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 > /2M and (< Q > +M ∆ − M)/2M respectively. These predictions seem to agree with the observed muon spectra in the K2K nearby detector. The corresponding muon spectra in the faraway (SK) detector are predicted to show characteristic spectral distortions induced by νμ 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. Recently the KEK to Kamioka long-baseline neutrino oscillation experiment (K2K) has published its result [1], which confirms the existence of νμ oscillation as seen in the Super-Kamiokande (SK) atmospheric neutrino data [2]. It uses an accelerator-produced νμ beam, which has a peak energy of 1.2 GeV and a spread of about 1 GeV on either side – the full width at half maximum being ∼ 1 GeV [1, 3]. The beam passes through a nearby neutrino detector (ND), comprising of a 1 kiloton water Cerenkov (1KT) and a finegrained detector (FGD) system, and then travels a distance of 250 km to enter the SK 50 kiloton water Cerenkov detector. The chargedand neutral-current event rates measured in the ND are used to predict the corresponding event rates at the SK detector in terms of the oscillation parameters. They report 56 fully contained (FC) events against the expectation of 80 without oscillation. The observed deficit agrees well with the neutrino mass and mixing angles deduced from the atmospheric neutrino oscillation data [2] sin 2θ ≃ 1 and ∆m ≃ 3× 10eV . (1) We estimate that the QE, 1-pion production and multi-pion events constitute 35%, 50% and 15% at Eν = 1.2GeV. In this region the ∆(1232) resonance contribution accounts for 80 − 90% of the 1-pion events [4], with the remainder produced from the P11(1440), S11(1535) and D13(1520) resonances. In this note we use kinematic considerations to predict the muon energy spectra of the QE and 1-Pion resonance production events which constitute the bulk of the chargedcurrent νμ scattering events in the K2K experiment. These predictions can be checked with the observed muon energy spectra from the ND. We also present the distortion of these muon spectra due to νμ oscillation, which one expects to see at the SK detector. Comparison of the predicted muon spectra with those of the observed QE and 1-Pion events at the SK detector will be very useful in determining the oscillation parameters. Since the ∆ resonance width of 120 MeV is very small compared to the spread of the ν beam energy, one can make a narrow resonance approximation for ∆. A common property