Charm-quark mass effects in NRQCD matching coefficients and the leptonic decay of the $\Upsilon(1S)$ meson

TL;DR

This paper calculates two-loop charm-quark mass effects in NRQCD matching coefficients and applies these to improve theoretical predictions of the leptonic decay widths of the $
$ and $J/$ mesons, comparing with experimental data.

Contribution

It introduces the calculation of charm-quark mass effects at two-loop order in NRQCD matching coefficients and applies this to meson decay width predictions.

Findings

Charm quark mass effects significantly impact decay width calculations.

Theoretical predictions align better with experimental data after including charm mass effects.

Second-order perturbative corrections improve the accuracy of meson decay width estimates.

Abstract

We compute two-loop corrections to the vector current matching coefficient involving two heavy quark masses. The result is applied to the computation of the $\Upsilon(1S)$ decay width into an electron or muon pair. We complement the next-to-next-to-next-to-leading order corrections of Ref. arXiv:1401.3005 by charm quark mass effects up to second order in perturbation theory. Furthermore, we apply the formalism to $\Gamma(J/\Psi\to \ell^+\ell^-)$ and compare to the experimental data.