Hypothetical Lorentz invariance violation and the muon content of extensive air showers

TL;DR

The paper investigates whether a tiny LIV in the photon sector can explain the observed muon excess in EAS. By adopting a subluminal photon dispersion $E_ ext{gamma}^2 = k_ ext{gamma}^2 - k_ ext{gamma}^4/M_{ ext{LIV}}^2$ within a photon-sector EFT and modifying the Bethe–Heitler cross section, the authors show that high-energy electromagnetic sub-showers can be suppressed, biasing energy reconstruction and increasing the inferred muon content without changing true muon production. Using CORSIKA-based Monte Carlo simulations, they parameterize electron-content suppression as $r_e(\xi)$ with $\xi = (m_e M_{ ext{LIV}})^{-1/2} A^{-1} E$ and find $r_ ext{mu}(\xi)=0$, then constrain $M_{ ext{LIV}}$ with Auger data via a maximum-likelihood analysis. The results yield a best-fit $M_{ ext{LIV}} \\approx 1.9\times 10^{16}$ GeV and a robust 95% CL lower bound $M_{ ext{LIV}} > 2.4\times 10^{14}$ GeV, offering a falsifiable LIV explanation for the muon puzzle and highlighting tests with ground-level muon spectra and cosmogenic photons. The work connects to broader LIV and quantum gravity contexts, including Horava-Lifshitz-inspired scales, and outlines future observations that could decisively confirm or rule out this scenario.

Abstract

Extensive air showers (EAS), produced by cosmic rays in the atmosphere, serve as probes of particle interactions, providing access to energies and kinematical regimes beyond the reach of laboratory experiments. Measurements from multiple cosmic-ray detectors indicate a significant, yet unexplained, discrepancy between the observed muon content in EAS and that predicted by state-of-the-art interaction models, suggesting a need for refinements in our understanding of fundamental physics. Here we show that a tiny, experimentally allowed, violation of the Lorentz invariance (LIV) may result in the suppression of the number of electrons in EAS, leaving the muon number intact and explaining both the ''muon excess'' and its energy dependence. On the other hand, we use the lack of a much stronger discrepancy between EAS data and simulations to obtain strict constraints on the LIV scale. Future experimental tests of this LIV scenario are outlined.

Figures (4)

• Figure 1: LI--to--LIV ratios for the ground-level average number of particles, training data set (top: electrons, bottom: muons). The colored points and the error bars correspond to MC simulations (red: proton-induced, blue: iron-induced EASs) average and $68\%$ C.L. uncertainty, respectively. The solid black lines represent the model defined by Eq. \ref{['eq:r-xi']}. See text for a detailed discussion.
• Figure 2: LI--to--LIV ratios for the ground-level average number of particles, test data set (main figures: electrons, inset figures: muons). The gray points and the error bars correspond to MC simulations (proton-induced EASs) average and $68\%$ C.L. uncertainty, respectively. The solid black lines represent the model defined by Eq. \ref{['eq:r-xi']}. Top: fixed $M_{\text{LIV}} = 3\times 10^{17}$ GeV, bottom: fixed $E=10^{19}$ eV. See text for a detailed discussion.
• Figure 3: The solid black line corresponds to $\chi^2$ at various $M_{\text{LIV}}$, see Eq. \ref{['eq:chi-2']}. The dashed gray line shows the $\chi^2$ value for the LI scenario. The shaded region represents the parameter range excluded at $95\%$ C.L.
• Figure 4: $z$-scale in experiments (see metaanalysis ArteagaVelazquez:2023fda) in comparison with the LIV scenario prediction. The shaded region corresponds to the LIV scenario (a) favored by the composition-independent maximum likelihood analysis, $M_{\text{LIV}}=1.9\times 10^{16}$ GeV; (b) excluded at $95\%$ C.L. by the Auger data, $M_{\text{LIV}}=2.4\times 10^{14}$ GeV; (c) consistent with the LI scenario expectation, $M_{\text{LIV}}=6.3\times 10^{19}$ GeV. The dashed gray line assumes a composition from the Global Spline Fit GSF_2017ICRC...35..533D.