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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-changing
decay modes. We employ self-consistent covariant light-front quark model to
obtain the weak transition form factors. The self-consistent covariant
light-front quark model uses type-II correspondence to eliminate
inconsistencies in the traditional type-I covariant light-front quark model. We
confirm that type-II correspondence produces self-consistent form factors
involving $B_c$ to axial-vector meson transitions free from zero-mode
contributions. We also study the $q^2$ dependence of the form factors in weak
hadronic currents for the whole accessible kinematic range $0 \leq q^2 \leq
q^2_{max}$ for both bottom-conserving as well as bottom-changing transitions.
We thoroughly investigate the effects of self-consistency between type-I and
type-II schemes using a comparative analysis. We predict the branching ratios
of the semileptonic weak decays by adopting the factorization hypothesis. 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, the asymmetry parameter, and longitudinal
polarization asymmetries and fractions. Finally, we obtain the
lepton-flavor-universality ratios for various decays.
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