Constraining Lorentz invariance violation from the depth of air-shower maximum

Hypothetical Lorentz invariance violation (LIV) remains strongly constrained but has not been excluded as a possible manifestation of new high-energy physics. In subluminal photon-sector LIV, suppressed Bethe$\unicode{x2013}$Heitler pair production modifies the electromagnetic component of extensive air showers. We present a simulation-based toy analysis of this effect using published Pierre Auger fluorescence-detector distributions of the reconstructed depth of air-shower maximum. The modified distributions of the depth of the shower maximum are folded with the Auger detector-response parametrizations and compared with the data using free composition fractions in each reconstructed-energy bin. Within this approach, the comparison gives a sensitivity to LIV compatible with that expected from ultra-high-energy photon-induced showers. We obtain $M_{\rm LIV}>1.5\times 10^{21}\,\text{GeV}$ ($95\%$ confidence level). This result should not be interpreted as a detector-level experimental limit because the detector response and reconstruction are simplified, and the result remains composition dependent. However, the approach presented here opens the way for constraining LIV in hadronic air showers with more detailed analyses.