Abstract
We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with Nf=2+1+1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210–450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI′-MOM method. The results for the quark masses converted to the MS¯ scheme are: mud(2 GeV)=3.70(17) MeV, ms(2 GeV)=99.6(4.3) MeV and mc(mc)=1.348(46) GeV. We obtain also the quark mass ratios ms/mud=26.66(32) and mc/ms=11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate mu/md=0.470(56), leading to mu=2.36(24) MeV and md=5.03(26) MeV.
Highlights
The precise knowledge of the quark masses and of the hadronic parameters in general plays a fundamental role both in testing the Standard Model (SM) and in the search for new physics (NP)
In this paper we present an accurate determination of the up, down, strange and charm quark masses using the gauge configurations produced by the European Twisted Mass (ETM) Collaboration with four flavors of dynamical quarks (Nf = 2 + 1 + 1), which include in the sea, besides two light mass degenerate quarks, the strange and charm quarks with masses close to their physical values
The analyses C1 (C2) and D1 (D2) proceed in the same way: the average up/down quark mass mud is determined through the experimental value of the ratio Mπ2 /fπ2, while the mass Ms s is obtained by combining the value of fπ /Ms s, calculated at the physical point, and the experimental value of fπ
Summary
The precise knowledge of the quark masses and of the hadronic parameters in general plays a fundamental role both in testing the Standard Model (SM) and in the search for new physics (NP). In the determination of the quark masses lattice QCD (LQCD) plays a primary role as it is a non-perturbative approach based on first principles. It consists in simulating QCD by formulating the Lagrangian on a discrete and finite Euclidean space–time which allows for a numerical computation of the path integral via Monte Carlo methods. The finite volume, the lattice spacing and generally the lower bound on the simulated light quark masses, which are limited by the currently available computing power, introduce errors which have to be well under control and accounted for
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