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

TL;DR

This paper refines the determination of the charm quark mass using QCD sum rules at order alpha_s^3, incorporating comprehensive experimental data and careful uncertainty analysis, resulting in a more conservative estimate of perturbative errors.

Contribution

It introduces an improved analysis of QCD sum rules for charm mass, including all available e+e- data and a detailed perturbative uncertainty assessment at O(alpha_s^3).

Findings

Determined m_c(m_c) = 1.282 ± 0.027 GeV with comprehensive error analysis.

Demonstrated the importance of careful scale variation for perturbative uncertainties.

Showed that experimental data up to 10.538 GeV suffices for reliable moments without theoretical input above resonances.

Abstract

We determine the MS-bar charm quark mass from a charmonium QCD sum rules analysis. On the theoretical side we use input from perturbation theory at O(alpha_s^3). Improvements with respect to previous O(alpha_s^3) 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 \pm 0.006_stat \pm 0.009_syst \pm 0.019)_pert \pm 0.010_alpha \pm 0.002_GG GeV. The perturbative error is an order of magnitude larger than the one obtained in previous O(alpha_s^3) sum rule analyses.