Determination of the mass anomalous dimension for $N_f=12$ and $N_f=9$ SU($3$) gauge theories

TL;DR

This paper presents numerical results for the mass anomalous dimension of SU(3) gauge theories with 12 and 9 fundamental fermions, using two independent methods near the infrared fixed point, contributing to understanding the conformal window.

Contribution

It provides the first continuum-extrapolated determinations of the mass anomalous dimension for Nf=12 and reports new simulation results for Nf=9, advancing knowledge of the conformal window boundaries.

Findings

Mass anomalous dimension for Nf=12 near IR fixed point

Continuum extrapolated results using two methods

Initial results for Nf=9 gauge theory simulations

Abstract

We show the numerical simulation result for the mass anomalous dimension of the SU($3$) gauge theory coupled to $N_f = 12$ fundamental fermions. We use two independent methods, namely the step scaling method and the hyperscaling method of the Dirac mode number, to determine the anomalous dimension in the vicinity of the infrared fixed point of the theory. We show the continuum extrapolations keeping the renormalized coupling constant as a reference in both analyses. Furthermore, some recent works seems to suggest the lower boundary of the conformal window of the SU($3$) gauge theory exists between $N_f=8$ and $10$. We also briefly report our new project, in which the numerical simulation of the SU($3$) gauge theory coupled to $N_f=9$ fundamental fermions has been performed.