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We present a comprehensive analysis of the semileptonic weak decays of $B_c$meson decaying to axial-vector mesons for bottom-conserving and bottom-changingdecay modes. We employ self-consistent covariant light-front quark model toobtain the weak transition form factors. The self-consistent covariantlight-front quark model uses type-II correspondence to eliminateinconsistencies in the traditional type-I covariant light-front quark model. Weconfirm that type-II correspondence produces self-consistent form factorsinvolving $B_c$ to axial-vector meson transitions free from zero-modecontributions. We also study the $q^2$ dependence of the form factors in weakhadronic currents for the whole accessible kinematic range $0 \leq q^2 \leqq^2_{max}$ for both bottom-conserving as well as bottom-changing transitions.We thoroughly investigate the effects of self-consistency between type-I andtype-II schemes using a comparative analysis. We predict the branching ratiosof the semileptonic weak decays by adopting the factorization hypothesis. Weevaluate the lepton mass effect on these branching ratios and various otherimportant physical observables such as forward-backward asymmetries,lepton-side convexity parameter, the asymmetry parameter, and longitudinalpolarization asymmetries and fractions. Finally, we obtain thelepton-flavor-universality ratios for various decays.

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