A Way of Fast Calculating Lepton Magnetic Moments in Quantum Electrodynamics

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 BPHZ; 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.

arXiv commentprepared for submission to PEPAN (FFK-2021 Proceedings)

References in corpus (15)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The anomalous magnetic moment of the muon in the Standard Model
• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• Measurement of the fine-structure constant as a test of the Standard Model
• Complete Tenth-Order QED Contribution to the Muon g-2
• New determination of the fine structure constant and test of the quantum electrodynamics
• The analytical value of the electron (g-2) at order alpha^3 in QED
• Cavity Control of a Single-Electron Quantum Cyclotron:\\Measuring the Electron Magnetic Moment
• Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops
• Anomalous magnetic moment with heavy virtual leptons
• The muon anomalous magnetic moment in QED: three-loop electron and tau contributions
• The Analytical Value of the Corner-Ladder Graphs Contribution to the Electron G-2 in QED
• Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment
• Subtraction Procedure for Calculation of Anomalous Magnetic Moment of Electron in QED and its Application to Numerical Computation at 3-loop Level