Decay constants of cb mesons involving the ten heavy flavor-changing currents at N3LO QCD

Within the nonrelativistic QCD (NRQCD) framework, we complete the three-loop calculations of the NRQCD renormalization constants and the matching coefficients, for the heavy flavor-changing temporal vector, spatial-spatial tensor, spatial-temporal axial-tensor currents, which are coupled to the P-wave cb mesons. We further study the ten decay constants for the cb mesons (B-c, Bc*, B-c0*, B-c1) coupled with the ten heavy flavor-changing currents involving (pseudo-)scalar, (axial-)vector and (axial-)tensor up to the next-to-next-to-next-to-leading order ((NLO)-L-3) of alpha(s). We obtain the six ratios of decay constants by approximating them to the corresponding ratios of matching coefficients. We find the (NLO)-L-3 perturbative QCD results for the six ratios of decay constants have good convergence and weak scale-dependence. We finally predict the hierarchical relationship among the ten decay constants for the cb mesons coupled with the ten currents.