Determination of the charm quark mass in lattice QCD with 2 + 1 flavours on fine lattices

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 $$ \overline{\mathrm{MS}} $$ 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 $$ \overline{\mathrm{MS}} $$ MS ¯ scheme, and at finite energy scales conventional in phenomenology, we quote $$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ ($$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ ; Nf = 4) = 1296(19) MeV and $$ {m}_{\mathrm{c}}^{\overline{\mathrm{MS}}} $$ m c MS ¯ (3 GeV; Nf = 4) = 1007(16) MeV for the renormalised charm quark mass.

Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $$N_\mathrm {f}=3$$ QCD with Wilson quarks

“…(2.13) in Ref. [29]. Another application where r m plays a prominent rôle is the nucleon sigma-term, which is defined in terms of nucleon matrix elements of flavour singlet scalar densities; see Refs.…”

A lattice QCD perspective on weak decays of b and c quarks Snowmass 2022 White Paper

“…There are now several different strategies for determining quark mass -among these are approaches based on moments of current-current correlators [249,250], the implementation of momentum subtraction schemes on the lattice [251,252], spectroscopy of heavy meson masses and HQET [253,254], nonperturbative HQET determinations [255] and computations involving step-scaling in small volume [256,257]. These methods, though all relying crucially on lattice simulation, differ substantially in approach and are hence subject to differing sources of systematic uncertainty.…”

$m_c$ (and $m_b$) from lattice QCD

“…For the purposes of the talk I would like to especially focus on the four results at the top of the figure, which all separately claim percent-level uncertainty, and remarkably are arrived at through three completely different techniques. I would also like to highlight the new results based on small volume step-scaling techniques [4,5] from ALPHA and a new calculation from ETM using RI/MOM renormalization [6] (a variant of the type of calculation described in more detail in Sec. 3.3).…”