Effective Coupling Constant in Renormalization Group for the Quantum Electrodynamics

TL;DR

This paper investigates the effective coupling constant in quantum electrodynamics, addressing the pole issue via analytic regularization, and relates it to a scale parameter that aligns with experimental data.

Contribution

It introduces a method to eliminate the pole in the effective coupling constant using analytic regularization and expresses it in terms of a scale parameter for QED.

Findings

The pole in the effective coupling constant can be removed by analytic regularization.

The effective coupling constant is expressed in terms of a scale parameter Λ.

Calculated Λ value aligns with experimental data, around 1.64×10^{47} GeV.

Abstract

Effective coupling constant in quantum electrodynamics is investigated. A pole appears in the effective coupling constant for the space-like momentum if it is calculated by perturbation. The pole can be eliminated by the analytic regularization. For QED the effective coupling constant is written in terms of the scale parameter, $\Lambda$, having the dimension of mass as in the case of QCD. $\Lambda$ is determined by comparing with the experimental data. The calculated result agrees with experiment with $\Lambda\approx 1.64\times 10^{47}$ GeV; it is very large but much smaller than the mass scale of Landau ghost.