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 $\mathcal{B}(B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell })=(3.5\pm 1.4_{-2.4}^{+4.3})\times 10^{-5}$, which is accessible to the BELLEII and LHCb experiments.

Comments: 10 pages, 4 figures, 1 table