$B \to \pi \ell \nu_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules

Abstract

We employ the $B\to\pi$ form factors obtained from QCD light-cone sum rules and calculate the $B\to \pi \ell \nu_l$ width ($\ell=e,\mu$) in units of $1/|V_{ub}|^2$, integrated over the region of accessible momentum transfers, $0\leq q^2\leq 12.0 ~GeV^2$. Using the most recent BABAR-collaboration measurements we extract $|V_{ub}|=(3.50^{+0.38}_{-0.33}\big|_{th.}\pm 0.11 \big|_{exp.})\times 10^{-3}$. The sum rule results for the form factors, taken as an input for a $z$-series parameterization, yield the $q^2$-shape in the whole semileptonic region of $B\to \pi\ell\nu_\ell$. We also present the charged lepton energy spectrum in this decay. Furthermore, the current situation with $B\to \tau\nu_\tau$ is discussed from the QCD point of view. We suggest to use the ratio of the $B\to \pi \tau\nu_\tau$ and $B\to \pi\ell \nu_l ~(\ell =\mu,e) $ widths as an additional test of Standard Model. The sensitivity of this observable to new physics is illustrated by including a charged Higgs-boson contribution in the semileptonic decay amplitude.