  The semileptonic decay of heavy flavor mesons offers a clean environment for
extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, which
describes the CP-violating and flavor changing process in the Standard Model.
The involved form factors where the dynamical information is encoded play an
essential role in achieving any conclusive statement. That is, the knowledge of
the form factors should be under good control, requiring one to examine more
observables in addition to the branching fraction. In this paper, we provide
the mean value and the $q^2$-dependent shape for further observables
[differential decay distribution ($d\Gamma/dq^2$), forward-backward asymmetry
($\mathcal{A}_{FB}^l$), longitudinal ($P_L^l$) and transverse ($P_T^l$)
polarization of a charged lepton, longitudinal polarization of a vector meson
in the final state ($F_L^l(V)$), leptonic convexity parameter ($C_F^l$), and
trigonometric moments ($W_i^l$) in the decay of $D_{(s)}$ and $B_{(s)}$ to $P/V
l^+ \nu_l$ ($l=e$, $\mu$ or $\tau$)], based on the predictions of the relevant
form factors from the covariant light-front quark model. $P$ and $V$ denote the
pseudoscalar and vector meson, respectively. As a comparison, we find a good
agreement with the results from the covariant confining quark model and the
relativistic quark model in the literature. As it has been observed that the
$P_L^l$ and $F_L^l(V)$ are crucial quantities to discriminate various New
Physics models, the reexamination of these observables from a different method
is also essential and necessary.
