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.
Categories: hep-lat