Form factors of exclusive $b\to u$ transitions

Abstract

We present the form factors of the $B\to \pi ,\rho$ transitions induced by the $b\to u$ quark currents at all kinematically accessible $q^2$. Our analysis is based on the spectral representations of the form factors within the constituent quark picture: we fix the soft meson wave functions and the constituent quark masses by fitting $A_1(q^2)$ and $T_2(q^2)$ to the lattice results at small recoils ($17\lesssim q^2\lesssim 20Ge{V}^2$). We then calculate the $B\to \pi ,\rho$ transition form factors down to $q^2=0$. For the $B\to \pi$ case the region $q^2\lesssim 20Ge{V}^2$ however does not cover the whole kinematically accessible range. Due to the smallness of the pion mass the region of small recoils is close to the nearby $B^{\ast }(5234)$ resonance. We develop a parametrization which includes the $B^{\ast }$ dominance of the form factors $f_{+}$ and $f_{-}$ at small recoils and numerically reproduces the results of calculations at $q^2\lesssim 20Ge{V}^2$. We find $\Gamma (B\to \pi \ell \nu )=8.0_{-0.2}^{+0.8}|V_{ub}{|}^2$ps${}^{-1}$ and $\Gamma (B\to \rho \ell \nu )=15.8\pm 2.3|V_{ub}{|}^2$ps${}^{-1}$.

revtex, 6 pages, 1 figure

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