Measurement of the Branching Fraction of the Decay in Fully Reconstructed Events at Belle

We present an analysis of the exclusive $B^{+}\to {\pi }^{+}{\pi }^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ decay, where $\mathrm{\ell }$ represents an electron or a muon, with the assumption of charge-conjugation symmetry and lepton universality. The analysis uses the full $\mathrm{{\rm Y}}(4S)$ data sample collected by the Belle detector, corresponding to 711 fb${}^{-1}$ of integrated luminosity. We select the events by fully reconstructing one $B$ meson in hadronic decay modes, subsequently determining the properties of the other $B$ meson. We extract the signal yields using a binned maximum-likelihood fit to the missing-mass squared distribution in bins of the invariant mass of the two pions or the momentum transfer squared. We measure a total branching fraction of ${{\cal B}(B^{+}\to \pi^{+}\pi^{-}\ell^{+}\nu_{\ell})= [22.7 ^{+1.9}_{-1.6} ($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}$) \pm 3.5($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}$) ]\times 10^{-5}}$, where the uncertainties are statistical and systematic, respectively. This result is the first reported measurement of this decay.