Decay constants of \( c\overline{b} \) 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 $c\overline{b}$ \( c\overline{b} \) mesons. We further study the ten decay constants for the $c\overline{b}$ \( c\overline{b} \) mesons (B_c, $B_c^{\ast }$ \( {B}_c^{\ast } \) , $B_{c0}^{\ast }$ \( {B}_{c0}^{\ast } \) , 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 (N³LO) of α_s. 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 $c\overline{b}$ \( c\overline{b} \) mesons coupled with the ten currents.