Abstract
We determine the charm and strange quark masses in the $\overline{\text{MS}}$ scheme, using $n_f=2+1+1$ lattice QCD calculations with highly improved staggered quarks (HISQ) and the RI-SMOM intermediate scheme to connect the bare lattice quark masses to continuum renormalisation schemes. Our study covers analysis of systematic uncertainties from this method, including nonperturbative artefacts and the impact of the non-zero physical sea quark masses. We find $m_c^{\overline{\text{MS}}}(3 \text{GeV}) = 0.9896(61)$ GeV and $m_s^{\overline{\text{MS}}}(3 \text{GeV}) = 0.08536(85)$ GeV, where the uncertainties are dominated by the tuning of the bare lattice quark masses. These results are consistent with, and of similar accuracy to, those using the current-current correlator approach coupled to high-order continuum QCD perturbation theory, implemented in the same quark formalism and on the same gauge field configurations. This provides a strong test of the consistency of methods for determining the quark masses to high precision from lattice QCD. We also give updated lattice QCD world averages for $c$ and $s$ quark masses.
Highlights
Quark masses are fundamental parameters of the Standard Model which must be connected via theory to experimentally measured quantities
We find mMc Sð3 GeVÞ 1⁄4 0.9896ð61Þ GeV and mMs Sð3 GeVÞ 1⁄4 0.08536ð85Þ GeV, where the uncertainties are dominated by the tuning of the bare lattice quark masses
I, the key complication in determining quark masses is in providing the matching factor from the quark mass in a particular lattice QCD regularization scheme to the preferred MS continuum regularization scheme
Summary
Quark masses are fundamental parameters of the Standard Model which must be connected via theory to experimentally measured quantities. Uncertainties in the JJ method arise from missing higher orders in QCD perturbation theory, but these can be tested by implementing the perturbation theory at different scales [12] This method has given 1% accurate results for charm and bottom quark masses in the MS scheme [4,12,13,14,15,16]. Multiplying the lattice bare quark mass by the final ZMm SðμÞ 1⁄4 ZMmS=SMOMðμÞ × ZSmMOMðμÞ gives the required mðμÞ This method has been widely applied to operator renormalization in general and not just the determination of Zm, going under the name of the regularization-independent symmetric momentumsubtraction (RI-SMOM) scheme [24]. VI compares to earlier values, giving new world averages, and concludes with prospects for future improvements
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