Semileptonic $B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell$ decay with $\pi\pi$ invariant mass spectrum

Abstract

BELLE has recently reported the measurement of the branching fraction of the semileptonic $B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell$ decay, where $\ell$ represents an electron or a muon. With the new information on the $\pi\pi$ invariant mass spectrum, we extract $|V_{ub}|=(3.31\pm 0.61)\times 10^{-3}$ in agreement with those from the other exclusive $B$ decays. In particular, we determine the non-resonant $B\to\pi\pi$ transition form factors, and predict the non-resonant branching fraction ${\cal B}(B^{-}\to\pi^{+}\pi^{-}\ell^{-}\bar\nu_\ell)=(3.5\pm 1.4^{+4.3}_{-2.4})\times 10^{-5}$, which is accessible to the BELLEII and LHCb experiments.