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A Method of Fast Calculaion of Lepton Magnetic Moments in Quantum Electrodynamics

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Abstract

A new method of divergence subtraction in Feynman parametric integrals is presented. The method is suitable for calculating the lepton anomalous magnetic moments (AMM) in quantum electrodynamics (QED). The subtraction procedure eliminates all divergences before integration and leads to a finite Feynman parametric integral for each individual Feynman diagram. It is based on a forest formula with linear operators applied to the Feynman amplitudes of ultraviolet-divergent subdiagrams. The formula is similar to Bogoliubov–Parasiuk–Hepp–Zimmermann summation; the difference is only in the linear operators used and in the way of combining them. The subtraction is equivalent to the on-shell renormalization from the beginning: for obtaining the final result we should only sum up the contributions of all Feynman diagrams after subtraction. The developed method is an improvement of the method presented by the author in 2016. The modification is specifically designed for calculating the contributions dependent on the relations of particle masses. In comparison with the old version, the new subtraction formula does not contain redundant terms and possesses some flexibility that can be used for improving the precision of calculations. Numerical test results are presented up to four loops.

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Notes

  1. The value is the statistical average of the new experimental value and the old one [3].

  2. See the definitions in [12].

  3. See examples of applying Ward identities for individual diagrams in [13].

  4. The main path is a lepton path between external lepton lines.

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ACKNOWLEDGMENTS

The author thanks Lidia Kalinovskaya, Gudrun Heinrich, Savely Karshenboim, Andrey Arbuzov for the important assistance, and Andrey Kataev for valuable consultations. Also, the author thanks the Laboratory of Information Technologies of JINR (Dubna, Russia) for providing an access to its computational resources and additionally the organizers of the conference FFK-2021 for providing a possibility to make a presentation. And beyond that, the author considers it proper to honor the memory of Fyodor Tkachov.

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  1. Skobeltsyn Institute of Nuclear Physics at Lomonosov Moscow State University, Moscow, Russia

    S. Volkov

  2. Dzhelepov Laboratory of Nuclear Problems at Joint Institute of Nuclear Research, Dubna, Russia

    S. Volkov

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  1. S. Volkov
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Correspondence to S. Volkov.

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Volkov, S. A Method of Fast Calculaion of Lepton Magnetic Moments in Quantum Electrodynamics. Phys. Part. Nuclei 53, 805–810 (2022). https://doi.org/10.1134/S106377962204013X

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