Three-loop QCD corrections to the decay constant of $B_c$

TL;DR

This paper calculates the three-loop QCD corrections to the $B_c$ meson decay constant within NRQCD, revealing large radiative effects that significantly impact leptonic decay predictions.

Contribution

It provides the first analytical expressions for three-loop renormalization constants and anomalous dimensions for the pseudoscalar current of two different heavy flavors in NRQCD.

Findings

Three-loop QCD correction is overwhelmingly large.

High-precision numerical results for short-distance coefficients.

Implications for $B_c$ leptonic decay phenomenology.

Abstract

Within the framework of nonrelativistic QCD (NRQCD) factorization, we compute the three-loop QCD corrections to the decay constant of $B_c$. We reconstruct the analytical expressions for the three-loop renormalization constant and the corresponding anomalous dimension affiliated with the pseudoscalar current composed of two different heavy flavors in NRQCD, which are functions of the ratio between the charm and bottom quark masses. Meanwhile, the short-distance coefficient is obtained with very high numerical accuracy. The three-loop QCD correction turns out to be overwhelmingly large. The phenomenological implication of this new piece of radiative corrections for the $B_c$ leptonic decay is also addressed.