Self-consistent light-front quark model analysis of $B\to D\ell {\nu }_{\ell }$ transition form factors

Abstract

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 $(J^{+},{\mathbf{J}}_{\perp })$. 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 $(J^{+},{\mathbf{J}}_{\perp })$ 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 $\mathrm{Br}(B\to D\ell {\nu }_{\ell })$ show reasonable agreement with the experimental data except for the semitauonic $B^0\to D^{-}\tau {\nu }_{\tau }$ decay. The ratio $\mathcal{R}(D)=\frac{\mathrm{Br}(B\to D\tau {\nu }_{\tau })}{\mathrm{Br}(B\to D{\ell }^{\prime }{\nu }_{{\ell }^{\prime }})}$ $({\ell }^{\prime }=e,\mu )$ is also estimated and compared with the experimental data as well as other theoretical predictions.

10 pages, 3 figures, minor corrections in Sec. IV, version to appear in Phys. Rev. D

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