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

TL;DR

This paper analyzes the semileptonic B decay into two pions and a lepton, extracting the CKM matrix element |V_ub| and predicting the non-resonant branching fraction using recent experimental data.

Contribution

It provides a new extraction of |V_ub| and determines non-resonant B→ππ transition form factors based on recent measurements, offering predictions for upcoming experiments.

Findings

|V_ub| = (3.31 ± 0.61)×10^{-3}

Predicted non-resonant branching fraction ≈ 3.5×10^{-5}

Determined non-resonant B→ππ form factors

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.