Improvement of low energy atmospheric neutrino flux calculation using the JAM nuclear interaction model

We present the calculation of the atmospheric neutrino fluxes with an interaction model named JAM, which is used in PHITS (Particle and Heavy-Ion Transport code System) [K. Niita et al., Radiation Measurements 41, 1080 (2006).]. The JAM interaction model agrees with the HARP experiment [H. Collaboration, Astropart. Phys. 30, 124 (2008).] a little better than DPMJET-III [S. Roesler, R. Engel, and J. Ranft, arXiv:hep-ph/0012252.]. After some modifications, it reproduces the muon flux below $1\mathrm{GeV}/c$ at balloon altitudes better than the modified DPMJET-III, which we used for the calculation of atmospheric neutrino flux in previous works [T. Sanuki, M. Honda, T. Kajita, K. Kasahara, and S. Midorikawa, Phys. Rev. D 75, 043005 (2007).][M. Honda, T. Kajita, K. Kasahara, S. Midorikawa, and T. Sanuki, Phys. Rev. D 75, 043006 (2007).]. Some improvements in the calculation of atmospheric neutrino flux are also reported.

Figure 1

Comparison of interaction models and HARP data. The solid lines stand for JAM, and the dashed lines for DPMJET-III.

Figure 2

Comparison of the muon flux observed at Tsukuba (30 m a.s.l.) and the one calculated with the modified JAM. Dashed lines in right panel are the ratios of former calculations to present ones.

Figure 3

Comparison of the muon flux observed at Mt. Norikura (2770 m a.s.l) and the one calculated with the modified JAM. Dashed lines in right panel are the ratios of former calculations to present ones.

Figure 4

Comparison of the muon flux observed at the balloon altitudes ($5-2\mathrm{g}/{\mathrm{cm}}^2$) at Fort Sumner and the one calculated with the modified JAM. Dashed lines in right panel are the ratios of former calculations to present ones.

Figure 5

Comparison of pion production spectra between the original JAM (solid line) and the original DPMJET-III (dashed line) integrated all over the directions in the left panel, and those of the modified JAM (solid line) and the modified DPMJET-III (dashed line) in the right panel at 10 GeV. Here the $X$ denotes the ratio of secondary kinetic energy to projectile kinetic energy.

Figure 6

The ratio of statistical errors of the atmospheric neutrino flux calculated to the flux value in this work. We show the statistical errors for near-vertical directions ($0.9<\cos {\theta }_z<1$) in the left panel, and for near-horizontal directions ($0.9<\cos {\theta }_z<1$) in the right panel, both averaging over all azimuthal directions.

Figure 7

Comparison of atmospheric neutrino fluxes calculated for Kamioka averaged over all directions (left panel), and the flux ratios (right panel), with other calculations. The dashed lines are the calculation by the Bartol group [20, 21], dotted lines for the FLUKA group [22], and dash dot for our previous calculation (HKKM06).

Figure 8

Atmospheric neutrino fluxes calculated for Kamioka averaged over all directions, as a ratio to the HKKM06 calculation. The dashed lines are the calculation by Bartol group [20, 21] and dotted lines the FLUKA group [22].

Figure 9

The zenith angle dependence of atmospheric neutrino flux averaged over all azimuthal angles calculated for Kamioka. Here $\theta$ is the arrival direction of the neutrino, with $\cos \theta =1$ for vertically downward going neutrinos, and $\cos \theta =-1$ for vertically upward going neutrinos.

Figure 10

Ratio of the atmospheric neutrino flux averaged over azimuth angles as the function of zenith angle to the same quantity calculated in HKKM06. The short dash lines stand for the calculation by Bartol group [20, 21] and dotted lines for the FLUKA group [22].

Figure 11

The azimuthal angle dependence of atmospheric neutrino flux at 1 GeV, averaged over zenith angle bins of $1>\cos \theta >0.6$, $0.6>\cos \theta >0.2$, $0.2>\cos \theta >-0.2$, $-0.2>\cos \theta >-0.6$, and $-0.6>\cos \theta >-1$ calculated for Kamioka.

Figure 12

The azimuthal angle dependence of atmospheric neutrino flux at 3.2 GeV, averaged over zenith angle bins of $1>\cos \theta >0.6$, $0.6>\cos \theta >0.2$, $0.2>\cos \theta >-0.2$, $-0.2>\cos \theta >-0.6$, and $-0.6>\cos \theta >-1$ calculated for Kamioka.

Figure 13

The azimuthal angle dependence of atmospheric neutrino flux at 10 GeV, averaged over zenith angle bins of $1>\cos \theta >0.6$, $0.6>\cos \theta >0.2$, $0.2>\cos \theta >-0.2$, $-0.2>\cos \theta >-0.6$ and $-0.6>\cos \theta >-1$ calculated for Kamioka.

Figure 14

The azimuthal angle dependence of atmospheric neutrino flux at 32 GeV, averaged over zenith angle bins of $1>\cos \theta >0.6$, $0.6>\cos \theta >0.2$, $0.2>\cos \theta >-0.2$, $-0.2>\cos \theta >-0.6$, and $-0.6>\cos \theta >-1$ calculated for Kamioka. The straight lines in the figure show the flux values calculated in the 1D scheme.

Figure 15

The variation of the function $F(r)$ defined by (b6). It has a minimum value $\sqrt{5}\simeq 2.236$ at $r=1/\sqrt{2}\simeq 0.707$ indicated by “Optimized.” The “HKKM06” indicates the $r=0.5$ used in HKKM06, where the $F$-value is a little larger than the optimized one ($F(0.5)=2.517$).

Figure 16

Ratio of the atmospheric neutrino flux averaged over the virtual detector ($\varphi (10)$) to the flux for the true neutrino detector ($\varphi (0)$) estimated with the procedure explained in the text. The atmospheric neutrino fluxes are averaged over all the azimuth angles. Here, ${\theta }_z$ stands for the zenith angle of the arrival direction, and the left panel is for the near-vertical downward directions, and the right panel for the near-horizontal directions.

Figure 17

Ratio of the neutrino fluxes averaged over the virtual detector ($\varphi (10)$) to the flux for the true neutrino detector ($\varphi (0)$) calculated with the procedure explained in the text for near-horizontal east ($90°<{\varphi }_a<120°$) directions.