# Lorentz invariance violation as an explanation of muon excess in Auger data

## TL;DR

This paper proposes that Lorentz invariance violation in the photon sector can explain the excess of muons observed by the Auger experiment, by modifying the neutral pion decay process and increasing muon production.

## Contribution

It introduces a novel LIV-based mechanism affecting pion decay, providing a potential explanation for muon excess in cosmic ray data.

## Key findings

- LIV suppresses neutral pion decay width in the studied energy range.
- Modified decay width leads to increased muon production matching observations.
- Planck-suppressed LIV at order p^2/M_{Pl} is consistent with current bounds.

## Abstract

The Auger collaboration has observed the number of muons which is higher than its prediction by existing hadronic interaction models. We explain this excess of muons by using Lorentz invariance violation (LIV) in photon sector. As an outcome of Lorentz invariance violation, the dispersion relation of photon gets modified, which we use for the calculation of $\pi^0$ decay width. In the Auger data of primary energy $10^{9.8}<E(\mbox{GeV})<10^{10.2}$, we find that the neutral pion decay width is suppressed in comparison to its standard model (SM) counterpart. As a result, we get a large number of muons explaining the observed muon excess. We consider Planck suppressed LIV at order $\mathcal{O}(p^2/M^2_{\tiny \mbox{Pl}})$ for studying the photon sector, which is in agreement with the current bounds, and not as tightly constrained as LIV at order $\mathcal{O}(p/M_{\tiny \mbox{Pl}})$.