Abstract
We present a calculation of the up, down, strange and charm quark masses performed within the lattice QCD framework. We use the twisted mass fermion action and carry out simulations that include in the sea two light mass-degenerate quarks, as well as the strange and charm quarks. In the analysis we use gauge ensembles simulated at three values of the lattice spacing and with light quarks that correspond to pion masses in the range from 350 MeV to the physical value, while the strange and charm quark masses are tuned approximately to their physical values. We use several quantities to set the scale in order to check for finite lattice spacing effects and in the continuum limit we get compatible results. The quark mass renormalization is carried out non-perturbatively using the RI'-MOM method converted into the $\overline{\rm MS}$ scheme. For the determination of the quark masses we use physical observables from both the meson and the baryon sectors, obtaining $m_{ud} = 3.636(66)(^{+60}_{-57})$~MeV and $m_s = 98.7(2.4)(^{+4.0}_{-3.2})$~MeV in the $\overline{\rm MS}(2\,{\rm GeV})$ scheme and $m_c = 1036(17)(^{+15}_{-8})$~MeV in the $\overline{\rm MS}(3\,{\rm GeV})$ scheme, where the first errors are statistical and the second ones are combinations of systematic errors. For the quark mass ratios we get $m_s / m_{ud} = 27.17(32)(^{+56}_{-38})$ and $m_c / m_s = 11.48(12)(^{+25}_{-19})$.
Highlights
Quark masses are essential inputs of the Standard Model (SM) and play a primary role for the description of a large number of physical processes that can provide insights into the dynamics of the SM as well as in the search of beyond the Standard Model physics
We perform an analysis of ten Nf 1⁄4 2 þ 1 þ 1 ensembles simulated at three lattice spacings smaller than 0.1 fm and pion masses in the range from about 350 to 135 MeV
Having two ensembles simulated with the physical value of the pion mass at the two smallest lattice spacings enables us to extrapolate reliably to the physical and continuum limit
Summary
Quark masses are essential inputs of the Standard Model (SM) and play a primary role for the description of a large number of physical processes that can provide insights into the dynamics of the SM as well as in the search of beyond the Standard Model physics. Theoretical progress in lattice field theory and improvement in numerical algorithms, accompanied with a continuously increasing computational power, are allowing us to perform simulations using physical values of the light-quark masses Most of these simulations are still carried out using a single lattice spacing and volume, this is rapidly changing as more lattice QCD collaborations gain access to larger computational resources and can produce multiple ensembles of gauge configurations generated with physical values of the light quark masses. One set of observables is based on quantities from the meson sector of QCD, while the other set relies on baryonic observables In the former case, we use the pion mass and decay constant to set the scale and to determine the average up/down quark mass. VII, we discuss our final results and give our conclusions and outlook
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