Semileptonic decays $B\to(\pi,\rho)e\nu$ in relativistic quark model

Abstract

Quark model results for the $B\to \pi,\rho$ decays are analysed, making use of the dispersion formulation of the model: The form factors at $q^2>0$ are expressed as relativistic invariant double spectral representation over invariant masses of the initial and final mesons through their light--cone wave functions. The dependence of the results on the quark model parameters is studied. For various versions of the quark model the ranges $\Gamma(\bar B^0\to\pi^+e\bar\nu)=(7\pm2)\times10^{12}|V_{ub}|^2\; s^{-1}$, $\Gamma(\bar B^0\to\rho^+e\bar\nu)/\Gamma(\bar B^0\to\pi^+e\bar\nu)=1.45\pm0.1$, and $\Gamma_L/\Gamma_T=0.7\pm0.08$ are found. The effects of the constituent quark transition form factor are briefly discussed.