Measurement of the $B^0\to X_u^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ decays near the kinematic endpoint of the lepton spectrum and search for violation of isospin symmetry

We present the first measurement of the $B^0\to X_u^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ partial branching fraction in the end-point region of the lepton momentum spectrum, above the threshold for $B\to X_c\mathrm{\ell }{\nu }_{\mathrm{\ell }}$ decays. The analysis is based on a sample of 383 million $\mathrm{{\rm Y}}(4S)$ decays into $B{\bar B}$pairscollectedwiththe\text{sc}BaBardetectoratthePEP-II$e^+e^-$storagerings\mathrm{.}Weselect$B^0{\bar B}^0$eventsbypartiallyreconstructingone$\B$mesonviathe${\bar B}^0\to D^{*+} \ell^- \bar{\nu}\ell$ decays then select $B^0\to X_u^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ decays identifying a second high momentum lepton. In the momentum interval ranging from 2.3 to 2.6 GeV/c we measure the partial branching fraction $\Delta{\cal B}(B^0\to X_u\ell\nu)=(1.30\pm0.21{stat}\pm0.07_{syst})\times 10^{-4}$ where the first error is statistical and the second is systematic. By comparing this measurement with the one obtained from untagged B decays we obtain $R^{+/0}=\Delta{\cal B}(B^0\to X_u\ell\nu)/\Delta{\cal B}(B^+\to X_u\ell\nu)= 1.18 \pm 0.35_{stat} \pm 0.17_{syst}$. Using this measurement we extract a limit on the contributions from processes breaking isospin symmetry in charmless semileptonic B decays.