Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD

TL;DR

Using Nf=2+1+1 twisted mass lattice QCD, the paper determines up, down, strange and charm quark masses with controlled continuum and chiral extrapolations. It combines a unitary light sector with Osterwalder-Seiler valence quarks for strange/charm and employs nonperturbative RI'-MOM renormalization to connect lattice results to the MSbar scheme, performing two scaling strategies (r0 and M_{s′s′}) to manage discretization effects. The main results are m_ud = 3.70(17) MeV, m_s(2 GeV) = 99.6(4.3) MeV, m_c(m_c) = 1.348(46) GeV, with ratios ms/mud = 26.66(32), mc/m_s = 11.62(16) and mu/md = 0.470(56), and derived light-isospin breaking values mu = 2.36(24) MeV, md = 5.03(26) MeV. These constitute a first-principles Nf=2+1+1 determination that is consistent with FLAG averages and demonstrates robust control over finite-size, discretization, and renormalization-systematic uncertainties.

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 bar{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.

Figures (15)

• Figure 1: Chiral and continuum extrapolation of $r_0 M_\pi^2 / m_\ell$ based on the NLO ChPT fit given by Eq. (\ref{['eq:cptmpi2Ch']}). Lattice data have been corrected for FSE using the CWW approach Colangelo:2010cu and correspond to the RCs $Z_P$ calculated with the method M1 (see text).
• Figure 3: Chiral and continuum extrapolation of $r_0 M_{\pi}^2 / m_\ell$ obtained using the polynomial fit given by Eq. (\ref{['eq:cptmpi2FP']}).
• Figure 5: Chiral and continuum extrapolation of $M_\pi^2 / (m_\ell M_{s^\prime s^\prime})$ obtained using the NLO ChPT fit (\ref{['eq:mpi2suMss2']}).
• Figure 7: Chiral and continuum extrapolation of $M_K^2$ in units of $r_0$ using the SU(2) ChPT predictions given by Eq. (\ref{['eq:mk2Ch']}).
• Figure 9: Chiral and continuum extrapolation of $M_K^2$ in units of $M_{s^\prime s^\prime}^2$ using SU(2) ChPT at NLO.