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

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 ${\rm Y}(1S)$ 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.

18 pages

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• Three-loop matching coefficients for heavy flavor-changing currents and the phenomenological applications