A New calculation of the atmospheric neutrino flux in a 3-dimensional   scheme
  We have revised the calculation of the flux of atmospheric neutrinos based on a 3-dimensional scheme with the realistic IGRF geomagnetic model. The primary flux model has been revised, based on the AMS and BESS observations, and the interaction model updated to DPMJET-III. With a fast simulation code and computer system, the statistical errors in the Monte Carlo study are negligible. We estimate the total uncertainty of the atmospheric neutrino flux prediction is reduced to $\lesssim$ 10 % below 10 GeV. The `3-dimensional effects' are found to be almost the same as the study with the dipole magnetic field, but the muon curvature effect remains up to a few 10 GeV for horizontal directions. The uncertainty of the absolute normalization of the atmospheric neutrino is still large above 10 GeV due to the uncertainty of the primary cosmic ray flux above 100 GeV. However, the zenith angle variation is not affected by these uncertainties. 
M.Honda, T.Kajita, K.Kasahara, S.Midorikawa