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

Abstract

We employ the $B\toπ$ form factors obtained from QCD light-cone sum rules and calculate the $B\to π\ell ν_l$ width ($\ell=e,μ$) 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 $B\to π\ellν_\ell$. We also present the charged lepton energy spectrum in this decay. Furthermore, the current situation with $B\to τν_τ$ is discussed from the QCD point of view. We suggest to use the ratio of the $B\to πτν_τ$ and $B\to π\ell ν_l ~(\ell =μ,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.