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

TL;DR

This paper analyzes the $B o D\,\ell\nu$ transition form factors using a light-front quark model, showing that certain form factors can be computed without treacherous contributions and comparing results with experimental data.

Contribution

It demonstrates that the $f_-(q^2)$ form factor can be obtained consistently without treacherous contributions in the standard LFQM, challenging common beliefs.

Findings

Form factors agree with experimental data for most decays.

Branching ratios are consistent with experiments except for $B^0\to D^-\tau\nu_\tau$.

The ratio ${\cal R}(D)$ aligns with experimental and theoretical predictions.

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 $(J^+, {\bf J}_\perp)$. 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.