Contributions to the anomalous magnetic moment of leptons from vacuum polarization described by mixed diagrams in the framework of the Mellin – Barnes method
https://doi.org/10.29235/1561-2430-2025-61-2-118-127
Abstract
The explicit form of the third-order electromagnetic corrections in the fine structure constant α3 to the anomalous magnetic moment of lepton aL (L = e,μ,τ) from the contribution of the sixth – order vertex graph with insertion of fourth – order vacuum polarization. The approach is based on the consistent application of dispersion relations for the polarization operator and the Mellin – Barnes transform for massive particle propagators. Explicit analytical expressions for the corrections to aL are obtained at r = mℓ/mL > 1. Asymptotic expansions are found in the limit of both small and large values of the lepton mass ratio (r = mℓ/mL), r ^ 1 and r → ∞. The expansions obtained are compared with the corresponding expressions given in the literature.
Keywords
anomalous magnetic moments of the leptons,
higher-order quantum electromagnetic corrections,
Mellin – Barnes transform
Supporting agencies: This work was supported by the In ternational Program of Cooperation between the Repub lic of Belarus and JINR. The author expresses his gratitude to O. P. Solovtsova and L. P. Kaptari for the discussion and valuable comments.
About the Author
V. I. Lashkevich
Sukhoi State Technical University of Gomel
Belarus
Belarus
Vasil I. Lashkevich – Ph. D. (Physics and Mathematics), Associate Professor of the Higher Mathematics Department
Oktyabrya Ave., 48, 246746, Gomel
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