Abstract
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}.
Highlights
Ier flavours, if present in the theory, would be quenched degrees of freedom
We present a lattice QCD determination of light quark masses with three sea-quark flavours (Nf = 2 + 1)
This paper is based on large-scale Nf = 2 + 1 flavour ensembles produced by the Coordinated Lattice Simulation (CLS) effort [7,8]
Summary
The three-flavour theory adopted in this paper is presumably sufficient for determining light quark masses due to the decoupling of heavier quarks [1,2,3,4]. Lattice world averages of light quark masses mu/d, ms do not show a significant dependence on the number of flavours at low energies for Nf ≥ 2 within present-day errors [5] This holds for the more accurately known renormalisation group independent ratio mu/d/ms. The present work has combined all these elements, obtaining estimates of the up/down and strange quark masses, as well as their ratio These are expressed as renormalisation scheme-independent and scale-independent quantities, known as Renormalisation Group Invariant (RGI) quark masses. The bare dimensionless parameters of the lattice theory are the strong coupling g02 ≡ 6/β and the quark masses expressed in lattice units amq,1 = amq, and amq,, with a the lattice spacing They can be varied freely in simulations. In the present work results are obtained at non-zero lattice spacings and at quark masses which correspond to unphysical meson and decay constant values. Preliminary results have been presented in [21]
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