Self-consistent light-front quark model analysis of $B\to D\ell\nu_\ell$ transition form factors

We investigate the transition form factors $f_+(q^2)$ and $f_-(q^2)$ [or $f_0(q^2)$] for the exclusive semileptonic $B\to D\ell\nu_\ell$ $(\ell=e, \mu,\tau)$ decays in the standard light-front quark model (LFQM) based on the LF quantization. The common belief is that while $f_+(q^2)$ can be obtained without involving any treacherous contributions such as the zero mode and the instantaneous contribution, $f_-(q^2)$ receives those treacherous contributions since it involves at least two components of the current, e.g. $(J^+, J^-)$ or $(J^+, {\bf J}_\perp)$. Contrary to the common belief, we show in the Drell-Yan ($q^+=0$) frame that $f_-(q^2)$ obtained from $(J^+, J^-)$ gives identical result to $f_-(q^2)$ obtained from $(J^+, {\bf J}_\perp)$ without involving such treacherous contributions in the standard LFQM. In our numerical calculations, we obtain the form factors and branching ratios for $B\to D\ell\nu_\ell$ $(\ell=e, \mu,\tau)$ and compare with the experimental data as well as other theoretical model predictions. Our results for ${\rm Br}(B\to D\ell\nu_\ell)$ show reasonable agreement with the experimental data except for the semitauonic $B^0\to D^-\tau\nu_\tau$ decay. The ratio ${\cal R}(D)=\frac{{\rm Br}(B\to D\tau\nu_\tau)}{{\rm Br}(B\to D\ell'\nu_{\ell'})}$ $(\ell'=e,\mu)$ is also estimated and compared with the experimental data as well as other theoretical predictions.