The first direct measurement of electron-neutrino quasielastic and quasielastic-like scattering on hydrocarbon in the few-GeV region of incident neutrino energy has been carried out using the MINERvA detector in the NuMI beam at Fermilab. The flux-integrated differential cross sections in electron production angle, electron energy and $Q^{2}$ are presented. The ratio of the quasielastic, flux-integrated differential cross section in $Q^{2}$ for $\nu_{e}$ with that of similarly-selected $\nu_{\mu}$-induced events from the same exposure is used to probe assumptions that underpin conventional treatments of charged-current $\nu_{e}$ interactions used by long-baseline neutrino oscillation experiments. The data are found to be consistent with lepton universality and are well-described by the predictions of the neutrino event generator GENIE.
The $\nu_{e}+\bar{\nu}_{e}$ flux as a function of neutrino energy from the beam simulation for the data used in this analysis. The $\bar{\nu}_{e}$ fraction is shown separately to emphasize the dominance of $\nu_{e}$ in the sum.
Flux-integrated differential $\nu_{e}$ CCQE-like cross section versus electron energy.
Covariance matrix for flux-integrated differential $\nu_{e}$ CCQE-like cross section versus electron energy.
The first measurements of differential branching fractions of inclusive semileptonic ${B \to X_u \, \ell^+\, \nu_{\ell}}$ decays are performed using the full Belle data set of 711 fb$^{-1}$ of integrated luminosity at the $\Upsilon(4S)$ resonance and for $\ell = e, \mu$. Differential branching fractions are reported as a function of the lepton momentum, the four-momentum-transfer squared, light-cone momenta, the hadronic mass, and the hadronic mass squared. They are obtained by subtracting the backgrounds from semileptonic ${B \to X_c \, \ell^+\, \nu_{\ell}}$ decays and other processes, and corrected for resolution and acceptance effects. The measured distributions are compared to predictions from inclusive and hybrid ${B \to X_u \, \ell^+\, \nu_{\ell}}$ calculations.
The measured differential branching fractions as a function of the lepton energy in the $B$ rest frame ($E_\ell^B$).
The measured differential branching fractions as a function of the four-momentum-transfer squared of the $B$ to the $X_u$ system $q^{2}$.
The measured differential branching fractions as a function of the invariant hadronic mass of the $X_u$ system ($M_X$).