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

We present a lattice QCD determination of light quark masses with three sea-quark flavours ($N_\mathrm{f}=2+1$). 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) $m_{\mathrm{u}/\mathrm{d}}(2~\mathrm{GeV})= 3.54(12)(9)~\mathrm{MeV}$ and $m_{\mathrm{s}}(2~\mathrm{GeV}) = 95.7(2.5)(2.4)~\mathrm{MeV}$ in the $\overline{\mathrm{MS}}$ scheme. For the mass ratio we have $m_{\mathrm{s}}/m_{\mathrm{u}/\mathrm{d}}= 27.0(1.0)(0.4)$. The RGI values in the three-flavour theory are $M_{\mathrm{u}/\mathrm{d}}= 4.70(15)(12)~\mathrm{MeV}$ and $M_{\mathrm{s}}= 127.0(3.1)(3.2)~\mathrm{MeV}$.