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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 haveperformed measurements of the cross-section of these processes on a nucleartarget (mainly Carbon) normalizing it to the total $\nu_\mu$ ($\bar{\nu}_\mu$)charged current cross-section. The results for the flux averaged QELcross-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. Theaxial mass parameter $M_A$ was extracted from the measured quasi-elasticneutrino 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 recalculatedfrom the antineutrino cross-section and extracted from the pure $Q^2$ shapeanalysis 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 ofthis work. Our measured $M_A$ is found to be in good agreement with the worldaverage value obtained in previous deuterium filled bubble chamber experiments.The NOMAD measurement of $M_A$ is lower than those recently published by K2Kand MiniBooNE collaborations. However, within the large errors quoted by theseexperiments on $M_A$, these results are compatible with the more precise NOMADvalue.

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