Two-loop QCD Corrections to $B_c$ Meson Leptonic Decays

TL;DR

This paper computes two-loop QCD corrections to the $B_c$ meson leptonic decay rate using NRQCD, providing analytical master integrals and enhancing precision for decay constants and CKM matrix elements.

Contribution

It introduces the first analytical calculation of master integrals for two-loop corrections and determines the short-distance coefficient to order _s^2 in NRQCD.

Findings

Analytical master integrals for two-loop corrections obtained.

Short-distance coefficient calculated to order _s^2.

Improves accuracy of $B_c$ decay constant and $|V_{cb}|$ estimation.

Abstract

The two-loop QCD radiative corrections to the $B_c$ meson leptonic decay rate are calculated in the framework of NRQCD factorization formalism. Two types of master integrals appearing in the calculation are obtained analytically for the first time. We get the short-distance coefficient of the leading matrix element to order $\alpha_s^2$ by matching the full perturbative QCD calculation results to the corresponding NRQCD ones. The result in this work helps the evaluation of the $B_c$ leptonic decay constant, as well as the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$, to the full next-to-next-to-leading order degree of accuracy.