{"title":"Gauge Theory Bootstrap","authors":"Yifei He, Martin Kruczenski","doi":"10.1103/physrevlett.133.191601","DOIUrl":null,"url":null,"abstract":"We propose the gauge theory bootstrap, a method to compute the pion <mjx-container ctxtmenu_counter=\"9\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper S\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi></mjx-math></mjx-container> matrix that describes the low-energy physics of the strong interaction and other similar gauge theories. The phase shifts of the <mjx-container ctxtmenu_counter=\"10\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"0 2 1\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper S Baseline 0\" data-semantic-structure=\"(3 0 2 1)\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"3\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>0</mjx-c></mjx-mn></mjx-math></mjx-container>, <mjx-container ctxtmenu_counter=\"11\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"0 2 1\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper P Baseline 1\" data-semantic-structure=\"(3 0 2 1)\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑃</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"3\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>1</mjx-c></mjx-mn></mjx-math></mjx-container>, and <mjx-container ctxtmenu_counter=\"12\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"0 2 1\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper S Baseline 2\" data-semantic-structure=\"(3 0 2 1)\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"3\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn></mjx-math></mjx-container> waves obtained are in good agreement with experimental results. The only numerical inputs are the quark mass <mjx-container ctxtmenu_counter=\"13\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"m Subscript q\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑚</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c>𝑞</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math></mjx-container>, the QCD scale <mjx-container ctxtmenu_counter=\"14\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"normal upper Lamda Subscript upper Q upper C upper D\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>Λ</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" size=\"ss\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">Q</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">C</mjx-c><mjx-c style=\"padding-top: 0.669em;\">D</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math></mjx-container>, the pion mass <mjx-container ctxtmenu_counter=\"15\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"m Subscript pi\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑚</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c>𝜋</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math></mjx-container>, and the pion decay constant <mjx-container ctxtmenu_counter=\"16\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"f Subscript pi\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑓</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c>𝜋</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math></mjx-container> without any other experimental data. We make use of the form-factor bootstrap recently proposed by Karateev, Kuhn, and Penedones together with a finite energy version of the Shifman-Veinshtein-Zakharov sum rules.","PeriodicalId":20069,"journal":{"name":"Physical review letters","volume":null,"pages":null},"PeriodicalIF":8.1000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review letters","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevlett.133.191601","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We propose the gauge theory bootstrap, a method to compute the pion 𝑆 matrix that describes the low-energy physics of the strong interaction and other similar gauge theories. The phase shifts of the 𝑆0, 𝑃1, and 𝑆2 waves obtained are in good agreement with experimental results. The only numerical inputs are the quark mass 𝑚𝑞, the QCD scale ΛQCD, the pion mass 𝑚𝜋, and the pion decay constant 𝑓𝜋 without any other experimental data. We make use of the form-factor bootstrap recently proposed by Karateev, Kuhn, and Penedones together with a finite energy version of the Shifman-Veinshtein-Zakharov sum rules.
期刊介绍：
Physical review letters(PRL)covers the full range of applied, fundamental, and interdisciplinary physics research topics:
General physics, including statistical and quantum mechanics and quantum information
Gravitation, astrophysics, and cosmology
Elementary particles and fields
Nuclear physics
Atomic, molecular, and optical physics
Nonlinear dynamics, fluid dynamics, and classical optics
Plasma and beam physics
Condensed matter and materials physics
Polymers, soft matter, biological, climate and interdisciplinary physics, including networks
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
