NuFast-Earth: Efficient Atmospheric, Solar, and Supernova Neutrino Propagation Through the Earth

TL;DR

NuFast-Earth delivers an efficient, high-precision method for propagating neutrinos through the Earth for atmospheric, solar, and supernova sources. It builds on NuFast-LBL by employing a tilde basis and layer-by-layer amplitudes across a four-segment Earth trajectory, enabling fast reuse of calculations when varying parameters like θ23, δ, and production height. The approach supports diverse Earth density models (e.g., PREM-based) and provides two schemes for density variation, with detailed assessments of speed and precision that guide practical usage. The authors provide a public C++ implementation and demonstrate favorable speed-precision tradeoffs, making the tool valuable for next-generation experiments such as DUNE, Hyper-Kamiokande, IceCube upgrades, and KM3NeT.

Abstract

Algorithms for computing neutrino oscillation probabilities in sharply varying matter potentials such as the Earth are becoming increasingly important. As the next generation of experiments, DUNE and HyperK as well as the IceCube upgrade and KM3NeT, come online, the computational cost for atmospheric and solar neutrinos will continue to increase. To address these issues, we expand upon our previous algorithm for long-baseline calculations to efficiently handle probabilities through the Earth for atmospheric, nighttime solar, and supernova neutrinos. The algorithm is fast, flexible, and accurate. It can handle arbitrary Earth models with two different schemes for varying density profiles. We also provide a c++ implementation of the code called NuFast-Earth along with a detailed user manual. The code intelligently keeps track of repeated calculations and only recalculates what is needed on each successive call which can also help provide significant speed-ups.

Figures (11)

• Figure 1: A sample trajectory through an Earth model showing the four segments. First, the purple segment, $A$, is from the production point to the surface. Second, the red segment, $S$, is from the surface to the detector depth on the far side. Third, the blue segment, $I$, is from the detector depth on the far side to the deepest point of the trajectory. Fourth, the orange segment, $O$, is from the deepest point to the detector, the blue rectangle.
• Figure 2: The disappearance (top) and appearance (bottom) probabilities across parameters typical for atmospheric parameters in the normal ordering. The left (right) panels are for neutrinos (antineutrinos). The color scale for the appearance figure for antineutrinos is smaller to highlight hard to see features. The detector depth is 2 km and the production height is 10 km.
• Figure 3: The same as fig. \ref{['fig:oscillogram NO']} but in the inverted ordering. The color scale for the appearance figure for neutrinos is smaller to highlight hard to see features.
• Figure 4: The $\nu_e$ disappearance probability from the center of the Sun to a detector in the Earth as a function of energy and zenith angle. The bands on the right show the annual average exposure for nighttime neutrinos at the latitudes for DUNE (blue) and SK/HK (red). The detector depth is at 2 km which leads to some effects for daytime neutrinos as well.
• Figure 5: The daytime solar $\nu_e$ disappearance probability (blue) and the nighttime solar disappearance probability (orange dashed) averaged over a year of exposure at DUNE's latitude.