Up, down, strange and charm quark masses with \(\mathrm{N}_{\mathrm{f}} = 2 + 1 + 1\) twisted mass lattice QCD. (English) Zbl 1325.81170
Summary: 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 \(\mathrm{N}_{\mathrm{f}} = 2 + 1 + 1\) 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 \(210 - 450 \text{ MeV}\), allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the \(\mathrm{RI}^{\prime}-\mathrm{MOM}\) method. The results for the quark masses converted to the \(\overline{\mathrm{MS}}\) scheme are: \(\mathrm{m}_{\mathrm{u d}}(2 \text{GeV}) = 3.70(17) \text{ MeV}\), \(\mathrm{m}_{\mathrm{s}}(2 \text{GeV}) = 99.6(4.3) \text{ MeV}\) and \(\mathrm{m}_{\mathrm{c}}(\mathrm{m}_{\mathrm{c}}) = 1.348(46) \text{ GeV}\). We obtain also the quark mass ratios \(\mathrm{m}_{\mathrm{s}} / \mathrm{m}_{\mathrm{u d}} = 26.66(32)\) and \(\mathrm{m}_{\mathrm{c}} / \mathrm{m}_{\mathrm{s}} = 11.62(16)\). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate \(\mathrm{m}_{\mathrm{u}} / \mathrm{m}_{\mathrm{d}} = 0.470(56)\), leading to \(\mathrm{m}_{\mathrm{u}} = 2.36(24) \text{ MeV}\) and \(\mathrm{m}_{\mathrm{d}} = 5.03(26) \text{ MeV}\).
MSC:
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81T25 | Quantum field theory on lattices |
| 81T27 | Continuum limits in quantum field theory |
| 81V35 | Nuclear physics |
| 81V22 | Unified quantum theories |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 81T80 | Simulation and numerical modelling (quantum field theory) (MSC2010) |
| 81-04 | Software, source code, etc. for problems pertaining to quantum theory |
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