Current-Component Independent Transition Form Factors for Semileptonic and Rare D ⟶ π K Decays in the Light-Front Quark Model

We investigate the exclusive semileptonic and rare $D⟶\pi \left(K\right)$ 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 $f_{\pm }\left(q^2\right)$ for the semileptonic decays, we present the current-component independent tensor form factor $f_T\left(q^2\right)$ for the rare decays to make the complete set of hadronic matrix elements regulating the semileptonic and rare $D⟶\pi \left(K\right)$ decays in our LFQM. The tensor form factor $f_T\left(q^2\right)$ are obtained from two independent sets $\left(J_T^{+\perp },J_T^{+-}\right)$ of the tensor current $J_T^{uv}$ . As in our recent analysis of $f_{-}\left(q^2\right)$ , we show that $f_T\left(q^2\right)$ 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 instantaneou