$B_c$ to $A$ Transition Form Factors and Semileptonic Decays in Self-consistent Covariant Light-front Approach

We present a comprehensive analysis of the semileptonic weak decays of $B_c$ meson decaying to axial-vector ($A$) mesons for bottom-conserving and bottom-changing decay modes. We employ self-consistent covariant light-front quark model (CLFQM) that uses type-II correspondence to eliminate inconsistencies in the traditional type-I CLFQM. As a fresh attempt, we test the self-consistency in CLFQM through type-II correspondence for $B_c \to A$ meson transition form factors. We establish that in type-II correspondence the form factors for longitudinal and transverse polarization states are numerically equal and are free from zero-mode contributions, which confirms the self-consistency of type-II correspondence for $B_c \to A$ transition form factors. Furthermore, we ascertain that the problems of inconsistency and violation of covariance of CLFQM within the type-I correspondence are resolved in type-II correspondence for $B_c \to A$ transitions. We thoroughly investigate the effects of self-consistency between type-I and type-II schemes using a comparative analysis. We also study the $q^2$ dependence of the form factors in weak hadronic currents for the whole accessible kinematic range $0 \leqslant q^2 \leqslant q^2_{max}$ for both bottom-conserving as well as bottom-changing transitions. In addition, we extend our analysis to predict the branching ratios of the semileptonic weak decays of $B_c$ meson involving axial-vector meson in the final state to quantify the effects of self-consistency in these decays that were not studied before. We evaluate the lepton mass effect on these branching ratios and various other important physical observables, such as forward-backward asymmetries, lepton-side convexity parameter, asymmetry parameter, and longitudinal polarization asymmetries and fractions. Finally, we obtain the lepton flavor universality ratios for various decays.