A study of quasi-elastic muon neutrino and antineutrino scattering in the NOMAD experiment

We have studied the muon neutrino and antineutrino quasi-elastic (QEL) scattering reactions (${\nu }_{\mu }n\to {\mu }^{-}p$ 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 ${\nu }_{\mu }$ (${\bar{\nu }}_{\mu }$) charged current cross-section. The results for the flux averaged QEL cross-sections in the (anti)neutrino energy interval 3-100 GeV are $\sigma^{qel}{\nu\mu} = (0.92 \pm 0.02 (stat) \pm 0.06 (syst))\times 10^{-38} \cm^2$and$\sigma{qel}{\bar{\nu}\mu} = (0.81 \pm 0.05 (stat) \pm 0.08 (syst))\times 10^{-38} \cm^2$ 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 $M_A = 1.05 \pm 0.02 (stat) \pm 0.06 (syst) GeV$. 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 ${\nu }_{\mu }$ 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.