Analytical Calculations of Contributions to the Anomalous Magnetic Moments of Leptons from Vacuum Polarization by Lepton Loops within the Mellin–Barnes Representation
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Abstract—Explicit analytical expressions have been derived for electromagnetic corrections to the anomalous magnetic moments aL of leptons (L = e, μ, and τ) of the tenth order of the radiative corrections from Feynman diagrams with insertions of the polarization operator with four lepton loops, where one is formed by leptons of the same kind as initial the lepton L, and three others are formed by leptons of type \(\ell \ne L\). The studies are based on the consecutive application of dispersion relations for the polarization operator and Mellin–Barnes transform for the propagators of massive particles. The exact formulas of expansion in the limit of low and high values of the ratios of lepton masses r = \({{{{m}_{\ell }}} \mathord{\left/ {\vphantom {{{{m}_{\ell }}} {{{m}_{L}}}}} \right. \kern-0em} {{{m}_{L}}}}\), r → 0 and r → ∞, and compared with the corresponding asymptotic expressions of aL, available in the literature.
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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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