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At Leading Logarithmic (LL) accuracy the partonic amplitude is governed by Regge poles in the complex angular momentum plane. Beyond LL, Regge cuts in this plane begin to play an important role. Specifically, the real part of the amplitude at Next-to-Next-to-Leading Logarithmic (NNLL) accuracy presents for the first time both a Regge pole and a Regge cut. Analysing this tower of logarithms and computing it explicitly through four loops we are able to systematically separate between the Regge pole and the Regge cut. The former involves two fundamental parameters, namely the gluon Regge trajectory and impact factors. We explain how to consistently define the impact factors at two loops and the Regge trajectory at three loops. We confirm that the singularities of the trajectory are given by the cusp anomalous dimension. We also show that the Regge-cut contribution at four loop is nonplanar. The high-energy limit of $2\to 2$ scattering amplitudes offers an excellent setting to explore the universal features of gauge theories. At Leading Logarithmic (LL) accuracy the partonic amplitude is governed by Regge poles in the complex angular momentum plane. Beyond LL, Regge cuts in this plane begin to play an important role. Specifically, the real part of the amplitude at Next-to-Next-to-Leading Logarithmic (NNLL) accuracy presents for the first time both a Regge pole and a Regge cut. Analysing this tower of logarithms and computing it explicitly through four loops we are able to systematically separate between the Regge pole and the Regge cut. The former involves two fundamental parameters, namely the gluon Regge trajectory and impact factors. We explain how to consistently define the impact factors at two loops and the Regge trajectory at three loops. We confirm that the singularities of the trajectory are given by the cusp anomalous dimension. We also show that the Regge-cut contribution at four loop is nonplanar. 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At Leading Logarithmic (LL) accuracy the partonic amplitude is governed by Regge poles in the complex angular momentum plane. Beyond LL, Regge cuts in this plane begin to play an important role. Specifically, the real part of the amplitude at Next-to-Next-to-Leading Logarithmic (NNLL) accuracy presents for the first time both a Regge pole and a Regge cut. Analysing this tower of logarithms and computing it explicitly through four loops we are able to systematically separate between the Regge pole and the Regge cut. The former involves two fundamental parameters, namely the gluon Regge trajectory and impact factors. We explain how to consistently define the impact factors at two loops and the Regge trajectory at three loops. We confirm that the singularities of the trajectory are given by the cusp anomalous dimension. We also show that the Regge-cut contribution at four loop is nonplanar." property="og:description" /> <meta content="arXiv" property="og:description" />  <meta content="summary" name="twitter:card" /> <meta content="summary" name="twitter:card" /> <style></style> </head> <body class="CERN32Document32Server search" lang="en">  <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=en&referer=https%3A//cds.cern.ch/record/2861062%3Fln%3Den" 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=en">Search</a></li> <li class="menu-444 "><a class="" title="" href="https://cds.cern.ch/submit?ln=en">Submit</a></li> <li class="menu-426 "><a class="" href="https://cds.cern.ch/help/?ln=en">Help</a></li> <li class="leaf hassubcdsmenu"> <a hreflang="en" class="header" href="https://cds.cern.ch/youraccount/display?ln=en">Personalize</a> <ul class="subsubcdsmenu"><li><a href="https://cds.cern.ch/youralerts/list?ln=en">Your alerts</a></li><li><a href="https://cds.cern.ch/yourbaskets/display?ln=en">Your baskets</a></li><li><a href="https://cds.cern.ch/yourcomments?ln=en">Your comments</a></li><li><a href="https://cds.cern.ch/youralerts/display?ln=en">Your searches</a></li></ul></li> </ul> </div> </div> </div>  <table class="navtrailbox"> <tr> <td class="navtrailboxbody"> <a href="/?ln=en" class="navtrail">Home</a> > High-energy limit of 2->2 scattering amplitudes at NNLL </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/2861062/?ln=en">Information </a></li><li class=""><a href="/record/2861062/files?ln=en">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="2861062"></abbr> <style type="text/css">  </style> <table class="formatRecordTableFullWidth" > <tr> <td class="formatRecordHeader" style="background-image: url('https://cds.cern.ch/img/journals.jpg');" colspan="2">  Article </td> </tr> <script type="text/javascript"> $( document ).ready(function() { $('.showAuthor').on('click', function() { var author = '<p>' + $(this).data('name') + '</p>'; var affiliation = $(this).data('affiliation') + '</br>'; var contribution = $(this).data('contribution') + '</br>'; $.magnificPopup.open({ items: { src: '<div id="ovelary-mathjax" class="overlay-white oc-content overlay-white-500">' + author + affiliation + contribution + '</div>', type: 'inline' }, callbacks: { open: function() { var div = document.getElementById("overlay-mathjax") MathJax.Hub.Queue(["Typeset", MathJax.Hub, div]); }, } }) }) }); </script> <tr><td class="formatRecordLabel"> Report number </td><td style="padding-left:5px;"><a href="http://arxiv.org/abs/arXiv:2207.07441">arXiv:2207.07441</a></td></tr> <tr><td class="formatRecordLabel"> Title </td><td style="padding-left:5px;"><b>High-energy limit of 2->2 scattering amplitudes at NNLL</b></td></tr> <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=Milloy%2C%20Calum&ln=en">Milloy, Calum</a> (Turin U. ; INFN, Turin) ; <a href="https://cds.cern.ch/search?f=author&p=Falcioni%2C%20Giulio&ln=en">Falcioni, Giulio</a> (Edinburgh U. ; U. Edinburgh, Higgs Ctr. Theor. Phys.) ; <a href="https://cds.cern.ch/search?f=author&p=Gardi%2C%20Einan&ln=en">Gardi, Einan</a> (Edinburgh U. ; U. Edinburgh, Higgs Ctr. Theor. Phys.) ; <a href="https://cds.cern.ch/search?f=author&p=Maher%2C%20Niamh&ln=en">Maher, Niamh</a> (Edinburgh U. ; U. Edinburgh, Higgs Ctr. Theor. Phys.) ; <a href="https://cds.cern.ch/search?f=author&p=Vernazza%2C%20Leonardo&ln=en">Vernazza, Leonardo</a> (Turin U. ; INFN, Turin ; CERN)</td></tr> <tr><td class="formatRecordLabel"> Publication </td><td style="padding-left:5px;">2022-10-20</td></tr> <tr><td class="formatRecordLabel"> Imprint </td><td style="padding-left:5px;">2022-07-15</td></tr> <tr><td class="formatRecordLabel"> Number of pages </td><td style="padding-left:5px;">11</td></tr> <tr><td class="formatRecordLabel"> In: </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.22323/1.416.0044"><i>PoS</i> LL2022 (2022) 044</a> </a></td></tr> <tr><td class="formatRecordLabel"> In: </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/record/2824159">16th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory 2022</a>, Ettal, Germany, 25 - 30 Apr 2022, pp.044</td></tr> <tr><td class="formatRecordLabel"> DOI </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.22323/1.416.0044" title="DOI" target="_blank">10.22323/1.416.0044</a> <tr><td class="formatRecordLabel"> Subject category </td><td style="padding-left:5px;">hep-th ; Particle Physics - Theory ; hep-ph ; Particle Physics - Phenomenology</td></tr> <tr><td class="formatRecordLabel"> Abstract </td><td style="padding-left:5px;">The high-energy limit of $2\to 2$ scattering amplitudes offers an excellent setting to explore the universal features of gauge theories. At Leading Logarithmic (LL) accuracy the partonic amplitude is governed by Regge poles in the complex angular momentum plane. Beyond LL, Regge cuts in this plane begin to play an important role. Specifically, the real part of the amplitude at Next-to-Next-to-Leading Logarithmic (NNLL) accuracy presents for the first time both a Regge pole and a Regge cut. Analysing this tower of logarithms and computing it explicitly through four loops we are able to systematically separate between the Regge pole and the Regge cut. The former involves two fundamental parameters, namely the gluon Regge trajectory and impact factors. We explain how to consistently define the impact factors at two loops and the Regge trajectory at three loops. We confirm that the singularities of the trajectory are given by the cusp anomalous dimension. We also show that the Regge-cut contribution at four loop is nonplanar.</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>)<br/>publication: © 2022-2025 The author(s) (License: <a href="https://creativecommons.org/licenses/by-nc-nd/4.0/">CC-BY-NC-ND-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/2861062/plots#0"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2861062/files/MTree.png" title=" A representation of the $2\to 2$ scattering of eq.~(\ref{eq:22Scatter})." width="200px"/></a> <a href="/record/2861062/plots#1"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2861062/files/three_reggeon_tree.png" title=" : A two-loop MR diagram. The explicit result is given in eq.~(\ref{eq:MRSTwoLoop})." width="200px"/></a> <a href="/record/2861062/plots#2"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2861062/files/three_reggeon_one_exchange.png" title=" : A three-loop MR diagram." width="200px"/></a> <a href='/record/2861062/plots'>Show more plots</a></div></div><br /> <br/>Corresponding record in: <a href="http://inspirehep.net/record/2115298">Inspire</a> <small> </small> <br/> <br/><br/><div align="right"><div style="padding-bottom:2px;padding-top:30px;"><span class="moreinfo" style="margin-right:10px;"> <a href="" class="moreinfo">Back to search</a> </span></div></div> <div class="bottom-left-folded"><div class="recordlastmodifiedbox" style="position:relative;margin-left:1px"> Record created 2023-06-07, last modified 2024-10-02</div></div> <div class="bottom-right-folded" style="text-align:right;padding-bottom:2px;"> <span class="moreinfo" style="margin-right:10px;"><a href="/search?ln=en&p=recid%3A2861062&rm=wrd" class="moreinfo">Similar records</a></span></div> </div> </div> </div> <br/> <br /> <div class="detailedrecordminipanel"> <div class="top-left"></div><div class="top-right"></div> <div class="inside"> <div id="detailedrecordminipanelfile" style="width:33%;float:left;text-align:center;margin-top:0"> <div><small class="detailedRecordActions">Fulltext:</small> <br /><em>Publication</em> - <a href="/record/2861062/files/Publication.pdf"><img style="border:none" src="/img/file-icon-text-12x16.gif" alt="Download fulltext"/>PDF</a><br /><em>2207.07441</em> - <a href="/record/2861062/files/2207.07441.pdf"><img style="border:none" src="/img/file-icon-text-12x16.gif" alt="Download fulltext"/>PDF</a><br /></div> </div> <div id="detailedrecordminipanelreview" style="width:30%;float:left;text-align:center"> </div> <div id="detailedrecordminipanelactions" style="width:36%;float:right;text-align:right;"> <ul class="detailedrecordactions"> <li><a href="/yourbaskets/add?ln=en&recid=2861062">Add to personal basket</a></li> <li>Export as <a style="text-decoration:underline;font-weight:normal" href="/record/2861062/export/hx?ln=en">BibTeX</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2861062/export/hm?ln=en">MARC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2861062/export/xm?ln=en">MARCXML</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2861062/export/xd?ln=en">DC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2861062/export/xe?ln=en">EndNote</a>,  <a style="text-decoration:underline;font-weight:normal" href="/record/2861062/export/xn?ln=en">NLM</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2861062/export/xw?ln=en">RefWorks</a> </li> </ul> <div style='padding-left: 13px;'>  <div id="bookmark"></div> <div id="bookmark_sciencewise"></div> <style type="text/css"> #bookmark_sciencewise, #bookmark {float: left;} #bookmark_sciencewise li {padding: 2px; width: 25px;} #bookmark_sciencewise ul, #bookmark ul {list-style-image: none;} </style> <script type="text/javascript" src="/js/jquery.bookmark.min.js"></script> <style type="text/css">@import "/css/jquery.bookmark.css";</style> <script type="text/javascript">// <![CDATA[ $.bookmark.addSite('sciencewise', 'ScienceWise.info', 'https://cds.cern.ch/img/sciencewise.png', 'en', 'bookmark', 'http://sciencewise.info/bookmarks/2207.0744/add'); $('#bookmark_sciencewise').bookmark({sites: ['sciencewise']}); $('#bookmark').bookmark({ sites: ['facebook', 'twitter', 'linkedin', 'google_plusone'], icons: '/img/bookmarks.png', url: 'https://cds.cern.ch/record/2861062', addEmail: true, title: "High-energy limit of 2->2 scattering amplitudes at NNLL", description: "The high-energy limit of $2\\to 2$ scattering amplitudes offers an excellent setting to explore the universal features of gauge theories. At Leading Logarithmic (LL) accuracy the partonic amplitude is governed by Regge poles in the complex angular momentum plane. Beyond LL, Regge cuts in this plane begin to play an important role. Specifically, the real part of the amplitude at Next-to-Next-to-Leading Logarithmic (NNLL) accuracy presents for the first time both a Regge pole and a Regge cut. Analysing this tower of logarithms and computing it explicitly through four loops we are able to systematically separate between the Regge pole and the Regge cut. The former involves two fundamental parameters, namely the gluon Regge trajectory and impact factors. We explain how to consistently define the impact factors at two loops and the Regge trajectory at three loops. We confirm that the singularities of the trajectory are given by the cusp anomalous dimension. We also show that the Regge-cut contribution at four loop is nonplanar." }); // ]]> </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=en">Search</a> :: <a class="footer" href="https://cds.cern.ch/submit?ln=en">Submit</a> :: <a class="footer" href="https://cds.cern.ch/youraccount/display?ln=en">Personalize</a> :: <a class="footer" href="https://cds.cern.ch/help/?ln=en">Help</a> :: <a class="footer" href="https://cern.service-now.com/service-portal?id=privacy_policy&se=CDS-Service" target="_blank">Privacy Notice</a> :: <a class="footer" href="https://repository.cern/content-policy" target="_blank">Content Policy</a> :: <a class="footer" href="https://repository.cern/terms" target="_blank">Terms and Conditions</a> <br /> Powered by <a class="footer" href="http://invenio-software.org/">Invenio</a> <br /> Maintained by <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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