Heavy-to-heavy and heavy-to-light weak decay form factors in the light-front approach: the exclusive $ 0^- $ to $ 0^- $ case

Weak transition form factors among heavy pseudoscalar mesons are investigated within a relativistic quark model formulated on the light-front. It is shown that the light-front result derived in the time-like region for the matrix elements of the plus component of the weak vector current coincides with the spectator pole term of the quark triangle diagram. For the first time, the dependence of the form factors on the squared four-momentum transfer $q^2$ is calculated in the whole accessible kinematical region $0 \leq q^2 \leq q^2_{max}$. For the numerical investigations of the semileptonic $B \to D \ell \nu_{\ell}$, $B \to \pi \ell \nu_{\ell}$, $D \to K \ell \nu_{\ell}$ and $D \to \pi \ell \nu_{\ell}$, the equal-time wave functions corresponding to the updated version of the ISGW model are adopted. Our results for the form factors and the decay rates are presented and compared with available experimental data and predictions of different approaches. Moreover, the $K^0_L \to \pi^{\pm} ~ e^{\mp} ~ \nu_e$ decay is briefly discussed. Our approach is consistent with experimental data.