Charm Mass Determination from QCD Charmonium Sum Rules at Order alpha_s^3

Charm and Bottom Masses from Sum Rules with a Convergence Test

“…The final result quoted in Ref. [3] for α s (m Z ) = 0.1184 ± 0.0021 was m c (m c ) = 1.282 ± (0.006) stat ± (0.009) syst ± (0.019) pert ± (0.010) αs ± (0.002) GG GeV based on the expansion 3 (linearized iterative method).…”

“…Since the integration over the experimental R-ratio stretches from the quark pair threshold up to infinity and since useful experimental measurements only exist for energies up to around 11 GeV, the method relies on using theory input for energies above that scale (which we call "continuum"). For the charm case the combination of all available measurements is sufficient to render the experimental moments independent of uncertainties one assigns to the theory input for the continuum region [3]. For the bottom case the dependence on the continuum theory input is very large, and the dependence of the low-n experimental moments on unavoidable assumptions about the continuum error can be the most important component of the error budget.…”

“…In Ref. [3] we analyzed the perturbative series for the vector correlator moments M 1,2,3,4 at O(α 3 s ) with the aim to reliably assess their uncertainty coming from the truncation of the series and to find out whether renormalization scale variation with µ m = µ α gives a compatible estimate of this uncertainty. We considered four different alternatives, each of which providing a viable analytic expression to carry out the charm mass determination:…”

“…(a) For each pair (µ m , µ α ) the convergence parameter V c is calculated from the charm mass series m c (m c ) = m (0) + δm (1) + δm (2) + δm (3) that results from the fits at O(α 0,1,2,3 s ):…”

A new determination of the charm mass from the non-analytic reconstruction of the heavy quark correlator

“…An accurate determination of the charm mass plays an important role on the precise physical evaluation of several observables, from K and B decays to CKM matrix elements and in lattice QCD. One of the usual techniques to extract the charm mass is to use the sum rules approach based on the relation between the moments of the production rate R and the inverse power of the square mass of the c quark, and the Padé method (see [1,2]). This approach should confront the fact that one have to employ the moments of the integral of R over the whole energy range, which are global properties, even though they are only known up to a certain scale Λ (since we only know experimentally R in a finite window).…”