Charm mass determination from QCD charmonium sum rules at order $ \alpha_s^3 $

Abstract

We determine the MS charm quark mass from a charmonium QCD sum rules analysis. On the theoretical side we use input from perturbation theory at O(α 3 s ). Improvements with respect to previous O(α 3 s ) analyses include (1) an account of all available e + e − hadronic cross section data and (2) a thorough analysis of perturbative uncertainties. Using a data clustering method to combine hadronic cross section data sets from different measurements we demonstrate that using all available experimental data up to c.m. energies of 10.538 GeV allows for determinations of experimental moments and their correlations with small errors and that there is no need to rely on theoretical input above the charmonium resonances. We also show that good convergence properties of the perturbative series for the theoretical sum rule moments need to be considered with some care when extracting the charm mass and demonstrate how to set up a suitable set of scale variations to obtain a proper estimate of the perturbative uncertainty. As the final outcome of our analysis we obtain m c (m c ) = 1.282 ± (0.006) stat ± (0.009) syst ± (0.019) pert ± (0.010) αs ± (0.002) GG GeV. The perturbative error is an order of magnitude larger than the one obtained in previous O(α 3 s ) sum rule analyses.

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

“…The agreement of the lattice data and the phenomenological estimates is remarkable. In particular, our data are consistent with the updated estimates with reduced error of [7,27], and the size of total error is comparable. 0 , respectively.…”

“…We take the mean value of these two Phenomenological estimates of corresponding quantities are plotted on the left: Dehnadi et al [27] (filled circle), Kuhn et al [7] (open circle), Kuhn et al [25] (filled square), and Hoang et al [26] (open square).…”

“…Namely, we reorganize the perturbative series in terms of α s (µ α ) and m c (µ m ) with µ α = µ m [27,28]. This can be done by inserting an expansion of α s (µ = µ m ) in terms of α s (µ α ) into the formula of r n (α s (µ), m c (µ)) and rearranging the perturbative series.…”

Lattice QCD and QCD sum rule determination of the decay constants of ηc, J/ψ and Bečirević1, Duplančić2, Klajn3 et al. 2014Nuclear Physics B941282View full textAdd to dashboardCite

“…(η c → γ γ ) = 5.0(4) keV, which together with our f η c = 0.387(8) GeV, allows us to deduce the value of δ = 0.15(5) GeV 2 . That value is too large to be interpreted as k 2 ⊥ = 0.81(14) GeV, 7 and also too large to be identified as b η c = δm η c = 0.46 (16) GeV. Finally, we should say that the VMD is actually quite good an approximation.…”

Inclusive semileptonic fits, heavy quark masses, andVcb

“…have become available, see, e.g., Refs. [11][12][13][14][15]. Radiative moments remain very interesting, but they are not competitive with the charm mass determinations and are, in principle, subject to additional OðΛ QCD =m b Þ effects, which have not yet been estimated [16].…”