Many theories of quantum gravity suggest that spacetime symmetries may not hold strictly at extreme energy scales. In particular, Lorentz Invariance Violation (LIV) – a breakdown of the fundamental symmetry underlying special relativity – could manifest near the Planck scale (∼ 1019 GeV). Although collisions in extensive air showers (EAS) induced by ultra-high-energy cosmic rays (UHECRs) occur at lower center-of-mass energies, subtle cumulative effects in hadronic cascades can leave detectable footprints.
In this publication, the Pierre Auger Collaboration introduces the use of muon fluctuations to constrain Lorentz invariance violation for the first time.
Why Muon Fluctuations?
When an ultra-high-energy cosmic ray enters Earth’s atmosphere, it initiates a shower. If Lorentz invariance is violated, modified interaction kinematics and particle decay rates alter how energy is split between electromagnetic and muonic components. This affects not only the mean muon count ⟨Nµ⟩, but also the relative fluctuations σ(Nµ)/⟨Nµ⟩. Since the relative fluctuations are mainly driven by the first interaction of the primary cosmic ray, they are less sensitive to the uncertainties associated with the hadronic interaction models governing the subsequent stages of the shower. This makes them a particularly useful observable for probing possible modifications of the initial high-energy interaction. The Pierre Auger Observatory’s excellent sensitivity to the muonic component of extensive air showers enables these fluctuations to be measured with high precision at ultra-high energies.
Key Results
By analyzing muon fluctuations measured by the Pierre Auger Observatory, the collaboration achieved major milestones:
- The derived limits do not require strong assumptions on the mass composition of ultrahigh-energy cosmic rays.
- Strongest experimental constraints to date in the hadronic sector: provides the most stringent experimental constraints on hadronic LIV parameters.
- Fundamental physics window: Establishes muon fluctuations as a novel observable to test quantum gravity phenomenology inaccessible to terrestrial particle accelerators.
Figure 1: Relative muon fluctuations as a function of primary energy for different violation strengths. Colours indicate the value of η LIV parameter, with increasing violation shown by the arrow. Black points show the measurements.
Related Paper:
Bounds on Lorentz invariance violation from muon fluctuations at the Pierre Auger Observatory
The Pierre Auger Collaboration, Phys. Rev. Lett. 137 (2026) 111001
[arxiv.org/abs/2602.14720] [doi: 10.1103/t5k4-2m32]
