Full Unitarity and the Moments of Scattering Amplitudes

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We introduce the semiarcs, calculable quantities in the EFT dispersively related to both real and imaginary parts of the UV amplitude for a fixed number of subtractions. It is observed that large hierarchies between consecutive moments are forbidden by unitarity. Bounds from full unitarity compete with the ones stemming from convexity, and become more important in EFTs where the loop expansion is more important than the derivative expansion. Riembau, Marc" /> <meta name="keywords" content="CERN Document Server, WebSearch, CERN Document Server" /> <script type="text/javascript" src="https://cds.cern.ch/js/jquery.min.js"></script>  <link rel="stylesheet" href="https://cds.cern.ch/img/webnews.css" type="text/css" />  <script type="text/javascript" src="https://cds.cern.ch/js/webnews.js?v=20131009"></script> <meta property="fb:app_id" content="137353533001720"/> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$']], processEscapes: true}, showProcessingMessages: false, messageStyle: "none" }); </script> <script src="/MathJax/MathJax.js?config=TeX-AMS_CHTML" type="text/javascript"> </script>  <meta content="arXiv : Full Unitarity and the Moments of Scattering Amplitudes" name="citation_title" /> <meta content="Riembau, Marc" name="citation_author" /> <meta content="2022/12/28" name="citation_publication_date" /> <meta name="citation_online_date" content="2023/01/03"> <meta content="CERN-TH-2022-210" name="citation_technical_report_number" /> <meta content="arXiv:2212.14056" name="citation_technical_report_number" /> <meta name="citation_pdf_url" content="https://cds.cern.ch/record/2845377/files/2212.14056.pdf" />  <meta content="Full Unitarity and the Moments of Scattering Amplitudes" property="og:title" /> <meta content="arXiv" property="og:title" /> <meta content="website" property="og:type" /> <meta content="https://cds.cern.ch/record/2845377" property="og:url" /> <meta name="twitter:image" content="https://cds.cern.ch/record/2845377/files/LRcontour_v2.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2845377/files/LRcontour_v2.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2845377/files/LRcontour_v2.png" /> <meta content="CERN Document Server" property="og:site_name" /> <meta content="We study the impact of full unitarity on the moment structure of forward scattering amplitudes. We introduce the semiarcs, calculable quantities in the EFT dispersively related to both real and imaginary parts of the UV amplitude for a fixed number of subtractions. It is observed that large hierarchies between consecutive moments are forbidden by unitarity. Bounds from full unitarity compete with the ones stemming from convexity, and become more important in EFTs where the loop expansion is more important than the derivative expansion." property="og:description" /> <meta content="arXiv" property="og:description" />  <meta content="summary" name="twitter:card" /> <style></style> </head> <body class="CERN32Document32Server search" lang="no">  <div id="cern-toolbar"> <h1><a href="http://cern.ch" title="CERN">CERN <span>Accelerating science</span></a></h1> <ul> <li class="cern-accountlinks"><a class="cern-account" href="https://cds.cern.ch/youraccount/login?ln=no&referer=https%3A//cds.cern.ch/record/2845377%3Fln%3Dno" title="Sign in to your CERN account">Sign in</a></li> <li><a class="cern-directory" href="http://cern.ch/directory" title="Search CERN resources and browse the directory">Directory</a></li> </ul> </div>   <div role="banner" class="clearfix" id="header"> <div class="header-inner inner"> <hgroup class="clearfix"> <h2 id="site-name"> <a rel="home" title="Home" href="/"><span>CERN Document Server</span></a> </h2> <h3 id="site-slogan">Access articles, reports and multimedia content in HEP</h3> </hgroup> <div role="navigation" id="main-navigation" class="cdsmenu"> <h2 class="element-invisible">Main menu</h2><ul class="links inline clearfix"> <li class="menu-386 first active-trail"><a class="active-trail" href="https://cds.cern.ch/?ln=no">Søk</a></li> <li class="menu-444 "><a class="" title="" href="https://cds.cern.ch/submit?ln=no">Send inn</a></li> <li class="menu-426 "><a class="" href="https://cds.cern.ch/help/?ln=no">Hjelp</a></li> <li class="leaf hassubcdsmenu"> <a hreflang="en" class="header" href="https://cds.cern.ch/youraccount/display?ln=no">Brukerinnstillinger</a> <ul class="subsubcdsmenu"><li><a href="https://cds.cern.ch/youralerts/list?ln=no">Your alerts</a></li><li><a href="https://cds.cern.ch/yourbaskets/display?ln=no">Your baskets</a></li><li><a href="https://cds.cern.ch/yourcomments?ln=no">Your comments</a></li><li><a href="https://cds.cern.ch/youralerts/display?ln=no">Your searches</a></li></ul></li> </ul> </div> </div> </div>  <table class="navtrailbox"> <tr> <td class="navtrailboxbody"> <a href="/?ln=no" class="navtrail">Hovedsiden</a> > Full Unitarity and the Moments of Scattering Amplitudes </td> </tr> </table> </div> <div class="pagebody"><div class="pagebodystripemiddle"> <div class="detailedrecordbox"> <div class="detailedrecordtabs"> <div> <ul class="detailedrecordtabs"><li class="on first"><a href="/record/2845377/?ln=no">Informasjon </a></li><li class=""><a href="/record/2845377/files?ln=no">Files </a></li></ul> <div id="tabsSpacer" style="clear:both;height:0px"> </div></div> </div> <div class="detailedrecordboxcontent"> <div class="top-left-folded"></div> <div class="top-right-folded"></div> <div class="inside">  <abbr class="unapi-id" title="2845377"></abbr>  <link href="/img/download_and_embed_buttons.css" rel="stylesheet" type="text/css" /> <style type="text/css">  .video_talk_wrapper{ max-width: 640px; min-height: 360px; } </style> <table class="formatRecordTableFullWidth"> <tr> <td class="formatRecordHeader" style="background-image: url('/img/journals.jpg');" colspan="2">  Preprint </td> </tr> <tr><td class="formatRecordLabel"> Report number </td><td style="padding-left:5px;"><a href="http://arxiv.org/abs/arXiv:2212.14056">arXiv:2212.14056</a> ; CERN-TH-2022-210</td></tr> <tr><td class="formatRecordLabel"> Title </td><td style="padding-left:5px;"><b>Full Unitarity and the Moments of Scattering Amplitudes</b></td></tr> <style> .video_control_container, #video_controlbutton { display: none; }#video_detailbox_download {display: none;}#video_detailbox_embed {display: none;}</style> <div class="video_control_container"> <div style="box-sizing: inherit;position: relative;min-height: 1em;margin: 1em 0;background: #f8f8f9;padding: 1em 1.5em;line-height: 1.4285em;transition: opacity .1s ease,color .1s ease,background .1s ease,box-shadow .1s ease,-webkit-box-shadow .1s ease;border-radius: .28571429rem;font-size: 1.1em;margin-top: 0;margin-bottom: 6px;background-color: #f8ffff;color: #276f86;box-shadow: 0 0 0 1px #a9d5de inset,0 0 0 0 transparent;"> <i class="fa fa-info"></i><span style="padding-left: 9px;">If you experience any problem watching the video, click the download button below</span> </div> <a id="video_controlbutton_download" rel="download_button" class="video_controlbutton" href="#">Download</a> <a id="video_controlbutton_embed" class="video_controlbutton" href="#">Embed</a> </div> <div id="video_detailbox_download" style="margin:10px"> </div> <div id="video_detailbox_embed" style="margin:10px"> </div> <tr><td class="formatRecordLabel"> <span style="white-space:nowrap;">Author(s)</span> </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/search?f=author&p=Riembau%2C%20Marc&ln=no">Riembau, Marc</a> (CERN)</td></tr>  <script type="text/javascript"> /* * Changes the Imprint title to Date - Duration as requested by RQF0820114 * This is a hack not to touch the general imprint format element */ $(document).ready(function() { var collections = 'PREPRINT'; if (collections.indexOf('E-LEARNING') > -1) { $('.cern-imprint-label').text('Date - Duration'); } }) </script> <tr><td class="formatRecordLabel cern-imprint-label"> Imprint </td><td style="padding-left:5px;">2022-12-28</td></tr> <tr><td class="formatRecordLabel"> Number of pages </td><td style="padding-left:5px;">8</td></tr>  <tr><td class="formatRecordLabel"> Note </td><td style="padding-left:5px;">8 pages, 1 figure</td></tr> <tr><td class="formatRecordLabel"> Subject category </td><td style="padding-left:5px;">hep-th ; Particle Physics - Theory</td></tr> <tr><td class="formatRecordLabel"> Abstract </td><td style="padding-left:5px;">We study the impact of full unitarity on the moment structure of forward scattering amplitudes. We introduce the semiarcs, calculable quantities in the EFT dispersively related to both real and imaginary parts of the UV amplitude for a fixed number of subtractions. It is observed that large hierarchies between consecutive moments are forbidden by unitarity. Bounds from full unitarity compete with the ones stemming from convexity, and become more important in EFTs where the loop expansion is more important than the derivative expansion.</td></tr> <tr><td class="formatRecordLabel"> Other source </td><td style="padding-left:5px;"><a href="http://inspirehep.net/record/2619271">Inspire</a></td></tr> <tr><td class="formatRecordLabel"> Copyright/License </td><td style="padding-left:5px;">preprint: (License: <a href="http://creativecommons.org/licenses/by/4.0/">CC-BY-4.0</a>)</td></tr> </table> <br /><div style="max-width:1024px;margin:auto"><div style="overflow-x:auto;display:inline;width:100%;"><a href="/record/2845377/plots#0"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2845377/files/LRcontour_v2.png" title=" Contours in the complex $s$-plane that define the \textit{semiarcs}. The right contour leads to the relation in Eq.~\ref{eq:rightcontour}, while the left one leads to Eq.~\ref{eq:leftcontour}." width="200px"/></a> </div></div><br /> <br/><div><div style="clear: both;"> </div></div> <script type="text/javascript"> // Initially hide: $(".longCaption").hide(); // Allow to toggle visibility: $(".toggleLongCaption").toggle(function(){ $(this).siblings(".longCaption").show('fast'); var thisElem = $(this); thisElem.text(thisElem.text() === "mer" ? "mindre" : "mer"); },function(){ $(this).siblings(".longCaption").hide('fast'); var thisElem = $(this); thisElem.text(thisElem.text() === "mer" ? 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We introduce the semiarcs, calculable quantities in the EFT dispersively related to both real and imaginary parts of the UV amplitude for a fixed number of subtractions. It is observed that large hierarchies between consecutive moments are forbidden by unitarity. Bounds from full unitarity compete with the ones stemming from convexity, and become more important in EFTs where the loop expansion is more important than the derivative expansion." }); // ]]> </script>  </div> </div> <div style="clear:both;margin-bottom: 0;"></div> </div> <div class="bottom-left"></div><div class="bottom-right"></div> </div> </div></div> <footer id="footer" class="pagefooter clearfix">  <div class="pagefooterstripeleft"> CERN Document Server :: <a class="footer" href="https://cds.cern.ch/?ln=no">Søk</a> :: <a class="footer" href="https://cds.cern.ch/submit?ln=no">Send inn</a> :: <a class="footer" href="https://cds.cern.ch/youraccount/display?ln=no">Brukerinnstillinger</a> :: <a class="footer" href="https://cds.cern.ch/help/?ln=no">Hjelp</a> :: <a class="footer" href="https://cern.service-now.com/service-portal?id=privacy_policy&se=CDS-Service" target="_blank">Privacy Notice</a> <br /> Powered by <a class="footer" href="http://invenio-software.org/">Invenio</a> <br /> Vedlikeholdt av <a class="footer" href="https://cern.service-now.com/service-portal?id=service_element&name=CDS-Service">CDS Service</a> - Need help? 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