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

A bstract 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 cb̄ c b ¯ mesons. We further study the ten decay constants for the cb̄ c b ¯ mesons ( B c , Bc B c ∗ , Bc0 B c 0 ∗ , B c 1 ) 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 (N 3 LO) of α s . We obtain the six ratios of decay constants by approximating them to the corresponding ratios of matching coefficients. We find the N 3 LO 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 cb̄ c b ¯ mesons coupled with the ten currents.