Abstract. We describe the history of theory prediction of inclusive atmospheric neutrino flux shortly, then the 3-dimensional calculation of atmospheric neutrino flux in some detail. With the calculated atmospheric neutrino flux for INO and South Pole, we discuss on the relation of atmospheric neutrino flux and geomagnetic field. We find the full 3-dimensional scheme calculation is necessary for the theory prediction of the atmospheric neutrino flux.
Short history as the introductionThe atmospheric neutrino flux is calculated in the 1-dimensional scheme for long time [1,2]. It is believed that the 1-dimensional scheme calculation is good enough because of the nature of the hadronic interaction and the small muon bending angle in the geomagnetic field ( ∼5 degree) before the decay. Also the 3-dimensional scheme calculation is very inefficient computation compared to the 1dimensional scheme calculation. We had considered it is impossible to complete within a reasonable computation time.These situation continued until Fluka group [3] reported the calculation in a 3-dimensional scheme, limiting the effect of geomagnetic field only to the rigidity cutoff. In this scheme of the calculation, they could reduce the computation time largely, but find a large horizontal enhancement of neutrino flux, which is not seen in the 1-dimensional scheme calculation.The importance of the geomagnetic field in the atmosphere is discussed by Lipari [4] qualitatively, and a 3-dimensional scheme calculation with the geomagnetic field in the atmosphere was carried out by Barr et al. [5], supporting the discussion of Lipari quantitatively. However, they introduced many acceleration technique in their calculation. It is not a full 3-dimensional calculation yet.A calculation a little more close to the full 3-dimensional scheme was carried out by Honda et al. [6], with fast interaction code and virtual detector correction. We illustrate this work and the following developments in this paper.
Calculation SchemeFor the calculation of atmospheric neutrino flux, we need the primary cosmic ray spectra model, the atmosphere model, and the geomagnetic field model, other than the a e-mail: mhonda@icrr.u-tokyo.ac.jp hadronic interaction model. We used the primary flux model based on AMS [7] and BESS [8,9] data shown in Fig. 1 For the 3-dimensional calculation, we assumed the surface of the earth is a sphere with radius of R e =63781.80 km. In addition to the surface of the earth we assumed three more spheres, the injection sphere, the simulation sphere, and the escape sphere. We have taken the radius of the injection sphere as R in j = R e + 100km, and the radius of simulation sphere as R esc = R sim = 3 × R e , and that of escape sphere as R esc = R sim = 10 × R e =63781.80 km EPJ Web of Conferences