Improved Constraints on $B \to \pi\ell \bar\nu_{\ell}$ Form Factors

Abstract

The behavior of the $\bpi$ form factors in the entire physical range is examined in a model independent way. Unitarity bounds are further constrained by the lattice results (APE). From this analysis, we obtain $f^{+}(0) = 0.38 \pm .03$ if the $B^{*}$-pole dominance behavior is assumed. However, to get the information on the behavior of the form factor $f^{+}$, QSR results are included. We see the deviations from the pole dominance due to the contributions of the higher singularities which are to be treated with more precise lattice data.