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

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 $b_{\mathrm{A}}-b_{\mathrm{P}}$. The mass renormalisation at hadronic scales and the renormalisation group running over a wide range of scales are known non-perturbatively in the Schrödinger functional scheme. In the present paper we perform detailed extrapolations to the physical point, obtaining (for the four-flavour theory) $m_{u/d}(2\mathrm{GeV})=3.54(12)(9)$ MeV and $m_s(2\mathrm{GeV})=95.7(2.5)(2.4)$ MeV in the $\overline{MS}$ 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.

Comments: 27 pages, 5 figures. Published version of the paper. The present version contains additions and improvements proposed by the referee; the results remain unchanged