Decay constants of $$ c\overline{b} $$ mesons involving the ten heavy flavor-changing currents at N3LO QCD

Abstract

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 $$ c\overline{b} $$ c b ¯ mesons. We further study the ten decay constants for the $$ c\overline{b} $$ c b ¯ mesons (Bc, $$ {B}_c^{\ast } $$ B c ∗ , $$ {B}_{c0}^{\ast } $$ B c 0 ∗ , Bc1) 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 (N3LO) of αs. We obtain the six ratios of decay constants by approximating them to the corresponding ratios of matching coefficients. We find the N3LO 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 $$ c\overline{b} $$ c b ¯ mesons coupled with the ten currents.