Study of cosmic ray interaction model based on atmospheric muons for the   neutrino flux calculation
  We have studied the hadronic interaction for the calculation of the atmospheric neutrino flux by summarizing the accurately measured atmospheric muon flux data and comparing with simulations. We find the atmospheric muon and neutrino fluxes respond to errors in the $\pi$-production of the hadronic interaction similarly, and compare the atmospheric muon flux calculated using the HKKM04 code with experimental measurements. The $\mu^++\mu^-$ data show good agreement in the 1$\sim$30 GeV/c range, but a large disagreement above 30 GeV/c. The the $\mu^+/\mu^-$ ratio shows sizable differences at lower and higher momenta for opposite directions. As the disagreements are considered to be due to assumptions in the hadronic interaction model, we try to improve it phenomenologically based on the quark parton model. The improved interaction model reproduces the observed muon flux data well. The calculation of the atmospheric neutrino flux will be reported in the following paper 
T. Sanuki, M. Honda, T. Kajita, K. Kasahara, and S. Midorikawa