Reduction of the uncertainty in the atmospheric neutrino flux prediction below 1 GeV using accurately measured atmospheric muon flux

We examine the uncertainty of the calculation of the atmospheric neutrino flux and present a way to reduce it using accurately measured atmospheric muon flux. Considering the difference of the hadronic interaction model and the real one as a variation of hadronic interaction, we find a quantitative estimation method for the error of the atmospheric neutrino flux calculation from the residual of the reconstruction of the atmospheric muon flux observed in a precision experiment, by the study of atmospheric neutrino and muon fluxes response to the variation of hadronic interaction. However, the efficiencty of this method is largely dependent on the observation site of the atmospheric muon flux, as the relation of the error of the atmospheric neutrino flux calculation and the residual of the reconstruction of the atmospheric muon flux is also largely dependent on the muon observation site, especially for the low energy neutrinos. We calculate several observation sites, near Kamioka at sea level, same but 2770m a.s.l.., Hanle India (4500m a.s.l.), and at Balloon altitude ($\sim$ 32km). Then we estimate how stringently can the atmospheric muon reduce the error in the calculation of the atmospheric neutrino flux. We also discuss on the source of error which is difficult to reduce by only the observation of atmospheric muon.