Abstract
We present a determination of the charm quark mass in lattice QCD with three active quark flavours. The calculation is based on PCAC masses extracted from Nf = 2 + 1 flavour gauge field ensembles at five different lattice spacings in a range from 0.087 fm down to 0.039 fm. The lattice action consists of the O(a) improved Wilson-clover action and a tree-level improved Symanzik gauge action. Quark masses are non-perturbatively O(a) improved employing the Symanzik-counterterms available for this discretisation of QCD. To relate the bare mass at a specified low-energy scale with the renormalisation group invariant mass in the continuum limit, we use the non-pertubatively known factors that account for the running of the quark masses as well as for their renormalisation at hadronic scales. We obtain the renormalisation group invariant charm quark mass at the physical point of the three-flavour theory to be Mc = 1486(21) MeV. Combining this result with five-loop perturbation theory and the corresponding decoupling relations in the overline{mathrm{MS}} scheme, one arrives at a result for the renormalisation group invariant charm quark mass in the four-flavour theory of Mc(Nf = 4) = 1548(23) MeV, where effects associated with the absence of a charmed, sea quark in the non-perturbative evaluation of the QCD path integral are not accounted for. In the overline{mathrm{MS}} scheme, and at finite energy scales conventional in phenomenology, we quote {m}_{mathrm{c}}^{overline{mathrm{MS}}} ( {m}_{mathrm{c}}^{overline{mathrm{MS}}} ; Nf = 4) = 1296(19) MeV and {m}_{mathrm{c}}^{overline{mathrm{MS}}} (3 GeV; Nf = 4) = 1007(16) MeV for the renormalised charm quark mass.
Highlights
Our determination of the charm quark mass is performed on a subset of the gauge configuration ensembles, generated by the Coordinated Lattice Simulations (CLS) cooperative effort of European lattice QCD teams, with Nf = 2 + 1 flavours of non-perturbatively O(a) improved Wilson quarks and the tree-level Symanzik-improved gauge action [4, 5]
Once bare quark masses based on the PCAC relation on the lattice are extracted, they need to be properly renormalised for their continuum limit to exist
For connecting the bare (PCAC) mass at a specified low-energy scale with the renormalisation group invariant (RGI) mass in the continuum limit, we can draw on the study exposed in ref. [20], where the renormalisation group running of the quark mass over a wide range of scales for the present three-flavour discretisation of QCD was performed with full non-perturbative precision in the Schrödinger functional scheme, following the strategy of ref
Summary
Our determination of the physical charm quark mass is based on various different definitions of the quark mass in the formulation of lattice QCD with Wilson quarks. [35, 36] have shown that the scaling of meson observables involving heavy quarks towards the continuum limit benefits from including these mass dependent cutoff effects in the LCP definition of the improvement coefficients and renormalisation factor in question. This conjecture will be tested later, when we discuss the chiral-continuum extrapolation of our results. For the improvement coefficient ( ̄bA − ̄bP) andbm multiplying cutoff effects depending on the sea quark masses, non-perturbative results with errors of O(100%) were obtained in refs. We note that the associated contributions from the sea quark masses are highly suppressed compared to the heavy valence quark mass effects that are removed non-perturbatively
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