Running Coupling Constants of Fermions with Masses in Quantum Electro Dynamics and Quantum Chromo Dynamics

TL;DR

This paper calculates the running coupling constants of fermions with masses in QED and QCD using a simple regularization-renormalization method, revealing their different behaviors across energy scales.

Contribution

It introduces a straightforward regularization-renormalization method to compute fermion running coupling constants in QED and QCD, providing new insights into their energy dependence.

Findings

RCC in QED increases with energy transfer Q.

Quark RCCs vary with flavor and decrease at low Q.

Different behaviors of RCCs explained physically.

Abstract

Based on a simple but effective regularization-renormalization method (RRM), the running coupling constants (RCC) of fermions with masses in quantum electrodynamics (QED) and quantum chromodynamics (QCD) are calculated by renormalization group equation (RGE). Starting at Q=0 ($Q$ being the momentum transfer), the RCC in QED increases with the increase of $Q$ whereas the RCCs for different flavors of quarks with masses in QCD are different and they increase with the decrease of $Q$ to reach a maximum at low $Q$ for each flavor of quark and then decreases to zero at $Q\longrightarrow 0$. The physical explanation is given.