Differences in Quasi-Elastic Cross-Sections of Muon and Electron Neutrinos

Accelerator neutrino oscillation experiments seek to make precision measurements of the neutrino flavor oscillations muon (anti)neutrino to electron (anti)neutrino in order to determine the mass hierarchy of neutrinos and to search for CP violation in neutrino oscillations. These experiments are currently performed with beams of muon neutrinos at energies near 1 GeV where the charged-current quasi-elastic interactions nu+n\rightarrow(l^-)+p and anti-nu+p\rightarrow(l^+)+n dominate the signal reactions. We examine the difference between the quasi-elastic cross-sections for muon and electron neutrinos and anti-neutrinos and estimate the uncertainties on these differences.