R. Cousins

We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confidence intervals if the choice is based on the data. We apply the construction to two related problems which have recently been a battleground between classical and Bayesian statistics: Poisson processes with background and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construction avoids unphysical confidence intervals. In contrast with some popular Bayesian intervals, our intervals eliminate conservatism (frequentist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experiments searching for neutrino oscillations. We show that this technique both gives correct coverage and is powerful, while other classical techniques that have been used by neutrino oscillation search experiments fail one or both of these criteria.

We have studied the muon neutrino and antineutrino quasi-elastic (QEL) scattering reactions (ν μ n→μ − p and $\bar{\nu }_{\mu}p\to\mu^{+}n$ ) using a set of experimental data collected by the NOMAD Collaboration. We have performed measurements of the cross-section of these processes on a nuclear target (mainly carbon) normalizing it to the total ν μ ( $\bar{\nu}_{\mu}$ ) charged-current cross section. The results for the flux-averaged QEL cross sections in the (anti)neutrino energy interval 3–100 GeV are $\langle \sigma_{\mathrm{qel}}\rangle_{\nu_{\mu}}=(0.92\pm0.02(\mathrm{stat})\pm0.06(\mathrm{syst}))\times10^{-38}~\mathrm{cm}^{2}$ and $\langle\sigma_{\mathrm{qel}}\rangle_{\bar{\nu}_{\mu}}=(0.81\pm0.05(\mathrm{stat})\pm0.09(\mathrm{syst}))\times10^{-38}~\mathrm{cm}^{2}$ for neutrino and antineutrino, respectively. The axial mass parameter M A was extracted from the measured quasi-elastic neutrino cross section. The corresponding result is M A =1.05±0.02(stat)±0.06(syst) GeV. It is consistent with the axial mass values recalculated from the antineutrino cross section and extracted from the pure Q 2 shape analysis of the high purity sample of ν μ quasi-elastic 2-track events, but has smaller systematic error and should be quoted as the main result of this work. Our measured M A is found to be in good agreement with the world average value obtained in previous deuterium filled bubble chamber experiments. The NOMAD measurement of M A is lower than those recently published by K2K and MiniBooNE Collaborations. However, within the large errors quoted by these experiments on M A , these results are compatible with the more precise NOMAD value.

We present the results of a search for νμ→νe oscillations in the NOMAD experiment at CERN. The experiment looked for the appearance of νe in a predominantly νμ wide-band neutrino beam at the CERN SPS. No evidence for oscillations was found. The 90% confidence limits obtained are Δm2<0.4 eV2 for maximal mixing and sin2(2θ)<1.4×10−3 for large Δm2. This result excludes the LSND allowed region of oscillation parameters with Δm2≳10 eV2.