Methods to Determine Neutrino Flux at Low Energies:Investigation of the Low $\nu$ Method

We investigate the "low-$\nu$" method (developed by the CCFR/NUTEV collaborations) to determine the neutrino flux in a wide band neutrino beam at very low energies, a region of interest to neutrino oscillations experiments. Events with low hadronic final state energy $\nu<\nu_{cut}$ (of 1, 2 and 5 GeV) were used by the MINOS collaboration to determine the neutrino flux in their measurements of neutrino ($\nu_\mu$) and antineutrino ($\nub_\mu$) total cross sections. The lowest $\nu_\mu$ energy for which the method was used in MINOS is 3.5 GeV, and the lowest $\nub_\mu$ energy is 6 GeV. At these energies, the cross sections are dominated by inelastic processes. We investigate the application of the method to determine the neutrino flux for $\nu_\mu$, $\nub_\mu$ energies as low as 0.7 GeV where the cross sections are dominated by quasielastic scattering and $\Delta$(1232) resonance production. We find that the method can be extended to low energies by using $\nu_{cut}$ values of 0.25 and 0.50 GeV, which is feasible in fully active neutrino detectors such as MINERvA.