-track-dest="link:Figure2 Full size image" aria-label="Full size image figure 2" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-3" data-title="Fig. 3"><figure><figcaption><b id="Fig3" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 3</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/3" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig3_HTML.png?as=webp"><img aria-describedby="Fig3" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig3_HTML.png" alt="figure 3" loading="lazy" width="685" height="563"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-3-desc"><p>Charged particle multiplicity distributions <i>P</i>(<i>N</i>) as a function of the number of particles <i>N</i> at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV ep collisions in the range <span class="mathjax-tex">$5<Q^2<10~\mathrm {GeV}^2 $</span>. Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. Different panels correspond to different <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span> and <i>y</i> bins, as indicated by the text in the figure. Predictions from DJANGOH, RAPGAP and PYTHIA 8 are also shown. The total uncertainty is denoted by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/3" data-track-dest="link:Figure3 Full size image" aria-label="Full size image figure 3" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-4" data-title="Fig. 4"><figure><figcaption><b id="Fig4" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 4</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/4" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig4_HTML.png?as=webp"><img aria-describedby="Fig4" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig4_HTML.png" alt="figure 4" loading="lazy" width="685" height="563"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-4-desc"><p>Charged particle multiplicity distributions <i>P</i>(<i>N</i>) as a function of the number of particles <i>N</i> at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV ep collisions in the range <span class="mathjax-tex">$10<Q^2<20~\mathrm {GeV}^2 $</span>. Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. Different panels correspond to different <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span> and <i>y</i> bins, as indicated by the text in the figure. Predictions from DJANGOH, RAPGAP and PYTHIA 8 are also shown. The total uncertainty is denoted by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/4" data-track-dest="link:Figure4 Full size image" aria-label="Full size image figure 4" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-5" data-title="Fig. 5"><figure><figcaption><b id="Fig5" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 5</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/5" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig5_HTML.png?as=webp"><img aria-describedby="Fig5" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig5_HTML.png" alt="figure 5" loading="lazy" width="685" height="563"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-5-desc"><p>Charged particle multiplicity distributions <i>P</i>(<i>N</i>) as a function of the number of particles <i>N</i> at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV ep collisions in the range <span class="mathjax-tex">$20<Q^2<40~\mathrm {GeV}^2 $</span>. Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. Different panels correspond to different <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span> and <i>y</i> bins, as indicated by the text in the figure. Predictions from DJANGOH, RAPGAP and PYTHIA 8 are also shown. The total uncertainty is denoted by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/5" data-track-dest="link:Figure5 Full size image" aria-label="Full size image figure 5" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-6" data-title="Fig. 6"><figure><figcaption><b id="Fig6" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 6</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/6" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig6_HTML.png?as=webp"><img aria-describedby="Fig6" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig6_HTML.png" alt="figure 6" loading="lazy" width="685" height="565"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-6-desc"><p>Charged particle multiplicity distributions <i>P</i>(<i>N</i>) as a function of the number of particles <i>N</i> at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV ep collisions in the range <span class="mathjax-tex">$40<Q^2<100~\mathrm {GeV}^2 $</span>. Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. Different panels correspond to different <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span> and <i>y</i> bins, as indicated by the text in the figure. Predictions from DJANGOH, RAPGAP and PYTHIA 8 are also shown. The total uncertainty is denoted by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/6" data-track-dest="link:Figure6 Full size image" aria-label="Full size image figure 6" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-7" data-title="Fig. 7"><figure><figcaption><b id="Fig7" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 7</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/7" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig7_HTML.png?as=webp"><img aria-describedby="Fig7" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig7_HTML.png" alt="figure 7" loading="lazy" width="685" height="710"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-7-desc"><p>Charged particle multiplicity distributions <i>P</i>(<i>N</i>) as a function of the number of particles <i>N</i> at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV ep collisions with additional restriction to the current hemisphere <span class="mathjax-tex">$0<\eta ^{*}<4$</span>. Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. Different panels correspond to different <span class="mathjax-tex">$Q^2$</span> and <i>y</i> bins, as indicated by the text in the figure. Predictions from DJANGOH, RAPGAP and PYTHIA 8 are also shown. The total uncertainty is denoted by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/7" data-track-dest="link:Figure7 Full size image" aria-label="Full size image figure 7" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-8" data-title="Fig. 8"><figure><figcaption><b id="Fig8" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 8</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/8" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig8_HTML.png?as=webp"><img aria-describedby="Fig8" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig8_HTML.png" alt="figure 8" loading="lazy" width="685" height="321"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-8-desc"><p>Mean multiplicity <span class="mathjax-tex">$\langle N \rangle $</span> as a function of <i>W</i> measured at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV <i>ep</i> collisions (left) and with an additional restriction to the current hemisphere <span class="mathjax-tex">$0<\eta ^{*}<4$</span> (right). Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. The corresponding <span class="mathjax-tex">$\langle y \rangle $</span> is indicated by the top axis for each measured <i>W</i>. Predictions from the RAPGAP model are shown by dashed lines. The total uncertainty is represented by the error bar</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/8" data-track-dest="link:Figure8 Full size image" aria-label="Full size image figure 8" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>DJANGOH and RAPGAP, as well as the PYTHIA 6 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 44" title="T. Sjöstrand, L. Lönnblad, S. Mrenna, 
 arXiv:hep-ph/0108264
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR44" id="ref-link-section-d48852095e6686">44</a>] photoproduction events, are also used together with the H1 detector simulation in order to determine acceptance, efficiency and backgrounds. as well as to estimate systematic uncertainties associated with the measurement. DJANGOH and RAPGAP are interfaced to HERACLES [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="H. Spiesberger et al., Radiative corrections at HERA, in Workshop on Physics at HERA, 3 (1992)" href="#ref-CR45" id="ref-link-section-d48852095e6689">45</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="A. Kwiatkowski, H. Spiesberger, H.J. Mohring, Comput. Phys. Commun. 69, 155 (1992). 
 https://doi.org/10.1016/0010-4655(92)90136-M
 
 " href="#ref-CR46" id="ref-link-section-d48852095e6689_1">46</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 47" title="A. Kwiatkowski, H. Spiesberger, H. Mohring, Z. Phys. C 50, 165 (1991). 
 https://doi.org/10.1007/BF01558572
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR47" id="ref-link-section-d48852095e6692">47</a>] to simulate QED radiative effects. The generated events are passed through a detailed simulation of the H1 detector response based on the GEANT3 simulation program [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 48" title="R. Brun, F. Bruyant, F. Carminati, S. Giani, M. Maire, A. McPherson, G. Patrick and L. Urban" href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR48" id="ref-link-section-d48852095e6695">48</a>] and are processed using the same reconstruction and analysis chain as used for the data. For the determination of the detector effects both the RAPGAP and DJANGOH predictions are studied.</p></div></div></section><section data-title="Event selection"><div class="c-article-section" id="Sec4-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec4"><span class="c-article-section__title-number">4 </span>Event selection</h2><div class="c-article-section__content" id="Sec4-content"><p>The data set used for this analysis was collected with the H1 detector in the years 2006 and 2007 when positrons and protons were collided at energies of 27.6 GeV and 920 GeV, respectively. The integrated luminosity of the data set is 136 pb<span class="mathjax-tex">$^{-1}$</span>[<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 49" title="H1 Collaboration, F.D. Aaron et al., Eur. Phys. J. C 72, 2163 (2012). 
 https://doi.org/10.1140/epjc/s10052-014-2733-6
 
 . 
 arXiv:1205.2448
 
 [Erratum: Eur. Phys. J. C 74, 2733 (2012)]" href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR49" id="ref-link-section-d48852095e6733">49</a>]. DIS events were recorded using triggers based on electromagnetic energy deposits in the SpaCal calorimeter. The trigger inefficiency is determined using independently triggered data and is negligible in the kinematic region of the analysis.</p><p>The scattered positron is defined by the energy cluster in the SpaCal calorimeter with the highest transverse momentum. The energy of the cluster is further required to be larger than 12 GeV, and the radial position of the cluster is required to be between 15 and 70 cm with respect to the beam axis. The <i>z</i> coordinate of the event vertex is required to be within <span class="mathjax-tex">$|z_v|<35~\mathrm{cm}$</span> of the nominal interaction point. The <span class="mathjax-tex">$E-p_{z}$</span> variable is required to be between 35 and 75 GeV in order to reduce QED radiation and photoproduction backgrounds. Here <span class="mathjax-tex">$E-p_{z}$</span> is defined as the sum of <span class="mathjax-tex">$E_{i}-p_{z,i}$</span> of both the scattered positron and the hadronic final-state (HFS) particles. The HFS particles are reconstructed using an energy flow algorithm [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="M. Peez, Search for deviations from the standard model in high transverse energy processes at the electron proton collider HERA. Thesis, Lyon University (2003) . 
 https://doi.org/10.3204/DESY-THESIS-2003-023
 
 " href="#ref-CR50" id="ref-link-section-d48852095e6888">50</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="S. Hellwig, Untersuchung der D
 
 
 
 $$\ast - \pi $$
 
 
 *
 -
 π
 
 
 slow Double Tagging Methode in Charmanalysen. Thesis, Hamburg University (2005). 
 http://www-h1.desy.de/publications/theses_list.html
 
 " href="#ref-CR51" id="ref-link-section-d48852095e6888_1">51</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="B. Portheault, First measurement of charged and neutral current cross sections with the polarized positron beam at HERA II and QCD-electroweak analyses. Thesis, Paris XI University (2004). 
 http://www-h1.desy.de/publications/theses_list.html
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR52" id="ref-link-section-d48852095e6891">52</a>]. This algorithm combines charged particle tracks and calorimetric energy clusters into hadronic objects, taking into account their respective resolution and geometric overlap, while avoiding double counting of energy.</p><p>Tracks measured in the CTD alone (central tracks) and the combination of CTD and FTD (combined tracks) are used in this analysis. Both central and combined tracks are required to have transverse momenta <span class="mathjax-tex">$p_{\mathrm{T, lab}}>150$</span> MeV. Furthermore, the total momentum for the combined tracks is required to be larger than 500 MeV in order to ensure particles have enough momentum to cross the material between the CJC and FTD. The pseudorapidity of both central and combined tracks is required to be within <span class="mathjax-tex">$|\eta _{_{\text {lab}}}|<1.6$</span>. In addition, the central tracks are required to have their <span class="mathjax-tex">$|dca'\sin {\theta }|<2~\mathrm{cm}$</span>, where <span class="mathjax-tex">$dca'$</span> is the distance of closest approach with respect to the primary vertex and <span class="mathjax-tex">$\theta $</span> is the polar angle of the track. The innermost hit in the CTD is required for central tracks to be less than 50 cm away from the <i>z</i> axis, where the radial track length is required to be larger than 10 cm. Neutral particles are not considered in the multiplicity analysis. Using only tracks assigned to the primary event vertex, the contributions from in-flight decays of <span class="mathjax-tex">$K^{0}_{S}$</span>, <span class="mathjax-tex">$\Lambda $</span>, from photon conversions and from other secondary decays and interactions with detector material are reduced. Details of the track selection are described elsewhere [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 53" title="H1 Collaboration, C. Alexa et al., Eur. Phys. J. C 73, 2406 (2013). 
 https://doi.org/10.1140/epjc/s10052-013-2406-x
 
 . 
 arXiv:1302.1321
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR53" id="ref-link-section-d48852095e7128">53</a>].</p><h3 class="c-article__sub-heading" id="Sec5"><span class="c-article-section__title-number">4.1 </span>Event reconstruction</h3><p>The scattered positron and the HFS particles are used for the reconstruction of the kinematic variables, <span class="mathjax-tex">$x_{\mathrm{bj}}$</span>, <i>y</i> and <span class="mathjax-tex">$Q^2$</span>. Similar to the H1 measurement of charged particle momentum spectra [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 53" title="H1 Collaboration, C. Alexa et al., Eur. Phys. J. C 73, 2406 (2013). 
 https://doi.org/10.1140/epjc/s10052-013-2406-x
 
 . 
 arXiv:1302.1321
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR53" id="ref-link-section-d48852095e7186">53</a>], the <i>e</i>-<span class="mathjax-tex">$\Sigma $</span> method is used [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 54" title="U. Bassler, G. Bernardi, Nucl. Instrum. Meth. A 361, 197 (1995). 
 https://doi.org/10.1016/0168-9002(95)00173-5
 
 . 
 arXiv:hep-ex/9412004
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR54" id="ref-link-section-d48852095e7211">54</a>], where these variables are defined as</p><div id="Equ2" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} Q^2= & {} 4E_{e}E^{'}_{e}\cos {\frac{\theta _{e}}{2}}^{2},\nonumber \\ y= & {} 2E_{e}\frac{\Sigma }{[\Sigma +E^{'}_{e}(1-\cos {\theta _{e}})]^{2}},\nonumber \\ x_{\mathrm{bj}}= & {} \frac{Q^2}{sy}. \end{aligned}$$</span></div><div class="c-article-equation__number"> (2) </div></div><p>Here, <i>s</i> is the <i>ep</i> centre-of-mass energy squared, <span class="mathjax-tex">$E_e$</span> is the incoming lepton energy, <span class="mathjax-tex">$E^{'}_e$</span> and <span class="mathjax-tex">$\theta _{e}$</span> are the scattered positron energy and polar angle, respectively. The quantity <span class="mathjax-tex">$\Sigma $</span> is defined as <span class="mathjax-tex">$\sum {E_{i}-p_{z,i}}$</span>, where the sum runs over all the HFS particles. This method provides an optimum in resolution of the kinematic variables and shows only little sensitivity to QED radiative effects. The hadronic centre-of-mass energy <i>W</i> is defined as:</p><div id="Equ3" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned} W = \sqrt{sy-Q^{2}+M^{2}_{p}}, \end{aligned}$$</span></div><div class="c-article-equation__number"> (3) </div></div><p>where <span class="mathjax-tex">$M_{p}$</span> is the proton rest mass.</p><p>The hadronic centre-of-mass frame is defined as the frame where <span class="mathjax-tex">$p+q=0$</span>, with <i>p</i> and <i>q</i> being the four-momenta of the proton and the virtual photon, respectively. In this frame, the positive <i>z</i> axis is aligned with the direction of the virtual photon.</p><p>In Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig1">1</a>, distributions of the reconstructed quantities of <span class="mathjax-tex">$Q^2$</span>, <i>y</i>, <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span>, and the number of charged particles <span class="mathjax-tex">$N_\mathrm{rec}$</span>, are shown in comparison with predictions from DJANGOH and RAPGAP. The panels of the <span class="mathjax-tex">$Q^2$</span> and <i>y</i> distribution also contain the contribution of expected photoproduction background estimated based on PYTHIA 6.4 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 55" title="T. Sjöstrand, S. Mrenna, P. Skands, JHEP 05, 026 (2006). 
 https://doi.org/10.1088/1126-6708/2006/05/026
 
 . 
 arXiv:hep-ph/0603175
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR55" id="ref-link-section-d48852095e7841">55</a>]. The photoproduction background is found to be less than 0.5%, and therefore is neglected in the subsequent analysis.</p><h3 class="c-article__sub-heading" id="Sec6"><span class="c-article-section__title-number">4.2 </span>Experimental observables and kinematic phase space</h3><p>For a given range in <span class="mathjax-tex">$Q^2$</span> and <i>y</i>, the probability <i>P</i>(<i>N</i>) is defined as the fraction of events for which <i>N</i> charged particles are produced in the specified <span class="mathjax-tex">$\eta $</span> range relative to the total number of events in that <span class="mathjax-tex">$Q^2$</span>,<i>y</i> range. Based on the distribution <i>P</i>(<i>N</i>), the first and second moments of the multiplicity distributions, the KNO function <span class="mathjax-tex">$\Psi (z)$</span> and the final-state hadron entropy <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> are defined as:</p><div id="Equ4" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned}&\langle N \rangle \equiv \frac{\sum {N\cdot P(N)}}{\sum {P(N)}},\nonumber \\&Var(N) \equiv \frac{\sum {(N-\langle N \rangle )^{2}\cdot P(N)}}{\sum {P(N)}}, \end{aligned}$$</span></div><div class="c-article-equation__number"> (4) </div></div><div id="Equ5" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned}&\Psi (z)=\langle N \rangle P(N), \end{aligned}$$</span></div><div class="c-article-equation__number"> (5) </div></div><div id="Equ6" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\begin{aligned}&S_{\mathrm{hadron}} = -\sum {P(N)\ln {P(N)}}. \end{aligned}$$</span></div><div class="c-article-equation__number"> (6) </div></div><p>Here, the sum runs over the number of charged particles and the <i>z</i> variable is equal to <span class="mathjax-tex">$N/\langle N \rangle $</span>. These quantities are measured within the fiducial kinematic phase space listed in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. The selection in the HCM frame relative to the laboratory frame differs only by the additional restriction of the charged particles properties to the current hemisphere, <span class="mathjax-tex">$0<\eta ^{*}<4$</span>.</p><h3 class="c-article__sub-heading" id="Sec7"><span class="c-article-section__title-number">4.3 </span>Data correction</h3><p>The detector-level charged track multiplicity distributions are corrected to stable particles with proper lifetime <span class="mathjax-tex">$c\tau >10~\mathrm{mm}$</span> including charged hyperons. The probabilities <i>P</i>(<i>N</i>) are derived from the distributions of events with <span class="mathjax-tex">$N=0,1,2,\ldots $</span> tracks reconstructed in the specified <span class="mathjax-tex">$\eta $</span> range and with <span class="mathjax-tex">$Q^2$</span> and <i>y</i> reconstructed in the kinematic bin of interest. First, the observed event counts in the three-dimensional grid of <i>N</i>, <span class="mathjax-tex">$Q^2$</span>, <i>y</i> are unfolded, such that migrations between bins as well as efficiency and acceptance distortions are removed. The second step is to normalize the event counts as a function of <i>N</i> to the total number of events in each <span class="mathjax-tex">$Q^2$</span>, <i>y</i> bin and thus obtain the probabilities <i>P</i>(<i>N</i>). The last step is to correct for QED radiation from the electron line.</p><p>The unfolding is done within the TUnfold framework [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 56" title="S. Schmitt, JINST 7, T10003 (2012). 
 https://doi.org/10.1088/1748-0221/7/10/T10003
 
 . 
 arXiv:1205.6201
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR56" id="ref-link-section-d48852095e8606">56</a>]. In order to better resolve migration effects, the number of bins in <span class="mathjax-tex">$Q^2$</span>, <i>y</i> and <i>N</i> is chosen to be higher when counting events in reconstructed quantities as compared to the truth quantities. The phase space in <span class="mathjax-tex">$Q^2$</span> and <i>y</i> is enlarged over the phase space given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>, such that the measured phase space is guarded against migrations at the phase space boundaries. The unfolding turns out to be robust against variations of the regularisation scheme. The dominant systematic uncertainty in the detector correction procedure arises from constructing the matrix of migration with an alternative MC model, DJANGOH instead of the RAPGAP default.</p><p>In this paragraph QED radiative effects are discussed. In the radiative MC, the scattered positron at the particle level is defined to be a scattered positron with photons that are within a cone of 0.4 radian. The QED radiative effects are corrected for based on the MC event generator. The correction factors are derived bin-by-bin in each measured phase space at the particle level using radiative and non-radiative MC samples.</p><p>The binning of the multiplicity <i>N</i> at the particle level after the unfolding is made to be wider than at the detector level when <span class="mathjax-tex">$N>3$</span>, in order to avoid large negative bin-to-bin correlations. For those wide bins, the reported values of <i>P</i>(<i>N</i>) are defined as <span class="mathjax-tex">$\sum {P(N)/\Delta }$</span>, where <span class="mathjax-tex">$\Delta $</span> is the number of distinct values of <i>N</i> included in the bin. In order to determine moments and the hadron entropy, the measured distribution is extrapolated within the wide bins using an exponentiated cubic spline. Correlations between the extrapolated values are taken into account. Bin centres of the wide bins are also reported.</p></div></div></section><section data-title="Systematic uncertainties"><div class="c-article-section" id="Sec8-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec8"><span class="c-article-section__title-number">5 </span>Systematic uncertainties</h2><div class="c-article-section__content" id="Sec8-content"><p>Systematic uncertainties are studied based on systematic variations on fully corrected results, where details of the variations are listed below. The systematic uncertainties are found to depend on <i>N</i>, <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span>, <span class="mathjax-tex">$Q^2$</span> and <i>y</i>. They are are observed to be similar in size for the HCM results as compared to those obtained in the laboratory frame. The following systematic uncertainty sources are considered in this analysis:</p><ul class="u-list-style-bullet"> <li> <p>Sys. 1 – <b>Radiative corrections</b>: the difference in correction factors between the MC generators, the DJANGOH and RAPGAP is taken as systematic uncertainty. It is found to be 1–2% for the <i>P</i>(<i>N</i>) distributions and up to 1% for their moments.</p> </li> <li> <p>Sys. 2 – <b>MC model dependence</b>: the <i>P</i>(<i>N</i>) distributions and their moments are compared between results that are corrected by DJANGOH or RAPGAP. This leads to 1–4% systematic uncertainty on the multiplicity distributions and their moments.</p> </li> <li> <p>Sys. 3 – <b>SpaCal energy scale and angular resolution</b>: a variation of 1% on the energy scale of the SpaCal [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 57" title="H1 Collaboration, F. Aaron et al., Eur. Phys. J. C 63, 625 (2009). 
 https://doi.org/10.1140/epjc/s10052-009-1128-6
 
 . 
 arXiv:0904.0929
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR57" id="ref-link-section-d48852095e8870">57</a>] and <span class="mathjax-tex">$1^{\circ }$</span> on the angular direction is considered. The combined systematic uncertainty on the distribution of <i>P</i>(<i>N</i>) and its moments is found to be 1–5% and 2%, respectively.</p> </li> <li> <p>Sys. 4 – <b>Hadronic energy scale</b>: a variation of 2% on the energy scale of hadronic final-state objects [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 58" title="D. Šálek, Measurement of the Longitudinal Proton Structure Function in Diffraction at the H1 Experiment and Prospects for Diffraction at LHC. PhD thesis, Charles University (2010). 
 http://www-h1.desy.de/publications/theses_list.html
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR58" id="ref-link-section-d48852095e8910">58</a>] results in 1–3% systematic uncertainty on the multiplicity distribution and 2% on the moments.</p> </li> <li> <p>Sys. 5 – <b>Single track efficiency</b>: 0.5% of tracking efficiency uncertainty on central tracks and 10% uncertainty on combined tracks are applied. This leads to 1–5% systematic uncertainty on the <i>P</i>(<i>N</i>) distributions, and 1% on the moments.</p> </li> <li> <p>Sys. 6 – <b>V0 particle contamination</b>: 50% of uncertainty on tracks originating from <span class="mathjax-tex">$K^{0}_{s}$</span> decay and 0.5% uncertainty on tracks from photon conversion and Dalitz-decays surviving the primary track selection result in 1–7% of systematic uncertainty on the <i>P</i>(<i>N</i>) distributions and up to 2% for the moments.</p> </li> <li> <p>Sys. 7 – <b>Diffractive contributions</b>: variation of the diffractive MC contribution by a factor of 2 results in 1–5% systematic uncertainty on the <i>P</i>(<i>N</i>) distributions and up to 1% on the moments.</p> </li> <li> <p>Sys. 8 – <b>Extrapolation</b>: values of <i>P</i>(<i>N</i>) that are not explicitly measured are extrapolated and 1% of difference is found for the mean, variance, and entropy with respect to the generator value based on MC.</p> </li> </ul><p>Systematic uncertainties associated with photoproduction background are negligible. A summary of systematic uncertainties as a function of the multiplicity <i>N</i> can be found in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab2">2</a>. The total systematic uncertainties are obtained by adding in quadrature all individual contributions. The tables of the results contain a complete breakdown of the systematic uncertainty contributions from different sources for each measured data point.</p></div></div></section><section data-title="Results"><div class="c-article-section" id="Sec9-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec9"><span class="c-article-section__title-number">6 </span>Results</h2><div class="c-article-section__content" id="Sec9-content"><h3 class="c-article__sub-heading" id="Sec10"><span class="c-article-section__title-number">6.1 </span>Multiplicity distributions</h3><p>The charged particle multiplicity distributions in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV are measured in different bins of <span class="mathjax-tex">$Q^2$</span> and <i>y</i> for particles with <span class="mathjax-tex">$p_{_{\mathrm{T,lab}}}>150~\,\text{ MeV }$</span> and <span class="mathjax-tex">$|\eta _{_{\mathrm{lab}}}|<1.6$</span> in the laboratory frame. The data are presented in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig2">2</a>, numerical values are reported in the appendix. The data are compared with predictions from the DJANGOH, RAPGAP, and PYTHIA 8 event generators without simulation of QED radiation. The multiplicity distributions <i>P</i>(<i>N</i>) are found to broaden as <i>y</i> increases for fixed <span class="mathjax-tex">$Q^2$</span>. Since <i>y</i> can be related to the hadronic centre-of-mass energy <i>W</i> (cf. Eq. <a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Equ3">3</a>), the increase in multiplicity is qualitatively expected because more energy is available for hadronisation. On the other hand, the <i>P</i>(<i>N</i>) distributions are found to be almost independent of <span class="mathjax-tex">$Q^2$</span> for fixed <i>y</i>. Qualitatively, the MC predictions can describe the peak position of the multiplicity distributions well. However, they tend to underestimate the data both at low and high multiplicities, especially towards low <span class="mathjax-tex">$Q^2$</span> and high <i>y</i>. Among all MC models considered, the PYTHIA 8 model gives the poorest description and peaks significantly below the data, especially at high <i>y</i>.</p><p>In Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig3">3</a>, <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig4">4</a>, <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig5">5</a> and <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig6">6</a> the charged particle multiplicity distributions <i>P</i>(<i>N</i>) are presented in four bins of <span class="mathjax-tex">$Q^2$</span>. In each figure, the <i>P</i>(<i>N</i>) distributions are shown differentially in bins of <i>y</i> (identical binning as in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig2">2</a>) and in three different ranges of <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span>. Numerical values are given in the appendix. The overlapping <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span> ranges are chosen such that a pseudorapidity window of 1.4 units around the scattered parton direction in the leading order Quark Parton Model (QPM) picture can be selected. Similar to the measurements over the full <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span> range, the <i>P</i>(<i>N</i>) distributions are found to broaden as <i>y</i> increases, independent of the considered <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span> ranges. For fixed <i>y</i>, the <i>P</i>(<i>N</i>) distributions also broaden as <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span> increases. Similar to the results presented in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig2">2</a>, the MC models underestimate the high multiplicity tail, where the deviation is found to be the strongest at low <span class="mathjax-tex">$Q^2$</span>.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-3"><figure><figcaption class="c-article-table__figcaption"><b id="Tab3" data-test="table-caption">Table 3 Mean multiplicity measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeVas a function of <i>W</i>. The measurement is repeated in four ranges of <span class="mathjax-tex">$Q^2$</span> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/3" aria-label="Full size table 3"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-4"><figure><figcaption class="c-article-table__figcaption"><b id="Tab4" data-test="table-caption">Table 4 Mean multiplicity measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV as a function of <i>W</i>. The measurement is repeated in four ranges of <span class="mathjax-tex">$Q^2$</span> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. For this dataset, the track pseudorapidities in the hadronic centre-of-mass frame are restricted to the range <span class="mathjax-tex">$0<\eta ^* <4$</span></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/4" aria-label="Full size table 4"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-9" data-title="Fig. 9"><figure><figcaption><b id="Fig9" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 9</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/9" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig9_HTML.png?as=webp"><img aria-describedby="Fig9" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig9_HTML.png" alt="figure 9" loading="lazy" width="685" height="321"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-9-desc"><p>Second moment (variance) of the multiplicity distributions <i>Var</i>(<i>N</i>) as a function of <i>W</i> measured at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV <i>ep</i> collisions (left) and with an additional restriction to the current hemisphere <span class="mathjax-tex">$0<\eta ^{*}<4$</span> (right). Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. The corresponding <span class="mathjax-tex">$\langle y \rangle $</span> is indicated by the top axis for each measured <i>W</i>. Predictions from the RAPGAP model are shown by dashed lines. The total uncertainty is represented by the error bar</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/9" data-track-dest="link:Figure9 Full size image" aria-label="Full size image figure 9" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-5"><figure><figcaption class="c-article-table__figcaption"><b id="Tab5" data-test="table-caption">Table 5 Variance of multiplicity distributions measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV as a function of <i>W</i>. The measurement is repeated in four ranges of <span class="mathjax-tex">$Q^2$</span> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/5" aria-label="Full size table 5"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-6"><figure><figcaption class="c-article-table__figcaption"><b id="Tab6" data-test="table-caption">Table 6 Variance of multiplicity distributions measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV as a function of <i>W</i>. The measurement is repeated in four ranges of <span class="mathjax-tex">$Q^2$</span> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. For this dataset, the track pseudorapidities in the hadronic centre-of-mass frame are restricted to the range <span class="mathjax-tex">$0<\eta ^* <4$</span></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/6" aria-label="Full size table 6"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-10" data-title="Fig. 10"><figure><figcaption><b id="Fig10" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 10</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/10" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig10_HTML.png?as=webp"><img aria-describedby="Fig10" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig10_HTML.png" alt="figure 10" loading="lazy" width="685" height="658"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-10-desc"><p>KNO function <span class="mathjax-tex">$\Psi (z)$</span> as a function of <i>z</i> measured at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV in <i>ep</i> collisions in bins of <span class="mathjax-tex">$Q^2$</span> with an additional restriction to the current hemisphere <span class="mathjax-tex">$0<\eta ^{*}<4$</span>. Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. The total uncertainty is denoted by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/10" data-track-dest="link:Figure10 Full size image" aria-label="Full size image figure 10" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <p>In Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig7">7</a>, the multiplicity distributions <i>P</i>(<i>N</i>) are presented with the additional restriction in the HCM frame <span class="mathjax-tex">$0<\eta ^{*}<4$</span>, mainly selecting particles originating from the current hemisphere. Numerical values are given in the appendix. Predictions obtained from DJANGOH, RAPGAP, and PYTHIA 8 are compared with data. Qualitatively, the comparisons are very similar to those of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig2">2</a>. For the quantities presented in the subsequent sections the differences between RAPGAP and DJANGOH are small, thus only RAPGAP is compared to the data.</p><h3 class="c-article__sub-heading" id="Sec11"><span class="c-article-section__title-number">6.2 </span>Moments of multiplicity distributions</h3><p>The mean multiplicity <span class="mathjax-tex">$\langle N \rangle $</span> as a function of <i>W</i> is presented in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig8">8</a> and Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab3">3</a> and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab4">4</a>, for both the full phase space and with an additional restriction in <span class="mathjax-tex">$\eta ^{*}$</span> (see Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>). Predictions from the RAPGAP model are also shown. The average multiplicity <span class="mathjax-tex">$\langle N \rangle $</span> rises with the hadronic centre-of-mass energy <i>W</i>, which is in agreement with previous observations [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 13" title="H1 Collaboration, S. Aid et al., Z. Phys. C 72, 573 (1996). 
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 " href="#ref-CR59" id="ref-link-section-d48852095e16421">59</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="ALICE Collaboration, S. Acharya et al., Eur. Phys. J. C 77, 852 (2017). 
 https://doi.org/10.1140/epjc/s10052-017-5412-6
 
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 arXiv:1708.01435
 
 " href="#ref-CR60" id="ref-link-section-d48852095e16421_1">60</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="CMS Collaboration, V. Khachatryan et al., JHEP 01, 079 (2011). 
 https://doi.org/10.1007/JHEP01(2011)079
 
 . 
 arXiv:1011.5531
 
 " href="#ref-CR61" id="ref-link-section-d48852095e16421_2">61</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 62" title="LHCb Collaboration, R. Aaij et al., Eur. Phys. J. C 74, 2888 (2014). 
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 . 
 arXiv:1402.4430
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR62" id="ref-link-section-d48852095e16424">62</a>]. For higher <span class="mathjax-tex">$Q^2$</span>, the increase in <i>W</i> is faster than that at lower <span class="mathjax-tex">$Q^2$</span>. For high <i>W</i>, the <span class="mathjax-tex">$Q^2$</span> dependence is observed to be stronger in the full phase space than with the <span class="mathjax-tex">$\eta ^{*}$</span> restriction of the current hemisphere. The RAPGAP prediction yields a reasonable description of the data. Only at high <i>W</i> and low <span class="mathjax-tex">$Q^2$</span> the MC tends to underestimate the data.</p><p>Similarly, in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig9">9</a> and Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab5">5</a> and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab6">6</a>, second moments of the multiplicity distributions (variances) are presented as a function of <i>W</i>, for both the full phase space and with the additional restriction in <span class="mathjax-tex">$\eta ^{*}$</span>. The variances rise strongly with <i>W</i>, almost independent of <span class="mathjax-tex">$Q^2$</span> within uncertainties. The restriction of the current hemisphere has little inpact on the variance. For <span class="mathjax-tex">$Q^2>40~\mathrm {GeV}^2 $</span>, RAPGAP describes the data reasonably well. However, towards high <i>W</i>, the MC not only underestimates the data but also shows a <span class="mathjax-tex">$Q^2$</span> dependence, which is absent in data. This effect is more pronounced when restricting the analysis to the current hemisphere.</p><h3 class="c-article__sub-heading" id="Sec12"><span class="c-article-section__title-number">6.3 </span>The KNO-scaling function <span class="mathjax-tex">$\Psi (z)$</span> </h3><p>In order to further study the multiplicity distribution, the KNO function <span class="mathjax-tex">$\Psi (z)$</span> measured as a function of <span class="mathjax-tex">$z=N/\langle N \rangle $</span> is shown in different bins of <span class="mathjax-tex">$Q^2$</span> in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig10">10</a>. Numerical values are given in the appendix. The analysis is restricted to the current hemisphere (<span class="mathjax-tex">$0<\eta ^{*}<4$</span>). In all <span class="mathjax-tex">$Q^2$</span> bins, KNO scaling is observed, in broad agreement with many past experiments. However, in proton-proton collisions at LHC energies, violations of KNO scaling have been reported recently [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 61" title="CMS Collaboration, V. Khachatryan et al., JHEP 01, 079 (2011). 
 https://doi.org/10.1007/JHEP01(2011)079
 
 . 
 arXiv:1011.5531
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR61" id="ref-link-section-d48852095e16876">61</a>].</p><h3 class="c-article__sub-heading" id="Sec13"><span class="c-article-section__title-number">6.4 </span>Entropy</h3><p>It was recently suggested [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="D.E. Kharzeev, E.M. Levin, Phys. Rev. D 95, 114008 (2017). 
 https://doi.org/10.1103/PhysRevD.95.114008
 
 . 
 arXiv:1702.03489
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR5" id="ref-link-section-d48852095e16887">5</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="Z. Tu, D.E. Kharzeev, T. Ullrich, Phys. Rev. Lett. 124, 062001 (2020). 
 https://doi.org/10.1103/PhysRevLett.124.062001
 
 . 
 arXiv:1904.11974
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR10" id="ref-link-section-d48852095e16890">10</a>] that the final-state hadron entropy <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> calculated from charged particle multiplicity distributions might be related to the entanglement entropy of gluons <span class="mathjax-tex">$S_{\mathrm{gluon}}$</span> at low <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> (Eq. <a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Equ1">1</a>). In Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig11">11</a> and Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab7">7</a>, <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> is studied as a function of <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span> in different <span class="mathjax-tex">$Q^2$</span> bins. Similar to the observable studied in Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="Z. Tu, D.E. Kharzeev, T. Ullrich, Phys. Rev. Lett. 124, 062001 (2020). 
 https://doi.org/10.1103/PhysRevLett.124.062001
 
 . 
 arXiv:1904.11974
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR10" id="ref-link-section-d48852095e17077">10</a>], a moving <span class="mathjax-tex">$\eta _{_{\mathrm{lab}}}$</span> window depending on <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span> is chosen to match the rapidity of the scattered quark in a leading order QPM picture. The respective selected pseudorapidity window in the laboratory frame is indicated in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab7">7</a>. The hadron entropy observed in data is consistent with being constant in <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span>, increasing only slightly with <span class="mathjax-tex">$Q^2$</span>. The same <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span> and <span class="mathjax-tex">$Q^2$</span> dependence is also observed for RAPGAP, however with slightly smaller values of <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span>. Predictions for the entanglement entropy <span class="mathjax-tex">$S_{\mathrm{gluon}}$</span> based on the gluon density <span class="mathjax-tex">$xG(x,Q^{2})$</span> are also shown at various <span class="mathjax-tex">$Q^2$</span> values, which correspond to the lower boundaries of the <span class="mathjax-tex">$Q^2$</span> bins in data. Here the PDF set HERAPDF 2.0 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 63" title="H1 and ZEUS Collaboration, H. Abramowicz et al., Eur. Phys. J. C 75, 580 (2015). 
 https://doi.org/10.1140/epjc/s10052-015-3710-4
 
 . 
 arXiv:1506.06042
 
 " href="/article/10.1140/epjc/s10052-021-08896-1#ref-CR63" id="ref-link-section-d48852095e17465">63</a>] at leading order is used. Neither the dependence on <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span> nor the magnitude agrees with data. Thus the prediction <span class="mathjax-tex">$S_{\mathrm{hadron}}=S_{\mathrm{gluon}}$</span> (Eq. <a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Equ1">1</a>) is not confirmed by the present measurement.</p><p>To investigate further, the hadron entropy determined in the current hemisphere, <span class="mathjax-tex">$0<\eta ^*<4$</span>, is presented in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig12">12</a> and Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab8">8</a>. The hadron entropy based on multiplicity distributions is shown as a function of <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span> in different bins of <span class="mathjax-tex">$Q^2$</span>. In contrast to Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig11">11</a>, there is no moving pseudorapidity range applied. Independent of <span class="mathjax-tex">$Q^2$</span>, the measured hadron entropy, <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span>, rises with decreasing <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span> with similar slopes in different <span class="mathjax-tex">$Q^2$</span> bins. Also shown are the predictions from RAPGAP which closely follow the data at high <span class="mathjax-tex">$Q^2$</span> but underestimate the data at low <span class="mathjax-tex">$Q^2$</span>. Since <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> is calculated from the multiplicity distributions, this behaviour of the MC is related to what has been observed for the moments, Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig8">8</a> and <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Fig9">9</a>. The predictions from the entanglement approach based on the gluon density again fail to describe <span class="mathjax-tex">$S_\mathrm{hadron}$</span> in magnitude. However, at low <span class="mathjax-tex">$Q^2$</span> the slope of <span class="mathjax-tex">$S_\mathrm{gluon}$</span> has some similarities with that observed for <span class="mathjax-tex">$S_\mathrm{hadron}$</span>, while it becomes steeper than observed with increasing <span class="mathjax-tex">$Q^2$</span>.</p></div></div></section><section data-title="Summary"><div class="c-article-section" id="Sec14-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec14"><span class="c-article-section__title-number">7 </span>Summary</h2><div class="c-article-section__content" id="Sec14-content"><p>The charged particle multiplicity distributions <i>P</i>(<i>N</i>) are measured in deep inelastic scattering at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV using the H1 detector at HERA. The integrated luminosity used in this analysis is 136 pb<span class="mathjax-tex">$^{-1}$</span>, recorded in the years 2006 and 2007 in positrons scattering off protons. The <i>P</i>(<i>N</i>) distributions are measured in bins of <span class="mathjax-tex">$Q^2$</span>, <i>y</i> and pseudorapidity <span class="mathjax-tex">$\eta $</span>. Predictions based on simulations of partonic tree level matrix elements, supplemented by parton shower and hadronisation are generally found to be consistent with the measurement at low multiplicities while they underestimate the data in the high multiplicity regions, especially at low <span class="mathjax-tex">$Q^2$</span>. For measurements of moments, the predictions generally describe the data well at low hadronic centre-of-mass energy <i>W</i> and high <span class="mathjax-tex">$Q^2$</span> but less so at high <i>W</i> and low <span class="mathjax-tex">$Q^2$</span>. In addition, KNO scaling is observed within the kinematic phase space of the analysis.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-7"><figure><figcaption class="c-article-table__figcaption"><b id="Tab7" data-test="table-caption">Table 7 Hadron entropy derived from multiplicity distributions measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV as a function of <span class="mathjax-tex">$\langle x_{\mathrm{bj}} \rangle $</span>. The measurement is repeated in four ranges of <span class="mathjax-tex">$Q^2$</span> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. For this dataset, the entropy is determined in a sliding window in pseudorapidity as indicated in the table</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/7" aria-label="Full size table 7"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-8"><figure><figcaption class="c-article-table__figcaption"><b id="Tab8" data-test="table-caption">Table 8 Hadron entropy derived from multiplicity distributions measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV as a function of <span class="mathjax-tex">$\langle x_{\mathrm{bj}} \rangle $</span>. The measurement is repeated in four ranges of <span class="mathjax-tex">$Q^2$</span> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. For this dataset, the entropy is determined with the track pseudorapidities in the hadronic centre-of-mass frame are restricted to the range <span class="mathjax-tex">$0<\eta ^* <4$</span></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/8" aria-label="Full size table 8"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-11" data-title="Fig. 11"><figure><figcaption><b id="Fig11" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 11</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/11" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig11_HTML.png?as=webp"><img aria-describedby="Fig11" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig11_HTML.png" alt="figure 11" loading="lazy" width="685" height="679"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-11-desc"><p>Hadron entropy <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> derived from multiplicity distributions, reported as a function of <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span> in different <span class="mathjax-tex">$Q^2$</span> ranges, measured in <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV <i>ep</i> collisions. For each <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span>, the multiplicity is determined in a dedicated pseudorapidity window as discussed in the text. Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. Predictions for <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> from the RAPGAP model and for the entanglement entropy <span class="mathjax-tex">$S_{\mathrm{gluon}}$</span> based on an entanglement model are shown by the dashed lines and solid lines, respectively. For each <span class="mathjax-tex">$Q^2$</span> range, the value of the lower boundary is used for predicting <span class="mathjax-tex">$S_{\mathrm{gluon}}$</span>. The total uncertainty on the data is represented by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/11" data-track-dest="link:Figure11 Full size image" aria-label="Full size image figure 11" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-12" data-title="Fig. 12"><figure><figcaption><b id="Fig12" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 12</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/12" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig12_HTML.png?as=webp"><img aria-describedby="Fig12" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-021-08896-1/MediaObjects/10052_2021_8896_Fig12_HTML.png" alt="figure 12" loading="lazy" width="685" height="679"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-12-desc"><p>Hadron entropy <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> derived from multiplicity distributions as a function of <span class="mathjax-tex">$\langle $</span> <span class="mathjax-tex">$x_{\mathrm{bj}}$</span> <span class="mathjax-tex">$\rangle $</span> measured in different <span class="mathjax-tex">$Q^2$</span> ranges, measured in <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV <i>ep</i> collisions. Here, a restriction to the current hemisphere <span class="mathjax-tex">$0<\eta ^{*}<4$</span> is applied. Further phase space restrictions are given in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. Predictions for <span class="mathjax-tex">$S_{\mathrm{hadron}}$</span> from the RAPGAP model and for the entanglement entropy <span class="mathjax-tex">$S_{\mathrm{gluon}}$</span> based on an entanglement model are shown by the dashed lines and solid lines, respectively. For each <span class="mathjax-tex">$Q^2$</span> range, the value of the lower boundary is used for predicting <span class="mathjax-tex">$S_\mathrm{gluon}$</span>. The total uncertainty on the data is represented by the error bars</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-021-08896-1/figures/12" data-track-dest="link:Figure12 Full size image" aria-label="Full size image figure 12" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <p>The measurement of the charged particle multiplicity distributions is also used to test for the first time predictions based on quantum entanglement on sub-nucleonic scales in deep-inelastic <i>ep</i> scattering. The predictions from the entropy of gluons are found to grossly disagree with the hadron entropy obtained from the multiplicity measurements presented here, and therefore the data do not support the basic concept of equality of the parton and hadron entropy with the current level of theory development.</p><p>The measurements reported in this paper not only provide valuable information for better understanding particle production mechanisms, but also set an important testing ground for the development of new concepts, like quantum entanglement at sub-nucleonic scales.</p></div></div></section> </div> <section data-title="Data Availability Statement"><div class="c-article-section" id="data-availability-statement-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="data-availability-statement">Data Availability Statement</h2><div class="c-article-section__content" id="data-availability-statement-content"> <p>This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All relevant data are included with this article in the form of tables.]</p> </div></div></section><section data-title="Notes"><div class="c-article-section" id="notes-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="notes">Notes</h2><div class="c-article-section__content" id="notes-content"><ol class="c-article-footnote c-article-footnote--listed"><li class="c-article-footnote--listed__item" id="Fn1" data-counter="1."><div class="c-article-footnote--listed__content"><p>The positive <span class="mathjax-tex">$\eta ^{*}$</span> region qualitatively corresponds to the current fragmentation region (predominantly negative <span class="mathjax-tex">$\eta _{_{\mathrm{lab}}}$</span>), while <span class="mathjax-tex">$\eta ^{*}<0$</span> corresponds to the direction of the target fragmentation region (predominantly positive <span class="mathjax-tex">$\eta _{_{\mathrm{lab}}}$</span>).</p></div></li></ol></div></div></section><div id="MagazineFulltextArticleBodySuffix"><section aria-labelledby="Bib1" data-title="References"><div class="c-article-section" id="Bib1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Bib1">References</h2><div class="c-article-section__content" id="Bib1-content"><div data-container-section="references"><ol class="c-article-references" data-track-component="outbound reference" data-track-context="references section"><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="1."><p class="c-article-references__text" id="ref-CR1">J.D. 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We thank the engineers and technicians for their work in constructing and maintaining the H1 detector, our funding agencies for financial support, the DESY technical staff for continual assistance and the DESY directorate for support and for the hospitality which they extend to the non-DESY members of the collaboration. We would like to give credit to all partners contributing to the EGI computing infrastructure for their support for the H1 Collaboration. We express our thanks to all those involved in securing not only the H1 data but also the software and working environment for long term use, allowing the unique H1 data set to continue to be explored in the coming years. The transfer from experiment specific to central resources with long term support, including both storage and batch systems, has also been crucial to this enterprise. We therefore also acknowledge the role played by DESY-IT and all people involved during this transition and their future role in the years to come.</p></div></div></section><section aria-labelledby="author-information" data-title="Author information"><div class="c-article-section" id="author-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="author-information">Author information</h2><div class="c-article-section__content" id="author-information-content"><h3 class="c-article__sub-heading" id="affiliations">Authors and Affiliations</h3><ol class="c-article-author-affiliation__list"><li id="Aff1"><p class="c-article-author-affiliation__address">I. Physikalisches Institut der RWTH, Aachen, Germany</p><p class="c-article-author-affiliation__authors-list">H.-U. Martyn</p></li><li id="Aff2"><p class="c-article-author-affiliation__address">School of Physics and Astronomy, University of Birmingham, Birmingham, UK</p><p class="c-article-author-affiliation__authors-list">A. Buniatyan, P. R. Newman & P. D. Thompson</p></li><li id="Aff3"><p class="c-article-author-affiliation__address">Inter-University Institute for High Energies ULB-VUB, Brussels and Universiteit Antwerpen, Antwerp, Belgium</p><p class="c-article-author-affiliation__authors-list">L. Favart, A. Grebenyuk, T. Hreus, X. Janssen, R. Roosen & P. Van Mechelen</p></li><li id="Aff4"><p class="c-article-author-affiliation__address">Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering (IFIN-HH), Bucharest, Romania</p><p class="c-article-author-affiliation__authors-list">M. Rotaru</p></li><li id="Aff5"><p class="c-article-author-affiliation__address">STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK</p><p class="c-article-author-affiliation__authors-list">D. P. C. Sankey</p></li><li id="Aff6"><p class="c-article-author-affiliation__address">Institute of Nuclear Physics Polish Academy of Sciences, 31342, Kraków, Poland</p><p class="c-article-author-affiliation__authors-list">L. Goerlich, S. Mikocki, G. Nowak & P. Sopicki</p></li><li id="Aff7"><p class="c-article-author-affiliation__address">Institut für Physik, TU Dortmund, Dortmund, Germany</p><p class="c-article-author-affiliation__authors-list">D. Wegener</p></li><li id="Aff8"><p class="c-article-author-affiliation__address">Joint Institute for Nuclear Research, Dubna, Russia</p><p class="c-article-author-affiliation__authors-list">M. Kapichine, A. Morozov & V. Spaskov</p></li><li id="Aff9"><p class="c-article-author-affiliation__address">Irfu/SPP, CE Saclay, Gif-sur-Yvette, France</p><p class="c-article-author-affiliation__authors-list">J. Feltesse & L. Schoeffel</p></li><li id="Aff10"><p class="c-article-author-affiliation__address">DESY, Hamburg, Germany</p><p class="c-article-author-affiliation__authors-list">A. J. Campbell, G. Eckerlin, M. Fleischer, J. Gayler, D. Haidt, H. Jung, J. Katzy, C. Kleinwort, D. Krücker, K. Krüger, S. Levonian, K. Lipka, B. List, J. List, A. B. Meyer, J. Meyer, C. Niebuhr, J. E. Olsson, D. Pitzl, S. Schmitt, F. Sefkow, D. South, M. Steder, E. Wünsch & R. Žlebčík</p></li><li id="Aff11"><p class="c-article-author-affiliation__address">Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany</p><p class="c-article-author-affiliation__authors-list">R. Kogler</p></li><li id="Aff12"><p class="c-article-author-affiliation__address">Physikalisches Institut, Universität Heidelberg, Heidelberg, Germany</p><p class="c-article-author-affiliation__authors-list">A. Bolz, F. Huber, M. Sauter & A. Schöning</p></li><li id="Aff13"><p class="c-article-author-affiliation__address">Department of Physics, University of Lancaster, Lancaster, UK</p><p class="c-article-author-affiliation__authors-list">R. C. W. Henderson</p></li><li id="Aff14"><p class="c-article-author-affiliation__address">Department of Physics, University of Liverpool, Liverpool, UK</p><p class="c-article-author-affiliation__authors-list">J. B. Dainton, T. Greenshaw, M. Klein, P. Kostka, J. Kretzschmar, P. Laycock, S. J. Maxfield, A. Mehta & G. D. Patel</p></li><li id="Aff15"><p class="c-article-author-affiliation__address">School of Physics and Astronomy, Queen Mary, University of London, London, UK</p><p class="c-article-author-affiliation__authors-list">M. P. J. Landon, E. Rizvi & D. Traynor</p></li><li id="Aff16"><p class="c-article-author-affiliation__address">Aix Marseille Université, CNRS/IN2P3, CPPM UMR 7346, 13288, Marseille, France</p><p class="c-article-author-affiliation__authors-list">C. Diaconu, D. Hoffmann, E. Sauvan & C. Vallée</p></li><li id="Aff17"><p class="c-article-author-affiliation__address">Departamento de Fisica Aplicada, CINVESTAV, Mérida, Yucatán, Mexico</p><p class="c-article-author-affiliation__authors-list">K. B. Cantun Avila & J. G. Contreras</p></li><li id="Aff18"><p class="c-article-author-affiliation__address">Institute for Theoretical and Experimental Physics, Moscow, Russia</p><p class="c-article-author-affiliation__authors-list">L. Bystritskaya & A. Fedotov</p></li><li id="Aff19"><p class="c-article-author-affiliation__address">Lebedev Physical Institute, Moscow, Russia</p><p class="c-article-author-affiliation__authors-list">V. Andreev, A. Belousov, A. Fomenko, N. Gogitidze, A. Lebedev, E. Malinovski & Y. Soloviev</p></li><li id="Aff20"><p class="c-article-author-affiliation__address">Max-Planck-Institut für Physik, Munich, Germany</p><p class="c-article-author-affiliation__authors-list">D. Britzger, V. Chekelian, G. Grindhammer, C. Kiesling & B. Lobodzinski</p></li><li id="Aff21"><p class="c-article-author-affiliation__address">LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France</p><p class="c-article-author-affiliation__authors-list">M. Jacquet, C. Pascaud, Z. Zhang & F. Zomer</p></li><li id="Aff22"><p class="c-article-author-affiliation__address">LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France</p><p class="c-article-author-affiliation__authors-list">V. Boudry & A. Specka</p></li><li id="Aff23"><p class="c-article-author-affiliation__address">Faculty of Science, University of Montenegro, Podgorica, Montenegro</p><p class="c-article-author-affiliation__authors-list">I. Picuric & N. Raicevic</p></li><li id="Aff24"><p class="c-article-author-affiliation__address">Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic</p><p class="c-article-author-affiliation__authors-list">J. Cvach, J. Hladkỳ & P. Reimer</p></li><li id="Aff25"><p class="c-article-author-affiliation__address">Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic</p><p class="c-article-author-affiliation__authors-list">R. Polifka, T. Sykora, A. Valkárová & J. Žáček</p></li><li id="Aff26"><p class="c-article-author-affiliation__address">Dipartimento di Fisica, Università di Roma Tre and INFN Roma 3, Rome, Italy</p><p class="c-article-author-affiliation__authors-list">B. Stella</p></li><li id="Aff27"><p class="c-article-author-affiliation__address">Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar, Mongolia</p><p class="c-article-author-affiliation__authors-list">K. Begzsuren, T. Ravdandorj & B. Tseepeldorj</p></li><li id="Aff28"><p class="c-article-author-affiliation__address">Paul Scherrer Institut, Villigen, Switzerland</p><p class="c-article-author-affiliation__authors-list">S. Egli, R. Horisberger & D. Ozerov</p></li><li id="Aff29"><p class="c-article-author-affiliation__address">Fachbereich C, Universität Wuppertal, Wuppertal, Germany</p><p class="c-article-author-affiliation__authors-list">K. Daum & H. Meyer</p></li><li id="Aff30"><p class="c-article-author-affiliation__address">Yerevan Physics Institute, Yerevan, Armenia</p><p class="c-article-author-affiliation__authors-list">A. Baghdasaryan & H. Zohrabyan</p></li><li id="Aff31"><p class="c-article-author-affiliation__address">DESY, Zeuthen, Germany</p><p class="c-article-author-affiliation__authors-list">W. Lange & Th. Naumann</p></li><li id="Aff32"><p class="c-article-author-affiliation__address">Institut für Teilchenphysik, ETH, Zurich, Switzerland</p><p class="c-article-author-affiliation__authors-list">C. Grab</p></li><li id="Aff33"><p class="c-article-author-affiliation__address">Physik-Institut der Universität Zürich, Zurich, Switzerland</p><p class="c-article-author-affiliation__authors-list">K. Müller, P. Robmann, U. Straumann & P. Truöl</p></li><li id="Aff34"><p class="c-article-author-affiliation__address">Université Claude Bernard Lyon 1, CNRS/IN2P3, Villeurbanne, France</p><p class="c-article-author-affiliation__authors-list">M. Gouzevitch & A. Petrukhin</p></li><li id="Aff35"><p class="c-article-author-affiliation__address">Now at Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, Moscow, Russia</p><p class="c-article-author-affiliation__authors-list">S. Shushkevich</p></li><li id="Aff36"><p class="c-article-author-affiliation__address">Palackỳ University Olomouc, Olomouc, Czech Republic</p><p class="c-article-author-affiliation__authors-list">K. Cerny</p></li><li id="Aff37"><p class="c-article-author-affiliation__address">Now at CERN, Geneva, Switzerland</p><p class="c-article-author-affiliation__authors-list">E. Elsen & E. Perez</p></li><li id="Aff38"><p class="c-article-author-affiliation__address">Also at Ulaanbaatar University, Ulaanbaatar, Mongolia</p><p class="c-article-author-affiliation__authors-list">B. Tseepeldorj</p></li><li id="Aff39"><p class="c-article-author-affiliation__address">Also at LAPP, Université de Savoie, CNRS/IN2P3, Annecy-le-Vieux, France</p><p class="c-article-author-affiliation__authors-list">E. Sauvan</p></li><li id="Aff40"><p class="c-article-author-affiliation__address">II. Physikalisches Institut, Universität Göttingen, Göttingen, Germany</p><p class="c-article-author-affiliation__authors-list">G. Brandt</p></li><li id="Aff41"><p class="c-article-author-affiliation__address">Now at Institute for Information Transmission Problems RAS, Moscow, Russia</p><p class="c-article-author-affiliation__authors-list">A. Rostovtsev</p></li><li id="Aff42"><p class="c-article-author-affiliation__address">Brookhaven National Laboratory, Upton, New York, 11973, USA</p><p class="c-article-author-affiliation__authors-list">Z. Tu & T. Ullrich</p></li><li id="Aff43"><p class="c-article-author-affiliation__address">Department of Physics and Astronomy, Purdue University, 525 Northwestern Ave, West Lafayette, IN, 47907, USA</p><p class="c-article-author-affiliation__authors-list">A. W. Jung</p></li><li id="Aff44"><p class="c-article-author-affiliation__address">Department of Physics, Oxford University, Oxford, UK</p><p class="c-article-author-affiliation__authors-list">V. Radescu</p></li><li id="Aff45"><p class="c-article-author-affiliation__address">Rice University, Houston, USA</p><p class="c-article-author-affiliation__authors-list">A. Baty & W. Li</p></li><li id="Aff46"><p class="c-article-author-affiliation__address">Shandong University, Shandong, People’s Republic of China</p><p class="c-article-author-affiliation__authors-list">Z. Chen</p></li><li id="Aff47"><p class="c-article-author-affiliation__address">Stony Brook University, Stony Brook, NY, 11794, USA</p><p class="c-article-author-affiliation__authors-list">A. Deshpande, C. Gal, M. M. Mondal, S. Park, B. A. Schmookler & J. Zhang</p></li></ol><div class="u-js-hide u-hide-print" data-test="author-info"><span class="c-article__sub-heading">Authors</span><ol class="c-article-authors-search u-list-reset"><li id="auth-V_-Andreev-Aff19"><span class="c-article-authors-search__title u-h3 js-search-name">V. Andreev</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?dc.creator=V.%20Andreev" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=V.%20Andreev" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22V.%20Andreev%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li><li id="auth-A_-Baghdasaryan-Aff30"><span class="c-article-authors-search__title u-h3 js-search-name">A. 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Zomer</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?dc.creator=F.%20Zomer" class="c-article-button" data-track="click" data-track-action="author link - publication" data-track-label="link" rel="nofollow">View author publications</a></div><div class="c-article-authors-search__item c-article-authors-search__list-item--right"><p class="search-in-title-js c-article-authors-search__text">You can also search for this author in <span class="c-article-identifiers"><a class="c-article-identifiers__item" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=search&term=F.%20Zomer" data-track="click" data-track-action="author link - pubmed" data-track-label="link" rel="nofollow">PubMed</a><span class="u-hide"> </span><a class="c-article-identifiers__item" href="http://scholar.google.co.uk/scholar?as_q=&num=10&btnG=Search+Scholar&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=%22F.%20Zomer%22&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en" data-track="click" data-track-action="author link - scholar" data-track-label="link" rel="nofollow">Google Scholar</a></span></p></div></div></li></ol></div><h3 class="c-article__sub-heading" id="corresponding-author">Corresponding author</h3><p id="corresponding-author-list">Correspondence to <a id="corresp-c1" href="mailto:sschmitt@mail.desy.de">S. Schmitt</a>.</p></div></div></section><section aria-labelledby="appendices"><div class="c-article-section" id="appendices-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="appendices">A Charged particle multiplicities and KNO function</h2><div class="c-article-section__content" id="appendices-content"><h3 class="c-article__sub-heading u-visually-hidden" id="App1">A Charged particle multiplicities and KNO function</h3><p>Numerical values of the charged particle multiplicity measured in the pseudorapidity range <span class="mathjax-tex">$-1.6<\eta _{_{\text {lab}}}<1.6$</span> are presented in four ranges of <span class="mathjax-tex">$Q^2$</span> and are further subdivided into four <i>y</i> ranges. The four <span class="mathjax-tex">$Q^2$</span> ranges are shown in the Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab9">9</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab10">10</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab11">11</a>, and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab12">12</a>, respectively. Further phase space restrictions are discussed in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a>. These restrictions apply to all measurements presented in the following.</p><p>The measurement is repeated in three overlapping subranges of <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span>. There are a total of twelve tables, each corresponding to selected range in both <span class="mathjax-tex">$Q^2$</span> and <span class="mathjax-tex">$\eta _{_{\text {lab}}}$</span>. The range <span class="mathjax-tex">$5<Q^2<10~\mathrm {GeV}^2 $</span> is given in Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab13">13</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab14">14</a>, and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab15">15</a>. The range <span class="mathjax-tex">$10<Q^2<20~\mathrm {GeV}^2 $</span> is given in Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab16">16</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab17">17</a>, and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab18">18</a>. The range <span class="mathjax-tex">$20<Q^2<40~\mathrm {GeV}^2 $</span> is given in Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab19">19</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab20">20</a>, and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab21">21</a>. The range <span class="mathjax-tex">$40<Q^2<100~\mathrm {GeV}^2 $</span> is given in Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab22">22</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab23">23</a>, and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab24">24</a>.</p><p>The measurement is also repeated over the full available pseudorapidity range <span class="mathjax-tex">$-1.6<\eta _{_{\text {lab}}}<1.6$</span> in the laboratory frame, however with the extra restriction of the track selection to the current hemisphere <span class="mathjax-tex">$0<\eta ^*<4$</span>. Again the data are given in four <span class="mathjax-tex">$Q^2$</span> ranges, shown in the Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab25">25</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab26">26</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab27">27</a>, and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab28">28</a>, respectively. For these data, the KNO function <span class="mathjax-tex">$\Psi (z)$</span> is also determined. It is reported in the Tables <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab29">29</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab30">30</a>, <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab31">31</a>, and <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab32">32</a>.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-9"><figure><figcaption class="c-article-table__figcaption"><b id="Tab9" data-test="table-caption">Table 9 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$5<Q^2<10~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$|\eta _{_{\mathrm{lab}}}|<1.6$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/9" aria-label="Full size table 9"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-10"><figure><figcaption class="c-article-table__figcaption"><b id="Tab10" data-test="table-caption">Table 10 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$10<Q^2<20~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$|\eta _{_{\mathrm{lab}}}|<1.6$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/10" aria-label="Full size table 10"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-11"><figure><figcaption class="c-article-table__figcaption"><b id="Tab11" data-test="table-caption">Table 11 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$20<Q^2<40~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$|\eta _{_{\mathrm{lab}}}|<1.6$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/11" aria-label="Full size table 11"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-12"><figure><figcaption class="c-article-table__figcaption"><b id="Tab12" data-test="table-caption">Table 12 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$40<Q^2<100~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$|\eta _{_{\mathrm{lab}}}|<1.6$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/12" aria-label="Full size table 12"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-13"><figure><figcaption class="c-article-table__figcaption"><b id="Tab13" data-test="table-caption">Table 13 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$5<Q^2<10~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$-1.2<\eta _{_{\mathrm{lab}}}<0.2$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/13" aria-label="Full size table 13"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-14"><figure><figcaption class="c-article-table__figcaption"><b id="Tab14" data-test="table-caption">Table 14 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$5<Q^2<10~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$-0.5<\eta _{_{\mathrm{lab}}}<0.9$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/14" aria-label="Full size table 14"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-15"><figure><figcaption class="c-article-table__figcaption"><b id="Tab15" data-test="table-caption">Table 15 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$5<Q^2<10~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0.2<\eta _{_{\mathrm{lab}}}<1.6$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/15" aria-label="Full size table 15"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-16"><figure><figcaption class="c-article-table__figcaption"><b id="Tab16" data-test="table-caption">Table 16 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$10<Q^2<20~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$-1.2<\eta _{_{\mathrm{lab}}}<0.2$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/16" aria-label="Full size table 16"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-17"><figure><figcaption class="c-article-table__figcaption"><b id="Tab17" data-test="table-caption">Table 17 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$10<Q^2<20~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$-0.5<\eta _{_{\mathrm{lab}}}<0.9$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/17" aria-label="Full size table 17"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-18"><figure><figcaption class="c-article-table__figcaption"><b id="Tab18" data-test="table-caption">Table 18 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$10<Q^2<20~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0.2<\eta _{_{\mathrm{lab}}}<1.6$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/18" aria-label="Full size table 18"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-19"><figure><figcaption class="c-article-table__figcaption"><b id="Tab19" data-test="table-caption">Table 19 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$20<Q^2<40~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$-1.2<\eta _{_{\mathrm{lab}}}<0.2$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/19" aria-label="Full size table 19"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-20"><figure><figcaption class="c-article-table__figcaption"><b id="Tab20" data-test="table-caption">Table 20 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$20<Q^2<40~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$-0.5<\eta _{_{\mathrm{lab}}}<0.9$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/20" aria-label="Full size table 20"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-21"><figure><figcaption class="c-article-table__figcaption"><b id="Tab21" data-test="table-caption">Table 21 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$20<Q^2<40~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0.2<\eta _{_{\mathrm{lab}}}<1.6$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/21" aria-label="Full size table 21"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-22"><figure><figcaption class="c-article-table__figcaption"><b id="Tab22" data-test="table-caption">Table 22 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$40<Q^2<100~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$-1.2<\eta _{_{\mathrm{lab}}}<0.2$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/22" aria-label="Full size table 22"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-23"><figure><figcaption class="c-article-table__figcaption"><b id="Tab23" data-test="table-caption">Table 23 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$40<Q^2<100~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$-0.5<\eta _{_{\mathrm{lab}}}<0.9$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/23" aria-label="Full size table 23"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-24"><figure><figcaption class="c-article-table__figcaption"><b id="Tab24" data-test="table-caption">Table 24 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$40<Q^2<100~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0.2<\eta _{_{\mathrm{lab}}}<1.6$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/24" aria-label="Full size table 24"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-25"><figure><figcaption class="c-article-table__figcaption"><b id="Tab25" data-test="table-caption">Table 25 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$5<Q^2<10~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0<\eta ^* <4$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/25" aria-label="Full size table 25"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-26"><figure><figcaption class="c-article-table__figcaption"><b id="Tab26" data-test="table-caption">Table 26 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$10<Q^2<20~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0<\eta ^* <4$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/26" aria-label="Full size table 26"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-27"><figure><figcaption class="c-article-table__figcaption"><b id="Tab27" data-test="table-caption">Table 27 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$20<Q^2<40~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0<\eta ^* <4$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/27" aria-label="Full size table 27"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-28"><figure><figcaption class="c-article-table__figcaption"><b id="Tab28" data-test="table-caption">Table 28 Charged particle multiplicity distributions <i>P</i>(<i>N</i>) measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$40<Q^2<100~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0<\eta ^* <4$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/28" aria-label="Full size table 28"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-29"><figure><figcaption class="c-article-table__figcaption"><b id="Tab29" data-test="table-caption">Table 29 KNO function <span class="mathjax-tex">$\Psi (z)$</span> of charged particle multiplicity distributions measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$5<Q^2<10~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0<\eta ^* <4$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/29" aria-label="Full size table 29"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-30"><figure><figcaption class="c-article-table__figcaption"><b id="Tab30" data-test="table-caption">Table 30 KNO function <span class="mathjax-tex">$\Psi (z)$</span> of charged particle multiplicity distributions measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$10<Q^2<20~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0<\eta ^* <4$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/30" aria-label="Full size table 30"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-31"><figure><figcaption class="c-article-table__figcaption"><b id="Tab31" data-test="table-caption">Table 31 KNO function <span class="mathjax-tex">$\Psi (z)$</span> of charged particle multiplicity distributions measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$20<Q^2<40~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0<\eta ^* <4$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/31" aria-label="Full size table 31"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-32"><figure><figcaption class="c-article-table__figcaption"><b id="Tab32" data-test="table-caption">Table 32 KNO function <span class="mathjax-tex">$\Psi (z)$</span> of charged particle multiplicity distributions measured in <i>ep</i> DIS at <span class="mathjax-tex">$\sqrt{s}=319$</span> GeV with in the ranges of photon virtuality <span class="mathjax-tex">$40<Q^2<100~\mathrm {GeV}^2 $</span> and charged particle pseudorapidity range <span class="mathjax-tex">$0<\eta ^* <4$</span>, presented in four ranges of inelasticity <i>y</i> as indicated. The phase-space is further restricted as shown in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-021-08896-1#Tab1">1</a></b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-021-08896-1/tables/32" aria-label="Full size table 32"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div></div></div></section><section data-title="Rights and permissions"><div class="c-article-section" id="rightslink-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="rightslink">Rights and permissions</h2><div class="c-article-section__content" id="rightslink-content"> <p><b>Open Access</b> This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 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