{"title":"Contributions of QED Diagrams with Vacuum Polarization Insertions to the Lepton Anomaly within the Mellin–Barnes Representation","authors":"O. Solovtsova, V. Lashkevich, L. Kaptari","doi":"10.1134/S1063779624700072","DOIUrl":null,"url":null,"abstract":"<p>We investigate the radiative QED corrections to the lepton (<span>\\(L = e,\\,\\, \\mu \\)</span>, and <span>\\(\\tau \\)</span>) anomalous magnetic moment arising from vacuum polarization diagrams by four closed lepton loops. The method is based on the consecutive application of dispersion relations for the polarization operator and the Mellin–Barnes transform for the propagators of massive particles. This allows one to obtain, for the first time, exact analytical expressions for the radiative corrections to the anomalous magnetic moments of leptons from diagrams with insertions of four identical lepton loops all of the same type <span>\\(\\ell \\)</span> different from the external one, <span>\\(L\\)</span>. The result is expressed in terms of the mass ratio <span>\\(r = {{{{m}_{\\ell }}} \\mathord{\\left/ {\\vphantom {{{{m}_{\\ell }}} {{{m}_{L}}}}} \\right. \\kern-0em} {{{m}_{L}}}}\\)</span>. We investigate the behaviour of the exact analytical expressions at <span>\\(r \\to 0\\)</span> and <span>\\(r \\to \\infty \\)</span> and compare with the corresponding asymptotic expansions known in the literature.</p>","PeriodicalId":729,"journal":{"name":"Physics of Particles and Nuclei","volume":"55 4","pages":"725 - 730"},"PeriodicalIF":0.6000,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of Particles and Nuclei","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1063779624700072","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the radiative QED corrections to the lepton (\(L = e,\,\, \mu \), and \(\tau \)) anomalous magnetic moment arising from vacuum polarization diagrams by four closed lepton loops. The method is based on the consecutive application of dispersion relations for the polarization operator and the Mellin–Barnes transform for the propagators of massive particles. This allows one to obtain, for the first time, exact analytical expressions for the radiative corrections to the anomalous magnetic moments of leptons from diagrams with insertions of four identical lepton loops all of the same type \(\ell \) different from the external one, \(L\). The result is expressed in terms of the mass ratio \(r = {{{{m}_{\ell }}} \mathord{\left/ {\vphantom {{{{m}_{\ell }}} {{{m}_{L}}}}} \right. \kern-0em} {{{m}_{L}}}}\). We investigate the behaviour of the exact analytical expressions at \(r \to 0\) and \(r \to \infty \) and compare with the corresponding asymptotic expansions known in the literature.
期刊介绍:
The journal Fizika Elementarnykh Chastits i Atomnogo Yadr of the Joint Institute for Nuclear Research (JINR, Dubna) was founded by Academician N.N. Bogolyubov in August 1969. The Editors-in-chief of the journal were Academician N.N. Bogolyubov (1970–1992) and Academician A.M. Baldin (1992–2001). Its English translation, Physics of Particles and Nuclei, appears simultaneously with the original Russian-language edition. Published by leading physicists from the JINR member states, as well as by scientists from other countries, review articles in this journal examine problems of elementary particle physics, nuclear physics, condensed matter physics, experimental data processing, accelerators and related instrumentation ecology and radiology.