A 3-dimensional calculation of the atmospheric neutrino fluxes

An extensive 3-dimensiona] MolUe Carlo calculation of the atmospheric neutrino flux is in progress with the FLUKA Monte Carlo code. The results are compared to those obtained under the 1-dimensional approximation, where secondary particles and decay products are assumed to be collinear lo the primary cosmic ray, as usually done in most of the already existing flux calculations. It is shown that the collinear approximation gives rise to a wrong angular distribution of neutrinos, essentially in the Sub-GeV region. However, the angular smearing introduced by the experimental inability of detecting recoils in neutrino interactions with nuclei is large enough to wash out, in practice, most of the differences between 3-dimensional and 1-dimensional flux calculations. Therefore, the use of the collinear approximation should not have introduced a significant bias in the determination of the flavor oscillation parameters in current experiments.