Next-to-next-to-leading order matching of beauty-charmed meson Bc and Bc* decay constants

Abstract

We present the next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) corrections to the decay constants for both the pseudoscalar ${B}_{c}$ meson and the vector ${B}_{c}^{*}$ meson in the nonrelativistic QCD (NRQCD) effective theory. The explicit NNLO calculations prove that the ${B}_{c}$ decay constant from the pseudoscalar current is identical with the ${B}_{c}$ decay constant from the axial-vector current. The NNLO result for the vector decay constant of ${B}_{c}^{*}$ meson is novel. Combining this result with the latest extraction of the NRQCD long-distance matrix elements of ${B}_{c}$ and ${B}_{c}^{*}$ meson, we calculate and show the theoretical predictions for the branching ratios of the leptonic decays ${B}_{c}^{+}/{B}_{c}^{*+}\ensuremath{\rightarrow}{l}^{+}{\ensuremath{\nu}}_{l}$ with ${l}^{+}=({e}^{+},{\ensuremath{\mu}}^{+},{\ensuremath{\tau}}^{+})$. In addition, the novel anomalous dimension for the flavor-changing heavy quark vector current in the NRQCD effective theory is helpful to investigate the threshold behaviors of the two different heavy quarks.