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Bibliographic Details
Main Authors: Solovtsova, O. P., Lashkevich, V. I., Kaptari, L. P.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2406.16645
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Table of Contents:
  • Analytical expressions for the tenth order electromagnetic corrections to the lepton ($L=e, ~μ$ and $τ$) anomaly $a_L$ are derived explicitly for a class of Feynman diagrams with insertions of the vacuum polarization operator consisting of four closed lepton loops. We consider a particular case when one loop is formed by the lepton $L$ of the same kind as the one under consideration, the other three loops being formed by leptons $\ell\neq L$. 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. The result is expressed in terms of the mass ratio $r=m_\ell/m_L$. We investigate the behaviour of the exact analytical expressions as $r\to 0$ and $r\to \infty$ and compare them with the corresponding asymptotic expansions known in the literature.