Light quark masses in $${N_\mathrm{f}=2+1}$$ Nf=2+1 lattice QCD with Wilson fermions

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