Measurement of the Branching Fraction of the Decay $boldsymbol{B^{+}topi^{+}pi^{-}ell^{+} u_ell}$ in Fully Reconstructed Events at Belle

We present an analysis of the exclusive $B^{+}topi^{+}pi^{-}ell^{+} u_{ell}$ decay, where $ell$ represents an electron or a muon, with the assumption of charge-conjugation symmetry and lepton universality. The analysis uses the full $Upsilon(4S)$ 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 ${{cal B}(B^{+}to pi^{+}pi^{-}ell^{+} u_{ell})= [22.7 ^{+1.9}_{-1.6} (mathrm{stat}) pm 3.5(mathrm{syst}) ]times 10^{-5}}$, where the uncertainties are statistical and systematic, respectively. This result is the first reported measurement of this decay.