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 nonperturbatively using the (modified) Regularization Independent Momentum Subtraction (${\mathrm{RI}}^{\prime }\text{−}\mathrm{MOM}$) method converted into the $\overline{\mathrm{MS}}$ scheme. For the determination of the quark masses, we use physical observables from both the meson and the baryon sectors, obtaining $m_{ud}=3.636(66)({}_{-57}^{+60})\mathrm{MeV}$ and $m_s=98.7(2.4)({}_{-3.2}^{+4.0})\mathrm{MeV}$ in the $\overline{\mathrm{MS}}(2\mathrm{GeV})$ scheme and $m_c=1036(17)({}_{-8}^{+15})\mathrm{MeV}$ in the $\overline{\mathrm{MS}}(3\mathrm{GeV})$ scheme, where the first errors are statistical and the second ones are combinations of systematic errors. For the quark mass ratios, we get $m_s/m_{ud}=27.17(32)({}_{-38}^{+56})$ and $m_c/m_s=11.48(12)({}_{-19}^{+25})$.

• Received 5 May 2021
• Accepted 15 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.074515

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Published by the American Physical Society