Radiative QED corrections to the lepton anomaly from four-loop vacuum polarization insertions with three identical leptons

2024/06/24 by Solovtsova, O. P., Lashkevich, V. I., Kaptari, L. P.
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2406.16645

Abstract

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 ℓ≠ 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_ℓ/m_L. We investigate the behaviour of the exact analytical expressions as r→ 0 and r→ ∞ and compare them with the corresponding asymptotic expansions known in the literature.

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