A three-dimensional calculation of atmospheric neutrinos

TL;DR

This work advances atmospheric neutrino flux modeling by implementing a fully three-dimensional Monte Carlo calculation that includes geomagnetic bending of secondaries and backtracking-based geomagnetic cutoffs. By systematically comparing 3D and traditional 1D approaches, the authors demonstrate that 1D is adequate above roughly 5 GeV, with only small azimuthal differences at high energies and notable horizon-related effects at low energies. The paper details a fast, flexible pipeline with a flat detector approximation, binlet weighting to control fluctuations, and modular decay/interaction generators, enabling precise quantification of 3D effects and guiding when the more complex 3D treatment is essential. These results are important for the accurate interpretation of atmospheric neutrino oscillation analyses and for refining oscillation parameter extractions in neutrino experiments.

Abstract

A Monte-Carlo calculation of the atmospheric neutrino fluxes [1,2] has been extended to take account of the three-dimensional (3D) nature of the problem, including the bending of secondary particles in the geomagnetic field. Emphasis has been placed on minimizing the approximations when introducing the 3D considerations. In this paper, we describe the techniques used and quantify the effects of the small approximations which remain. We compare 3D and 1D calculations using the same physics input in order to evaluate the conditions under which the 3D calculation is required and when the considerably simpler 1D calculation is adequate. We find that the 1D and 3D results are essentially identical for neutrino energy greater than 5 GeV except for small effects in the azimuthal distributions due to bending of the secondary muon by the geomagnetic field during their propagation in the atmosphere.

Figures (4)

• Figure 1: Comparison between a test Monte-Carlo calculation (points) which introduces a single bend through an angle $\alpha$ at an altitude of $h$ and an analytic calculation from Lipari1 (lines) for different values of $\alpha = 10^\circ$, $30^\circ$ and $60^\circ$. These curves show the basic features of a 3D calculation (see text).
• Figure 2: Comparison of 3D to 1D calculation of the angle averaged fluxes at Kamioka and Soudan. The $(\nu_\mu+\overline{\nu}_\mu)$ and $(\nu_e+\overline{\nu}_e)$ fluxes are plotted for the 3D calculation (points) and the 1D calculation (lines).
• Figure 3: Zenith angle distributions of $\nu_\mu$ at Kamioka for six different energy ranges. The full-line histograms are the 3D calculation and the dashed histograms are the pseudo-1D calculation. The energy ranges in the left hand panel are: 1) 100--158 MeV, 2) 250--400 MeV, and 3) 630 MeV--1 GeV. In the right hand panel we show the angular distribution for 4) 2.50--4.0 GeV, 5) 4.0--6.3 GeV, and 6) 6.3--10 GeV. The right panel also contains the angular distributions calculated with Bartol's original code (points).
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