Quark mass RG-running for $N_f$ =3 QCD in a $\chi SF$ setup

TL;DR

This paper nonperturbatively computes the quark mass RG-running in three-flavor QCD across a wide energy range using a mixed action approach with Schrödinger functional boundary conditions, confirming universality and establishing optimal tuning strategies.

Contribution

It introduces a mixed action approach with Schrödinger functional boundary conditions for nonperturbative quark mass RG-running, confirming universality between $ ext{SF}$ and $ ext{chiSF}$ and providing tuning strategies.

Findings

Results agree with previous SF studies, confirming universality.

Established optimal tuning for critical hopping parameter and boundary counterterm.

Provided RG-running results across multiple energy regimes.

Abstract

We compute the nonperturbative quark mass RG-running in the range $\Lambda_{QCD}\lessapprox\mu\lessapprox M_W$ for $N_f=3$ massless QCD with a mixed action approach: sea quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with Schr\"odinger functional (SF) boundary conditions, employing the configurations of 1802.05243, while valence quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with chirally rotated Schr\"odinger functional boundary conditions ($\chi$SF). Our result is compatible with its SF counterpart of ref.1802.05243, confirming the universality of $\chi$SF and SF in the continuum limit. We also establish the optimal tuning strategy for the critical hopping parameter $\kappa_c$ and the $\chi$SF boundary counterterm coefficient $z_{\rm f}$. We work in two energy regimes with two different definitions of the coupling: SF-coupling for 2 GeV $\lessapprox\mu\lessapprox M_W$ and GF-coupling for $\Lambda_{QCD} \lessapprox\mu\lessapprox 2 GeV$.