Weak decays of \({\varvec{B}}_{{\varvec{c}}}\) involving vector mesons in self-consistent covariant light-front approach

We present a comprehensive analysis of weak transition form factors, semileptonic decays, and nonleptonic decays of \(B_c\) mesons involving pseudoscalar (P) and vector (V) mesons for bottom-conserving and bottom-changing decay modes. We employ the self-consistent covariant light-front quark model (CLFQM), termed type-II correspondence, to calculate the \(B_c\) to P(V) transition form factors. The type-II correspondence in the CLF approach gives self-consistent results associated with the \(B^{(i)}_j\) functions, which vanish numerically after the replacement \(M^{\prime (\prime \prime )} \rightarrow M_0^{\prime (\prime \prime )}\) in traditional type-I correspondence, and the covariance of the matrix elements is also restored. We investigate these effects on bottom-conserving \(B_c\) to P(V) form factors that have not yet been studied in CLFQM type-II correspondence. In addition, we quantify the implications of self-consistency propagating to weak decays involving both bottom-conserving and bottom-changing \(B_c\) transition form factors. We use two different parameterizations, the usual three-parameter function of \(q^{2}\) and the model-independent z-series expansion, to establish a clear understanding of \(q^{2}\) dependence. Using the numerical values of the form factors, we predict the branching ratios other physical observables, including forward-backward asymmetries, polarization fractions, etc. of the semileptonic \(B_c\) decays. Subsequently, we predict the branching ratios of two-body nonleptonic weak decays using the factorization hypothesis in self-consistent CLFQM. We also compare our results with those of other theoretical studies.