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We examine the uncertainty of the calculation of the atmospheric neutrino flux and present a way to reduce it using accurately measured atmospheric muon flux. Considering the difference of the hadronic interaction model and the real one as a variation of hadronic interaction, we find a quantitative estimation method for the error of the atmospheric neutrino flux calculation from the residual of the reconstruction of the atmospheric muon flux observed in a precision experiment, by the study of atmospheric neutrino and muon fluxes response to the variation of hadronic interaction. However, the efficiencty of this method is largely dependent on the observation site of the atmospheric muon flux, as the relation of the error of the atmospheric neutrino flux calculation and the residual of the reconstruction of the atmospheric muon flux is also largely dependent on the muon observation site, especially for the low energy neutrinos. We calculate several observation sites, near Kamioka at sea level, same but 2770m a.s.l.., Hanle India (4500m a.s.l.), and at Balloon altitude ($\sim$ 32km). Then we estimate how stringently can the atmospheric muon reduce the error in the calculation of the atmospheric neutrino flux. We also discuss on the source of error which is difficult to reduce by only the observation of atmospheric muon., Comment: 14 pages, 30 fugures

In this paper, we extend the calculation of the atmospheric neutrino flux~\cite{hkkm2004,hkkms2006,hkkm2011} to the sites in polar and tropical regions. In our earliest full 3D-calculation~\cite{hkkm2004}, we used DPMJET-III~\cite{dpm} for the hadronic interaction model above 5~GeV, and NUCRIN~\cite{nucrin} below 5~GeV. We modified DPMJET-III as in Ref.~\cite{hkkms2006} to reproduce the experimental muon spectra better, mainly using the data observed by BESS group~\cite{BESSTeVpHemu}. In a recent work~\cite{hkkm2011}, we introduced JAM interaction model for the low energy hadronic interactions. JAM is a nuclear interaction model developed with PHITS (Particle and Heavy-Ion Transport code System)~\cite{phits}. In Ref.~\cite{hkkm2011}, we could reproduce the observed muon flux at the low energies at balloon altitude with DPMJET-III above 32 GeV and JAM below that better than the combination of DPMJET-III above 5~GeV and NUCRIN below that. Besides the interaction model, we have also improved the calculation scheme according to the increase of available computational power, such as the "virtual detector correction" introduced in Ref.~\cite{hkkms2006} and the optimization of it in Ref.~\cite{hkkm2011}. The statistics of the Monte Carlo simulation is also improved at every step of the work., Comment: 25 pages, 16 figures

We present the calculation of the atmospheric neutrino fluxes for the neutrino experiments proposed at INO, South Pole and Pyh\"asalmi. Neutrino fluxes have been obtained using ATMNC, a simulation code for cosmic ray in the atmosphere. Even using the same primary flux model and the interaction model, the calculated atmospheric neutrino fluxes are different for the different sites due to the geomagnetic field. The prediction of these fluxes in the present paper would be quite useful in the experimental analysis., Comment: 12Pages,9Figs

Using the ``modified DPMJET-III'' model explained in the previous paper, we calculate the atmospheric neutrino flux. The calculation scheme is almost the same as HKKM04 \cite{HKKM2004}, but the usage of the ``virtual detector'' is improved to reduce the error due to it. Then we study the uncertainty of the calculated atmospheric neutrino flux summarizing the uncertainties of individual components of the simulation. The uncertainty of $K$-production in the interaction model is estimated by modifying FLUKA'97 and Fritiof 7.02 so that they also reproduce the atmospheric muon flux data correctly, and the calculation of the atmospheric neutrino flux with those modified interaction models. The uncertainties of the flux ratio and zenith angle dependence of the atmospheric neutrino flux are also studied.

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

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., Comment: 31 pages, 19 figures, submitted to Phys. Rev. D

Precise knowledge of the hadronic interaction between primary cosmic rays and atmospheric nuclei is very important and fundamental to study atmospheric neutrinos and their oscillations. We studied hadronic interaction models using the data of primary and secondary cosmic rays observed by BESS experiments. By comparing the observed spectra with the ones calculated by several interaction models, we found DPMJET-III is most favored among them., Comment: 4 pages, 5 figures, a revise of the previous work, the proceeding of ICRC2003

We observed atmospheric gamma-rays around 10 GeV at balloon altitudes (15~25 km) and at a mountain (2770 m a.s.l). The observed results were compared with Monte Carlo calculations to find that an interaction model (Lund Fritiof1.6) used in an old neutrino flux calculation was not good enough for describing the observed values. In stead, we found that two other nuclear interaction models, Lund Fritiof7.02 and dpmjet3.03, gave much better agreement with the observations. Our data will serve for examining nuclear interaction models and for deriving a reliable absolute atmospheric neutrino flux in the GeV region., Comment: 9 pages 12 figures

A 3-dimensional calculation of atmospheric neutrinos flux is presented, and the results are compared with those of a 1-dimensional one. In this study, 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 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 by 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., Comment: 22 pages, 15figures

We compare several different calculations of the atmospheric neutrino flux in the energy range relevant for contained neutrino interactions, and we identify the major sources of difference among the calculations. We find nothing that would affect the predicted ratio of $\nu_e/\nu_\mu$, which is nearly the same in all calculations. Significant differences in normalization arise primarily from different treatment of pion production by interactions of protons in the atmosphere. Different assumptions about the primary spectrum and treatment of the geomagnetic field are also of some importance., Comment: 15 pages, RevTeX , 5 postscript figures, submitted to Phys. Rev. D

The atmospheric neutrino-flux is calculated over the wide energy range from 1 GeV to 3,000 GeV for the study of neutrino-physics using the data from underground neutrino-detectors. The uncertainty of atmospheric neutrino-flux is also discussed. A brief comment is made to interpret the anomaly in terms of neutrino oscillations., Comment: 8 pages, PTPTEX.sty, to appear in Proceedings of YKIS '95, From the Standard Model to Grand Unified Theories

Atmospheric neutrino-fluxes are calculated over the wide energy range from 30 MeV to 3,000 GeV for the study of neutrino-physics using the data from underground neutrino-detectors. The atmospheric muon-flux at high altitude and at sea level is studied to calibrate the neutrino-fluxes at low energies and high energies respectively. The agreement of our calculation with observations is satisfactory. The uncertainty of atmospheric neutrino-fluxes is also studied., Comment: 51 pages