Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass

Abstract

We calculate charmonium correlators on the lattice with 2+1-flavors of sea quarks and charm valence quark both described by the Möbius domain-wall fermion. Temporal moments of the correlators are calculated and matched to perturbative QCD formulae to extract the charm quark mass m c (µ) and strong coupling constant α s (µ). Lattice data at three lattice spacings, 0.044, 0.055, and 0.080 fm, are extrapolated to the continuum limit. The correlators in the vector channel are confirmed to be consistent with the experimental data for e + e − → cc, while the pseudo-scalar channel is used to extract m c (µ) and α s (µ). We obtain m c (3 GeV) = 1.003(10) GeV and α MS(4) s (3 GeV) = 0.253(13). Dominant source of the error is the truncation of perturbative expansion at α 3

Precise determination of αs from relativistic quarkonium sum rules

“…[8] estimates the perturbative uncertainty on α s from the M P,0 c moment by varying the renormalization scales setting 2 GeV ≤ µ α = µ m ≤ 4 GeV. The result 0.1174 (12) is quoted, with a central value in good agreement with our result in Table 9, but with a smaller error. If we use a correlated scale variation (taking the charm quark mass as the lowest scale) we obtain 0.1178 ± (0.0011) total , which has a very similar total uncertainty.…”

“…Nakayama et al [12] 1 0.1163 0.0018 0.0007 0.0003 0.0006 0.0020 2 0.1152 0.0018 0.0006 0.0003 0.0008 0.0021 Table 10. α (n f =5) s (m Z ) determination from ratios of charm pseudo-scalar correlator moments R P,n c .…”

“…Ref. [12] performs uncorrelated double scale variation, taking µ α = µ m ± 1 GeV with 2 GeV ≤ min{µ α , µ m } and max{µ α , µ m } ≤ 4 GeV. The value 0.1177 ± (0.0026) total is obtained from a combined analysis involving M P,n=0,1,2 c and their ratios.…”

Charm Quark Mass with Calibrated Uncertainty

“…Our result also agrees very well with those from lattice simulations based on the pseudo-scalar current [19], domain-wall fermions [20], and staggered quarks [21]. In summary, we used a physically motivated continuum ansatz that reproduces the experimental data, both the normalisation and -non-trivially and very importantly -the moment dependence, with a single adjustable parameter.…”

Determination of chiral condensate from low-lying eigenmodes of Mobius domain-wall Dirac operator

“…Details of the lattice parameters are in [5], where a full description of this work is available. The same set of lattice ensembles is also used for calculations of other physical quantities such as the η meson mass [6], charm quark mass [7], short-distance current correlator [8,9], as well as heavy-light meson decay constants [10] and semileptonic decay form factors [11].…”