Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme

TL;DR

This paper non-perturbatively evaluates the quark mass renormalization factor in Nf=2+1 QCD using the Schroedinger functional scheme, covering a wide energy range and enabling accurate conversion to the MS-bar scheme.

Contribution

It provides the first continuum limit calculation of the regularization independent step scaling function for quark mass in Nf=2+1 QCD using the Schroedinger functional scheme.

Findings

Obtained the continuum limit of the step scaling function for quark mass.

Calculated renormalization factors for pseudo scalar density and axial vector current.

Renormalized PCAC masses in large-scale Nf=2+1 simulations.

Abstract

We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy region, where renormalization of bare mass is performed on the lattice, to deep in the high energy perturbative region, where the conversion to the renormalization group invariant mass or the MS-bar scheme is safely carried out. For numerical simulations we adopted the Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy regions and three lattice spacings to take the continuum limit at each scale. The regularization independent step scaling function of the quark mass for the Nf=2+1 QCD is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than $m_\pi\sim 500$ MeV and that of PACS-CS collaboration for much lighter quark masses down to $m_\pi=155$ MeV. The quark mass renormalization factor is used to renormalize bare PCAC masses in these simulations.