The effective charm mass from the excited charmonium leptonic decays

Abstract

We use the covariant four-dimensional Bethe-Salpeter (BS) equation to determine the effective charm quark mass. The scale dependence of the effective charm quark mass is determined using experimentally known spin-one charmonium spectra and leptonic decay constants. The infrared finite, massive-like effective QCD running charge is used to solve the Bethe-Salpeter equation to achieve this. The obtained effective charm quark mass values run from 1.1 GeV for the $J/Psi$ meson to 1.5 GeV for its higher radial excitations. These values are substantially smaller than those extracted in the perturbative MS renormalization scheme, but they agree with the semi-perturbative solution of the quark Schwinger-Dyson equation in the momentum subtraction scheme. Within the interaction entirely governed by QCD running coupling, the sliding scale charm quark mass is crucial for the correct determination of leptonic decays. Notably, for leptonic decay constants of excited states, this is the first time the theory based on Bethe-Salpeter equation has met the precision of the experimental data.