{"title":"Hunting for Direct CP Violation in","authors":"Sheng-Tao Li, Gang Lü","doi":"10.1155/2022/3136459","DOIUrl":null,"url":null,"abstract":"In perturbative QCD approach, based on the first order of isospin symmetry breaking, we study the direct <svg height=\"8.98583pt\" style=\"vertical-align:-0.2324905pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.75334 16.1235 8.98583\" width=\"16.1235pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,8.645,0)\"></path></g></svg> violation in the decay of <span><svg height=\"18.3992pt\" style=\"vertical-align:-3.943601pt\" version=\"1.1\" viewbox=\"-0.0498162 -14.4556 34.598 18.3992\" width=\"34.598pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><rect height=\"0.65243\" width=\"7.84228\" x=\"0\" y=\"-11.1958\"></rect><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-67\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.842,-8.606)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.842,3.784)\"><use xlink:href=\"#g50-116\"></use></g><g transform=\"matrix(.013,0,0,-0.013,16.421,0)\"><use xlink:href=\"#g117-149\"></use></g><g transform=\"matrix(.013,0,0,-0.013,22.196,0)\"><use xlink:href=\"#g117-148\"></use></g></svg><span></span><svg height=\"18.3992pt\" style=\"vertical-align:-3.943601pt\" version=\"1.1\" viewbox=\"38.2581838 -14.4556 66.455 18.3992\" width=\"66.455pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,38.308,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,45.318,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,49.816,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,58.111,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,62.609,0)\"><use xlink:href=\"#g113-76\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,72.426,-5.741)\"><use xlink:href=\"#g50-43\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,77.986,-5.741)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,86.585,0)\"><use xlink:href=\"#g117-149\"></use></g><g transform=\"matrix(.013,0,0,-0.013,92.361,0)\"><use xlink:href=\"#g117-148\"></use></g></svg><span></span><span><svg height=\"18.3992pt\" style=\"vertical-align:-3.943601pt\" version=\"1.1\" viewbox=\"108.4231838 -14.4556 48.181 18.3992\" width=\"48.181pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,108.473,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,116.157,-5.741)\"><use xlink:href=\"#g54-36\"></use></g><g transform=\"matrix(.013,0,0,-0.013,122.236,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,129.92,-5.741)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.013,0,0,-0.013,135.999,0)\"><use xlink:href=\"#g113-76\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,145.816,-5.741)\"><use xlink:href=\"#g50-43\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,151.376,-5.741)\"><use xlink:href=\"#g50-49\"></use></g></svg>.</span></span> An interesting mechanism is applied to enlarge the <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 16.4758 8.8423\" width=\"16.4758pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,8.293,0)\"></path></g></svg> violating asymmetry involving the charge symmetry breaking between <svg height=\"9.39034pt\" style=\"vertical-align:-3.42943pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 7.13289 9.39034\" width=\"7.13289pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-239\"></use></g></svg> and <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 8.42472 6.1673\" width=\"8.42472pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-246\"></use></g></svg>.</span> We find that the <svg height=\"8.98583pt\" style=\"vertical-align:-0.2324905pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.75334 16.1235 8.98583\" width=\"16.1235pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g190-68\"></use></g><g transform=\"matrix(.013,0,0,-0.013,8.645,0)\"><use xlink:href=\"#g190-81\"></use></g></svg> violation is large by the <svg height=\"10.4342pt\" style=\"vertical-align:-3.4294pt\" version=\"1.1\" viewbox=\"-0.0498162 -7.0048 28.9286 10.4342\" width=\"28.9286pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-239\"></use></g><g transform=\"matrix(.013,0,0,-0.013,9.916,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,20.452,0)\"><use xlink:href=\"#g113-246\"></use></g></svg> mixing mechanism when the invariant masses of the <svg height=\"11.0031pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -10.7967 27.6813 11.0031\" width=\"27.6813pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.684,-5.741)\"><use xlink:href=\"#g54-36\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.763,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,21.448,-5.741)\"><use xlink:href=\"#g54-33\"></use></g></svg> pairs are in the vicinity of the <svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 8.42472 6.1673\" width=\"8.42472pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-246\"></use></g></svg> resonance. For the decay process of <span><svg height=\"18.3992pt\" style=\"vertical-align:-3.943601pt\" version=\"1.1\" viewbox=\"-0.0498162 -14.4556 34.598 18.3992\" width=\"34.598pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><rect height=\"0.65243\" width=\"7.84228\" x=\"0\" y=\"-11.1958\"></rect><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-67\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.842,-8.606)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.842,3.784)\"><use xlink:href=\"#g50-116\"></use></g><g transform=\"matrix(.013,0,0,-0.013,16.421,0)\"><use xlink:href=\"#g117-149\"></use></g><g transform=\"matrix(.013,0,0,-0.013,22.196,0)\"><use xlink:href=\"#g117-148\"></use></g></svg><span></span><svg height=\"18.3992pt\" style=\"vertical-align:-3.943601pt\" version=\"1.1\" viewbox=\"38.2581838 -14.4556 66.455 18.3992\" width=\"66.455pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,38.308,0)\"><use xlink:href=\"#g113-239\"></use></g><g transform=\"matrix(.013,0,0,-0.013,45.318,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,49.816,0)\"><use xlink:href=\"#g113-246\"></use></g><g transform=\"matrix(.013,0,0,-0.013,58.111,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,62.609,0)\"><use xlink:href=\"#g113-76\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,72.426,-5.741)\"><use xlink:href=\"#g50-43\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,77.986,-5.741)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,86.585,0)\"><use xlink:href=\"#g117-149\"></use></g><g transform=\"matrix(.013,0,0,-0.013,92.361,0)\"><use xlink:href=\"#g117-148\"></use></g></svg><span></span><span><svg height=\"18.3992pt\" style=\"vertical-align:-3.943601pt\" version=\"1.1\" viewbox=\"108.4231838 -14.4556 48.181 18.3992\" width=\"48.181pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,108.473,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,116.157,-5.741)\"><use xlink:href=\"#g54-36\"></use></g><g transform=\"matrix(.013,0,0,-0.013,122.236,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,129.92,-5.741)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.013,0,0,-0.013,135.999,0)\"><use xlink:href=\"#g113-76\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,145.816,-5.741)\"><use xlink:href=\"#g50-43\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,151.376,-5.741)\"><use xlink:href=\"#g50-49\"></use></g></svg>,</span></span> the maximum <svg height=\"8.98583pt\" style=\"vertical-align:-0.2324905pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.75334 16.1235 8.98583\" width=\"16.1235pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g190-68\"></use></g><g transform=\"matrix(.013,0,0,-0.013,8.645,0)\"><use xlink:href=\"#g190-81\"></use></g></svg> violation can reach <span><svg height=\"8.85534pt\" style=\"vertical-align:-0.4673595pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.38798 45.6528 8.85534\" width=\"45.6528pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g117-33\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.631,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,13.871,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,20.112,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,23.076,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,29.316,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,35.556,0)\"></path></g></svg>.</span> Furthermore, taking <svg height=\"10.4342pt\" style=\"vertical-align:-3.4294pt\" version=\"1.1\" viewbox=\"-0.0498162 -7.0048 28.9286 10.4342\" width=\"28.9286pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-239\"></use></g><g transform=\"matrix(.013,0,0,-0.013,9.916,0)\"><use xlink:href=\"#g117-33\"></use></g><g transform=\"matrix(.013,0,0,-0.013,20.452,0)\"><use xlink:href=\"#g113-246\"></use></g></svg> mixing into account, we calculate the branching ratio for <span><svg height=\"18.3992pt\" style=\"vertical-align:-3.943601pt\" version=\"1.1\" viewbox=\"-0.0498162 -14.4556 34.598 18.3992\" width=\"34.598pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><rect height=\"0.65243\" width=\"7.84228\" x=\"0\" y=\"-11.1958\"></rect><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-67\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.842,-8.606)\"><use xlink:href=\"#g50-49\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.842,3.784)\"><use xlink:href=\"#g50-116\"></use></g><g transform=\"matrix(.013,0,0,-0.013,16.421,0)\"><use xlink:href=\"#g117-149\"></use></g><g transform=\"matrix(.013,0,0,-0.013,22.196,0)\"><use xlink:href=\"#g117-148\"></use></g></svg><span></span><span><svg height=\"18.3992pt\" style=\"vertical-align:-3.943601pt\" version=\"1.1\" viewbox=\"38.2581838 -14.4556 44.866 18.3992\" width=\"44.866pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,38.308,0)\"><use xlink:href=\"#g113-239\"></use></g><g transform=\"matrix(.013,0,0,-0.013,45.318,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,49.816,0)\"><use xlink:href=\"#g113-246\"></use></g><g transform=\"matrix(.013,0,0,-0.013,58.111,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,62.609,0)\"><use xlink:href=\"#g113-76\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,72.426,-5.741)\"><use xlink:href=\"#g50-43\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,77.986,-5.741)\"><use xlink:href=\"#g50-49\"></use></g></svg>.</span></span> We also discuss the possibility of observing the predicted <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 16.4758 8.8423\" width=\"16.4758pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-68\"></use></g><g transform=\"matrix(.013,0,0,-0.013,8.293,0)\"><use xlink:href=\"#g113-81\"></use></g></svg> violation asymmetry at the LHC.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":"290 6","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in High Energy Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1155/2022/3136459","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
Abstract
In perturbative QCD approach, based on the first order of isospin symmetry breaking, we study the direct violation in the decay of . An interesting mechanism is applied to enlarge the violating asymmetry involving the charge symmetry breaking between and . We find that the violation is large by the mixing mechanism when the invariant masses of the pairs are in the vicinity of the resonance. For the decay process of , the maximum violation can reach . Furthermore, taking mixing into account, we calculate the branching ratio for . We also discuss the possibility of observing the predicted violation asymmetry at the LHC.
期刊介绍：
Advances in High Energy Physics publishes the results of theoretical and experimental research on the nature of, and interaction between, energy and matter. Considering both original research and focussed review articles, the journal welcomes submissions from small research groups and large consortia alike.
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