  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 $m_c / m_s = 11.48(12)(^{+25}_{-19})$.

High Energy Physics - Lattice;High Energy Physics - Phenomenology