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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">     <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en" xmlns:og="http://ogp.me/ns#" xmlns:fb="http://ogp.me/ns/fb#"> <head> <title>IR side of positivity bounds - CERN Document Server</title> <link href='https://framework.web.cern.ch/framework/2.0/fonts/PTSansWeb/PTSansWeb.css' rel='stylesheet' type='text/css' /> <link rel="stylesheet" href="https://cds.cern.ch/img/invenio.css?v=20141127" type="text/css" /> <link rel="stylesheet" href="https://cds.cern.ch/img/cern_theme/css/cern_theme.css?v=20141127" type="text/css" /> <link rel="stylesheet"href="/css/font-awesome.min.css"> <meta http-equiv="X-UA-Compatible" content="IE=Edge"/> <link rel="stylesheet" href="https://cds.cern.ch/img/cern_toolbar/css/toolbar.css" type="text/css" />    <link rel="canonical" href="https://cds.cern.ch/record/2798735" /> <link rel="alternate" hreflang="el" href="https://cds.cern.ch/record/2798735?ln=el" /> <link rel="alternate" hreflang="fr" href="https://cds.cern.ch/record/2798735?ln=fr" /> <link rel="alternate" hreflang="bg" href="https://cds.cern.ch/record/2798735?ln=bg" /> <link rel="alternate" hreflang="zh-TW" href="https://cds.cern.ch/record/2798735?ln=zh_TW" /> <link rel="alternate" hreflang="pt" href="https://cds.cern.ch/record/2798735?ln=pt" /> <link rel="alternate" hreflang="no" href="https://cds.cern.ch/record/2798735?ln=no" /> <link rel="alternate" hreflang="hr" href="https://cds.cern.ch/record/2798735?ln=hr" /> <link rel="alternate" hreflang="ca" href="https://cds.cern.ch/record/2798735?ln=ca" /> <link rel="alternate" hreflang="de" href="https://cds.cern.ch/record/2798735?ln=de" /> <link rel="alternate" hreflang="it" href="https://cds.cern.ch/record/2798735?ln=it" /> <link rel="alternate" hreflang="zh-CN" href="https://cds.cern.ch/record/2798735?ln=zh_CN" /> <link rel="alternate" hreflang="sv" href="https://cds.cern.ch/record/2798735?ln=sv" /> <link rel="alternate" hreflang="sk" href="https://cds.cern.ch/record/2798735?ln=sk" /> <link rel="alternate" hreflang="en" href="https://cds.cern.ch/record/2798735?ln=en" /> <link rel="alternate" hreflang="pl" href="https://cds.cern.ch/record/2798735?ln=pl" /> <link rel="alternate" hreflang="ru" href="https://cds.cern.ch/record/2798735?ln=ru" /> <link rel="alternate" hreflang="ka" href="https://cds.cern.ch/record/2798735?ln=ka" /> <link rel="alternate" hreflang="ja" href="https://cds.cern.ch/record/2798735?ln=ja" /> <link rel="alternate" hreflang="es" href="https://cds.cern.ch/record/2798735?ln=es" /> <link rel="alternate" type="application/rss+xml" title="CERN Document Server RSS" href="/rss?ln=en" /> <link rel="search" type="application/opensearchdescription+xml" href="https://cds.cern.ch/opensearchdescription" title="CERN Document Server" /> <link rel="unapi-server" type="application/xml" title="unAPI" href="https://cds.cern.ch/unapi" /> <link rel="apple-touch-icon" href="/apple-touch-icon.png"/> <link rel="apple-touch-icon-precomposed" href="/apple-touch-icon-precomposed.png"/> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <meta http-equiv="Content-Language" content="en" /> <meta name="description" content="We show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally we show that the singularity do not affect the bounds based on smearing in impact parameter. We show how calculable IR loop effects impact positivity bounds in effective field theories with causal and unitary UV completions. We identify infrared singularities that appear in dispersion relations at <math display="inline"><mrow><mo stretchy="false">|</mo><mi>t</mi><mo stretchy="false">|</mo><mo>≲</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in <math display="inline"><mi>s</mi></math> even for large negative <math display="inline"><mi>t</mi></math>, i.e., <math display="inline"><mo stretchy="false">|</mo><mi>t</mi><mo stretchy="false">|</mo><mo>≫</mo><msup><mi>m</mi><mn>2</mn></msup></math>, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally, we show that the singularity do not affect the bounds based on smearing in the impact parameter. Bellazzini, Brando; Riembau, Marc; Riva, Francesco" /> <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="APS : IR side of positivity bounds" name="citation_title" /> <meta content="Bellazzini, Brando" name="citation_author" /> <meta content="Riembau, Marc" name="citation_author" /> <meta content="Riva, Francesco" name="citation_author" /> <meta content="10.1103/PhysRevD.106.105008" name="citation_doi" /> <meta content="Phys. 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We identify infrared singularities that appear in dispersion relations at |t|≲m2. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in s even for large negative t, i.e., |t|≫m2, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally, we show that the singularity do not affect the bounds based on smearing in the impact parameter." property="og:description" /> <meta content="We show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally we show that the singularity do not affect the bounds based on smearing in impact parameter." property="og:description" />  <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/2798735" 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> > IR side of positivity bounds </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/2798735/?ln=en">Information </a></li><li class=""><a href="/record/2798735/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="2798735"></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:2112.12561">arXiv:2112.12561</a></td></tr> <tr><td class="formatRecordLabel"> Title </td><td style="padding-left:5px;"><b>IR side of positivity bounds</b></td></tr> <tr><td class="formatRecordLabel" style="vertical-align:top;">Related title</td><td style="padding-left:5px; ">The IR-Side of Positivity Bounds<br/></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=Bellazzini%2C%20Brando&ln=en">Bellazzini, Brando</a> (IPhT, Saclay ; EPFL, Lausanne, LPTP ; CERN) ; <a href="https://cds.cern.ch/search?f=author&p=Riembau%2C%20Marc&ln=en">Riembau, Marc</a> (EPFL, Lausanne, LPTP) ; <a href="https://cds.cern.ch/search?f=author&p=Riva%2C%20Francesco&ln=en">Riva, Francesco</a> (Geneva U., Dept. Theor. Phys.)</td></tr> <tr><td class="formatRecordLabel"> Publication </td><td style="padding-left:5px;">2022-11-10</td></tr> <tr><td class="formatRecordLabel"> Imprint </td><td style="padding-left:5px;">2021-12-23</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/10.1103/PhysRevD.106.105008"><i>Phys. Rev. D</i> 106 (2022) 105008</a> </a></td></tr> <tr><td class="formatRecordLabel"> DOI </td><td style="padding-left:5px;"><a href="http://dx.doi.org/10.1103/PhysRevD.106.105008" title="DOI" target="_blank">10.1103/PhysRevD.106.105008</a> <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 show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally we show that the singularity do not affect the bounds based on smearing in impact parameter.</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 authors (License: <a href="http://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a>), sponsored by <a href="http://scoap3.org">SCOAP³</a></td></tr> </table> <br /><div style="max-width:1024px;margin:auto"><div style="overflow-x:auto;display:inline;width:100%;"><a href="/record/2798735/plots#0"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2798735/files/tab.png" title=" \it In green, a schematic representation of the arcs and their derivatives (both at $t=0$) needed to reconstruct all Wilson coefficients, \eq{minimalarcs}. Red cells correspond instead to arc derivatives that are singular at $t=0$, according to \eq{singha}. " width="200px"/></a> <a href="/record/2798735/plots#1"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2798735/files/plot2d.png" title=" \it Bounds on ratio $g_{3,1}\bs/g_{2,0}$ as a function of the particle mass $m$, for fixed $\beta_4\bs^2=0.1$. Lower lying curves correspond to bounds involving more moments in the UV: in orange only Cauchy-Schwartz \eq{boundwithloopmoments}, in red moments ut to $\mu_2^2$ as in \eq{mu22bounds}, and in blue moments up to $\mu_4^4$ (numerical). All curves diverge as $m\rightarrow 0$. " width="200px"/></a> <a href="/record/2798735/plots#2"><img style="vertical-align:middle;" src="https://cds.cern.ch/record/2798735/files/P1.png" title=" \it Bounds on arc $a_0(\bs,t)$ as a function of $t$. In gray the region excluded by UV positivity bounds (in black the region excluded by the simple approximation on the extremes of \eq{Plbound}). Orange dashed lines illustrate IR arcs calculated with the approximated EFT ($a_0(\bs,t)$ in \eq{arcsexplicit} truncated at $O(t)$), for extremal values of~$g_{3,1}$." width="200px"/></a> <a href='/record/2798735/plots'>Show more plots</a></div></div><br /> <br/>Corresponding record in: <a href="http://inspirehep.net/record/1996655">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 2021-12-25, 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%3A2798735&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>2112.12561</em> - <a href="/record/2798735/files/2112.12561.pdf"><img style="border:none" src="/img/file-icon-text-12x16.gif" alt="Download fulltext"/>PDF</a><br /><em>Publication</em> - <a href="/record/2798735/files/Publication.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=2798735">Add to personal basket</a></li> <li>Export as <a style="text-decoration:underline;font-weight:normal" href="/record/2798735/export/hx?ln=en">BibTeX</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2798735/export/hm?ln=en">MARC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2798735/export/xm?ln=en">MARCXML</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2798735/export/xd?ln=en">DC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2798735/export/xe?ln=en">EndNote</a>,  <a style="text-decoration:underline;font-weight:normal" href="/record/2798735/export/xn?ln=en">NLM</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2798735/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/2112.1256/add'); $('#bookmark_sciencewise').bookmark({sites: ['sciencewise']}); $('#bookmark').bookmark({ sites: ['facebook', 'twitter', 'linkedin', 'google_plusone'], icons: '/img/bookmarks.png', url: 'https://cds.cern.ch/record/2798735', addEmail: true, title: "IR side of positivity bounds", description: "We show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally we show that the singularity do not affect the bounds based on smearing in impact parameter." }); // ]]> </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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