Current-component independent transition form factors for semileptonic and rare $D\to \pi(K)$ decays in the light-front quark model

We investigate the exclusive semileptonic and rare $D\to \pi(K)$ decays within the standard model together with the light-front quark model (LFQM) constrained by the variational principle for the QCD-motivated effective Hamiltonian. The form factors are obtained in the $q^+=0$ frame and then analytically continue to the physical timelike region. Together with our recent analysis of the current-component independent form factors $f_\pm(q^2)$ for the semileptonic decays, we present the current-component independent tensor form factor $f_T(q^2)$ for the rare decays to make the complete set of hadronic matrix elements regulating the semileptonic and rare $D\to\pi(K)$ decays in our LFQM. The tensor form factor $f_T(q^2)$ are obtained from two independent sets $(J^{+\perp}_T, J^{+-}_T)$ of the tensor current $J^{\mu\nu}_T$. As in our recent analysis of $f_-(q^2)$, we show that $f_T(q^2)$ obtained from the two different sets of the current components gives the identical result in the valence region of the $q^+=0$ frame without involving the explicit zero modes and the instantaneous contributions. The implications of the zero modes and the instantaneous contributions are also discussed in comparison between the manifestly covariant model and the standard LFQM. In our numerical calculations, we obtain the $q^2$-dependent form factors $(f_\pm, f_T)$ for $D\to\pi(K)$ and branching ratios for the semileptonic $D\to \pi(K)\ell\nu_\ell$ ($\ell=e,\mu$) decays. Our results show in good agreement with the available experimental data as well as other theoretical model predictions.