# Low energy neutrinos from stopped muons in the Earth

## TL;DR

This paper calculates low energy neutrino fluxes from stopped muons in the Earth, showing their dependence on detector depth and local geology, with implications for neutrino detection experiments.

## Contribution

It provides a detailed estimation of low energy neutrino fluxes from stopped muons, considering depth, decay, and capture probabilities, which was not comprehensively addressed before.

## Key findings

- Neutrino fluxes are a significant fraction of atmospheric neutrinos at 1000 m depth.
- Fluxes increase by 40% if detector is shallower than 30 m.
- Most neutrinos originate within 200 km and from near horizontal directions.

## Abstract

We explore the low energy neutrinos from stopped cosmic ray muons in the Earth. Based on the muon intensity at the sea level and the muon energy loss rate, the depth distributions of stopped muons in the rock and sea water can be derived. Then we estimate the $\mu^-$ decay and nuclear capture probabilities in the rock. Finally, we calculate the low energy neutrino fluxes and find that they depend heavily on the detector depth $d$. For $d = 1000$ m, the $\nu_e$, $\bar{\nu}_e$, $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes in the range of 13 MeV $ \leq E_\nu \leq$ 53 MeV are averagely $10.8 \%$, $6.3\%$, $3.7 \%$ and $6.2 \%$ of the corresponding atmospheric neutrino fluxes, respectively. The above results will be increased by a factor of 1.4 if the detector depth $d < 30$ m. In addition, we find that most neutrinos come from the region within 200 km and the near horizontal direction, and the $\bar{\nu}_e$ flux depends on the local rock and water distributions.