Light quark masses in N_f = 2+1 lattice QCD with Wilson fermions

TL;DR

This paper reports a precise lattice QCD calculation of light quark masses using $N_f=2+1$ Wilson fermions, including non-perturbative renormalization and extrapolation to physical quark masses.

Contribution

It provides the first detailed non-perturbative determination of light quark masses with Wilson fermions including recent improvements and renormalization techniques.

Findings

Quark masses are determined with high precision.

Mass ratios are consistent with previous estimates.

Results are given in both $ar{MS}$ and RGI schemes.

Abstract

We present a lattice QCD determination of light quark masses with three sea-quark flavours ($N_f = 2+1$). Bare quark masses are known from PCAC relations in the framework of CLS lattice computations with a non-perturbatively improved Wilson-Clover action and a tree-level Symanzik improved gauge action. They are fully non-perturbatively improved, including the recently computed Symanzik counter-term $b_{\rm A} - b_{\rm P}$. The mass renormalisation at hadronic scales and the renormalisation group running over a wide range of scales are known non-perturbatively in the Schr\"odinger functional scheme. In the present paper we perform detailed extrapolations to the physical point, obtaining (for the four-flavour theory) $m_{u/d}(2{\rm GeV}) = 3.54(12)(9)$ MeV and $m_s(2{\rm GeV}) = 95.7(2.5)(2.4)$ MeV in the $\bar{MS}$ scheme. For the mass ratio we have $m_s/m_{u/d} = 27.0(1.0)(0.4)$. The RGI values in the three-flavour theory are $M_{u/d} = 4.70(15)(12)$ MeV and $M_s = 127.0(3.1)(3.2)$ MeV.