Muon Spectra of Quasi-Elastic and 1-Pion Production Events in LBL Neutrino Oscillation Experiments

The muon energy spectra of the quasi-elastic and 1-pion production events in a LBL experiment, like K2K, are predicted to follow closely the neutrino energy spectrum, with downward shifts of the energy scale by $<Q^2>/2 M$ and $(<Q^2> + M_\Delta^2 - M^2)/2 M$ respectively. These predictions seem to agree with the observed muon spectra in the K2K nearby detector. The corresponding muon spectra in the far-away (SK) detector are predicted to show characteristic spectral distortions induced by $\nu_\mu$ oscillation. Comparison of the predicted spectral distortions with the observed muon spectra of the 1-Ring and 2-Ring muon events in the SK detector will help to determine the oscillation parameters. The results will be applicable to other LBL experiments as well.