Convergent decay constants for beauty-charm mesons at N${}^3$LO in QCD and phenomenological implications

Abstract

We show the three-loop calculation of the matching coefficients ${\mathcal{C}}_J$ for the four heavy flavor-changing currents in nonrelativistic Quantum Chromodynamics effective theory and confirm the surprising observation of the nonconvergence behaviors of the matching coefficients for beauty-charm mesons. We demonstrate that the higher-order correction to the wave function at origin can solve the nonconvergence problem. By employing the scaling relation, we simultaneously obtain the decay constants for beauty-charm mesons up to the three-loop accuracy and the hyperfine mass splitting in agreement with the experimental data. The perturbative predictions for the leptonic decays of the beauty-charm mesons shall provide a guide in ongoing and future precision heavy flavor experiments.

Comments: The content of this paper arXiv:2303.02692 substantially overlaps with that of the paper arXiv:2303.07220, the latter of which has already been published in the JHEP journal (JHEP 05 (2023) 189)