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

Abstract

We determine the $\overline{\mathrm{MS}}$ charm quark mass from a charmonium QCD sum rules analysis. On the theoretical side we use input from perturbation theory at $\mathcal{O}\left( {\alpha_s^3} \right)$. Improvements with respect to previous $\mathcal{O}\left( {\alpha_s^3} \right)$ 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 ${{\overline{m}}_c}\left( {{{\overline{m}}_c}} \right)=1.282\pm {{\left( {0.006} \right)}_{\mathrm{stat}}}\pm {{\left( {0.009} \right)}_{\mathrm{syst}}}\pm {{\left( {0.019} \right)}_{\mathrm{pert}}}\pm {{\left( {0.010} \right)}_{{{\alpha_s}}}}\pm {{\left( {0.002} \right)}_{{\left\langle {GG} \right\rangle }}}\mathrm{GeV}$. The perturbative error is an order of magnitude larger than the one obtained in previous $\mathcal{O}\left( {\alpha_s^3} \right)$ sum rule analyses.