Comparison of 3-dimensional and 1-dimensional schemes in the calculation of atmospheric neutrinos

A 3-dimensional calculation of atmospheric neutrino flux is presented, and the results are compared with those of a 1-dimensional calculation. In this study, the interaction and propagation of particles is treated in a 3-dimensional way including the curvature of charged particles due to the geomagnetic field, which is assumed to be a dipole field. The purpose of this paper is limited to the comparison of calculation schemes. The updated flux value with a new interaction model and primary flux model will be reported in a separate paper. Except for nearly horizontal directions, the flux is very similar to the result of 1-dimensional calculations. However, for near-horizontal directions an enhancement of the neutrino flux is seen even at energies as high as 1 GeV. The production height of neutrinos is lower than the prediction of the 1-dimensional calculation for near-horizontal directions, and is a little higher for near-vertical directions. However, the difference is not evident except for near-horizontal directions.