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 $\mathrm{\Upsilon }(1S)$ decay width into an electron or muon pair. We complement the next-to-next-to-next-to-leading order corrections of M. Beneke, et al. [Phys. Rev. Lett. 112, 151801 (2014)] by charm quark mass effects up to second order in perturbation theory. Furthermore, we apply the formalism to $\mathrm{\Gamma }(J/\mathrm{\Psi }\to {\ell }^{+}{\ell }^{-})$ and compare to the experimental data.

• Received 24 May 2021
• Accepted 30 August 2021

DOI:https://doi.org/10.1103/PhysRevD.104.054033

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Published by the American Physical Society