Next-to-next-to-leading order matching of beauty-charmed meson $B_{c}$ and $B^*_{c}$ decay constants

TL;DR

This paper calculates NNLO QCD corrections to decay constants of $B_c$ and $B_c^*$ mesons, providing precise theoretical predictions and new insights into heavy quark dynamics.

Contribution

It presents the first NNLO calculation of the vector decay constant for $B_c^*$ and verifies the equivalence of pseudoscalar and axial-vector decay constants for $B_c$.

Findings

NNLO corrections for $B_c$ and $B_c^*$ decay constants obtained.

The vector decay constant of $B_c^*$ is calculated for the first time.

Predictions for leptonic decay branching ratios of $B_c$ and $B_c^*$.

Abstract

We present the next-to-next-to-leading order (NNLO) QCD corrections to the decay constants for both the pseudoscalar and vector beauty-charmed mesons $B_{c}$ and $B^*_{c}$ in nonrelativistic QCD effective theory. Explicit NNLO calculation verified that the $B_c$ decay constant from pseudoscalar current is identical with the $B_c$ decay constant from axial-vector current. The NNLO result for the vector decay constant of $B^*_{c}$ meson is novel. Combined with the latest extraction of nonrelativistic QCD long-distance matrix elements of $B_c$ meson, we give the branching ratios of leptonic decays of $B_{c}$ and $B^*_{c}$ mesons. In addition, the novel anomalous dimension for the flavor-changing heavy quark vector current in nonrelativistic QCD effective theory are helpful to investigate the threshold behaviours of two different heavy quarks.