Recently, the BESIII collaboration has reported numerous measurements of various D_(s) meson semileptonic decays with significantly improved precision. Together with similar studies carried out at BABAR, Belle, and CLEO, new windows to a better understanding of weak and strong interactions in the charm sector have been opened. In light of new experimental data, we review the theoretical description and predictions for the semileptonic decays of D_(s) to a pseudoscalar or a vector meson. This review is essentially an extended discussion of our recently published results obtained in the framework of the covariant confining quark model.

We study the semileptonic decays of the $B_c$ meson into final charmonium states within the standard model and beyond. The relevant hadronic transition form factors are calculated in the framework of the covariant confined quark model developed by us. We focus on the tau mode of these decays, which may provide some hints of new physics effects. We extend the standard model by assuming a general effective Hamiltonian describing the $b\to c\tau \nu$ transition, which consists of the full set of the four-fermion operators. We then obtain experimental constraints on the Wilson coefficients corresponding to each operator and provide predictions for the branching fractions and other polarization observables in different new physics scenarios.

We study possible new physics (NP) effects in the exclusive decays ${\overline{B}}^0\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }$. We extend the Standard Model by taking into account right-handed vector (axial), left- and right-handed (pseudo)scalar, and tensor current contributions. The ${\overline{B}}^0\to D^{(*)}$ transition form factors are calculated in the full kinematic $q^2$ range by employing a covariant quark model developed by us. We provide constraints on NP operators based on measurements of the ratios of branching fractions $R(D^{(*)})\equiv \mathcal{B}({\overline{B}}^0\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}({\overline{B}}^0\to D^{(*)}{\mu }^{-}{\overline{\nu }}_{\mu })$ and consider the effects of these operators on physical observables in different NP scenarios. We also derive the fourfold angular distribution for the cascade decay ${\overline{B}}^0\to D^{*+}(\to D^0{\pi }^{+}){\tau }^{-}{\overline{\nu }}_{\tau }$ which allows one to analyze the polarization of the $D^{*}$ meson in the presence of NP effects. We discuss several strategies to distinguish between various NP contributions.

We study the longitudinal, transverse, and normal polarization components of the tau lepton in the decays ${\overline{B}}^0\to D^{(*)}{\tau }^{-}{\overline{\nu }}_{\tau }$ and discuss their role in searching for new physics (NP) beyond the standard model (SM). Starting with a model-independent effective Hamiltonian including non-SM four-Fermi operators, we obtain experimental constraints on different NP scenarios and investigate their effects on the polarization observables. In the SM the longitudinal and transverse polarizations of the tau lepton differ substantially from the corresponding zero lepton mass values of $P_L=-1$ and $P_T=0$. In addition, $P_L$ and $P_T$ are very sensitive to NP effects. For the transverse polarization this holds true, in particular, for the effective tensor operator in the case of ${\overline{B}}^0\to D^{*}$ and for the scalar operator in the case of ${\overline{B}}^0\to D$. The $T$-odd normal polarization $P_N$, which is predicted to be negligibly small in the SM, can be very sizable assuming NP complex Wilson coefficients. We also discuss in some detail how the three polarization components of the tau lepton can be measured with the help of its subsequent leptonic and semihadronic decays.

Inspired by recent improved measurements of charm semileptonic decays at BESIII, we study a large set of $D(D_s)$-meson semileptonic decays where the hadron in the final state is one of $D^0$, $\rho$, $\omega$, ${\eta }^{(\prime )}$ in the case of $D^{+}$ decays, and $D^0$, $\varphi$, $K^0$, $K^{*}(892{)}^0$, ${\eta }^{(\prime )}$ in the case of $D_s^{+}$ decays. The required hadronic form factors are computed in the full kinematical range of momentum transfer by employing the covariant confined quark model developed by us. A detailed comparison of the form factors with those from other approaches is provided. We calculate the decay branching fractions and their ratios, which show good agreement with available experimental data. We also give predictions for the forward-backward asymmetry and the longitudinal and transverse polarizations of the charged lepton in the final state.

We study the exclusive leptonic and semileptonic $B$ decays $B\to {\ell }^{-}{\overline{\nu }}_{\ell }$ and $B\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$ in the framework of the covariant quark model with built-in infrared confinement. We compute the relevant form factors in the full kinematical momentum transfer region. The calculated form factors are used to evaluate branching fractions and polarization observables of the above transitions. We compare our results with experimental data and results from other theoretical studies.