Matching-invariant running quark masses in Quantum Chromodynamics

TL;DR

This paper introduces matching-invariant quark masses in QCD that are continuous across thresholds, derived as functions of energy scale, with faster convergence and explicit four-loop expressions.

Contribution

It presents a novel formulation of quark masses that are continuous at thresholds, improving upon traditional definitions by deriving explicit four-loop expressions.

Findings

Matching-invariant quark masses are continuous at all energy scales.

The new mass expressions converge faster than traditional ones.

Explicit four-loop formulas are provided.

Abstract

The conventional quark mass is not continuous at thresholds. In this paper, we derive matchinginvariant quark masses which are continuous everywhere. They are expanded as an obvious function of the logarithmic Lambda scaled energy. The expansion coefficients are related to the original gamma and beta functions, with concretization to four loop level. The results show that the new expressions for the quark masses converge indeed much faster.