Mass effects on the QCD $\beta$-function

TL;DR

This paper presents lattice QCD results on how quark masses influence the three-loop QCD $eta$-function, with implications for precise strong coupling constant determination.

Contribution

It provides the first detailed analysis of quark mass effects on the QCD $eta$-function using lattice simulations and perturbative calculations.

Findings

Quark masses significantly affect the QCD $eta$-function.

The study explicitly shows dependence on $N_c$, $N_f$, and quark masses.

Results will improve the accuracy of strong coupling constant measurements.

Abstract

In this study we present lattice results on the QCD $\beta$-function in the presence of quark masses. The $\beta$-function is calculated to three loops in perturbation theory and for improved lattice actions; it is extracted from the renormalization of the coupling constant $Z_g$. The background field method is used to compute $Z_g$, where it is simply related to the background gluon field renormalization constant $Z_A$. We focus on the quark mass effects in the background gluon propagator; the dependence of the QCD $\beta$-function on the number of colors $N_c$, the number of fermionic flavors $N_f$ and the quark masses, is shown explicitly. The perturbative results of the QCD $\beta$-function will be applied to the precise determination of the strong coupling constant, calculated by Monte Carlo simulations removing the mass effects from the nonperturbative Green's functions.