Work

Some Mathematical Methods Relevant to Analytical Calculations of Anomalous Magnetic Moments of Leptons

Year: 2026

Type: preprint

Abstract: The mathematical methods and approaches used in our analytical calculations of electromagnetic corrections to the leptonic anomaly $a_L$, which is caused by a special class of Feynman diagrams with insertions of the vacuum polarization operator, are presented and examined in detail. The developed methods are essentially based on the Mellin--Barnes transform for the propagators of massive particles with subsequent application of the PSLQ algorithm to solve the emerging functional equations. Functional equations are also used in the procedure of analytic continuation of a particular type of hypergeometric functions to the entire complex plane of their parameters. It is shown that these approaches make it possible to obtain explicit expressions for radiative corrections of rather high orders.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.03152

Authors: Kaptari, L. P., Lashkevich, V. I., Solovtsova, O. P.

Institutions: Joint Institute for Nuclear Research, Sukhoi State Technical University of Gomel

Language: English

Topic: Particle physics theoretical and experimental studies

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220393825

Cites: 1

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Related to: 10