Weak decays of $\pmb{B_c}$ 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 $B_c$ meson involving pseudoscalar ($P$) and vector ($V$) meson for bottom-conserving and bottom-changing decay modes. We employ self-consistent covariant light-front quark model (CLFQM), termed as 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 $M^{\prime(\prime\prime)} \to M_0^{\prime(\prime\prime)}$ 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 and other physical observables, such as 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.