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

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 $\mathcal{O}(p/M_{\tiny \mbox{Pl}})$.