$B\to \pi \ell {\nu }_l$ 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, $0\le q^2\le 12.0Ge{V}^2$. Using the most recent BABAR-collaboration measurements we extract $|V_{ub}|=(3.50_{-0.33}^{+0.38}{|}_{th.}\pm 0.11{|}_{exp.})\times 10^{-3}$. 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.

22 pages, 8 figures; comments added in section 4, version to be published in Phys. Rev. D

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