Contributions of QED Diagrams with Vacuum Polarization Insertions to the Lepton Anomaly within the Mellin–Barnes Representation

IF 0.6 4区 物理与天体物理 Q4 PHYSICS, PARTICLES & FIELDS
O. Solovtsova, V. Lashkevich, L. Kaptari
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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.

Abstract Image

带有真空极化插入的 QED 图对梅林-巴恩斯表征中的质子反常的贡献
我们研究了由真空极化图产生的四个闭合轻子环对轻子(L = e,\,\,\mu \)和(\tau \)反常磁矩的辐射QED修正。该方法基于连续应用极化算子的色散关系和大质量粒子传播者的梅林-巴恩斯变换。这使得我们第一次可以从插入了四个相同的轻子环的图(所有这些轻子环都是相同类型的)中获得对轻子反常磁矩的辐射修正的精确分析表达式,而这些轻子环与外部的轻(L)是不同的。结果用质量比来表示 (r = {{{{m}_{\ell }}\mathord{left/ {\vphantom {{{{m}_{\ell }}}{{{m}_{L}}}}}\right.\kern-0em} {{{m}_{L}}}}\)。我们研究了精确分析表达式在 \(r \to 0\) 和 \(r \to \infty \) 时的行为,并与文献中已知的相应渐近展开进行了比较。
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来源期刊
Physics of Particles and Nuclei
Physics of Particles and Nuclei 物理-物理:粒子与场物理
CiteScore
1.00
自引率
0.00%
发文量
116
审稿时长
6-12 weeks
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.
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