[Paper Review] Evading the GZK Cosmic-Ray Cutoff

Sidney Coleman, Sheldon L. Glashow|ArXiv.org|Aug 27, 1998

Particle Detector Development and Performance18 citations

TL;DR

This paper proposes that tiny violations of Lorentz invariance—too small to be detected by current experiments—can suppress or forbid inelastic collisions between ultra-high-energy cosmic-ray protons and cosmic microwave background photons, thereby evading the Greisen-Zatsepin-Kuz’min (GZK) cutoff. If such Lorentz violation exists, it could allow cosmic rays above 5×10¹⁹ eV to travel cosmological distances, resolving the tension between observed high-energy cosmic rays and the predicted GZK cutoff.

ABSTRACT

Explanations of the origin of ultra-high energy cosmic rays are severely constrained by the Greisen-Zatsepin-Kuz'min effect, which limits their propagation over cosmological distances. We argue that possible departures from strict Lorentz invariance, too small to have been detected otherwise, can affect elementary-particle kinematics so as to suppress or forbid inelastic collisions of cosmic-ray nucleons with background photons. Thereby can the GZK cutoff be relaxed or removed.

Motivation & Objective

• To investigate whether small departures from Lorentz invariance could suppress the inelastic reactions responsible for the GZK cutoff.
• To address the discrepancy between observed ultra-high-energy cosmic rays (above 5×10¹⁹ eV) and the theoretical GZK cutoff limiting their propagation.
• To argue that the GZK cutoff is not an inevitable consequence of physics, but a hypothesis dependent on strict Lorentz invariance.
• To show that current experimental bounds on Lorentz violation are insufficient to rule out values that would relax or eliminate the GZK cutoff.
• To motivate future high-precision tests of Lorentz invariance to probe the existence of such violations.

Proposed method

• Formulate a perturbative framework for Lorentz-violating extensions of the Standard Model Lagrangian, preserving gauge invariance and rotational symmetry in a preferred frame.
• Define species-specific maximum attainable velocities (MAVs) for particles, introducing δab ≡ c²a − c²b as a measure of Lorentz violation.
• Analyze the kinematics of proton-CBR photon collisions, particularly the Δ(1232) resonance and single pion production, under Lorentz-violating conditions.
• Derive energy thresholds for these reactions as functions of δΔp and δπp, showing that thresholds diverge at critical values of δ.
• Use the thermal distribution of CBR photons (T = 2.73 K) to assess the cumulative effect of Lorentz violation on the overall suppression of inelastic processes.
• Compare theoretical thresholds for cutoff suppression with existing experimental bounds on δ parameters to assess viability.

Experimental results

Research questions

• RQ1 Can tiny violations of Lorentz invariance kinematically suppress the Δ(1232) resonance formation in proton-CBR photon collisions?
• RQ2 What magnitude of Lorentz violation is required to fully forbid the dominant GZK energy-loss processes?
• RQ3 Are current experimental constraints on Lorentz violation sufficient to rule out values that would evade the GZK cutoff?
• RQ4 Can the observed flux of ultra-high-energy cosmic rays above 5×10¹⁹ eV be reconciled with a cosmological origin if the GZK cutoff is relaxed by Lorentz violation?
• RQ5 What precision is required in future laboratory tests to detect Lorentz-violating parameters that could explain the absence of the GZK cutoff?

Key findings

• A critical value of δΔp ≈ 3.5×10⁻²⁵ [ω/ω₀]² is required to kinematically forbid Δ(1232) resonance formation with CBR photons.
• For single pion production, the threshold diverges when δπp exceeds ~1.1×10⁻²³ [ω/ω₀]², indicating complete suppression of this channel for larger δπp.
• Values of δΔp and δπp comparable to or exceeding these critical thresholds would effectively eliminate the GZK cutoff by suppressing both resonant and non-resonant photo-pion production.
• Existing experimental bounds on Lorentz violation—such as |δmγ| < 6×10⁻²² and δνν′ < 2×10⁻²¹—are too weak to rule out the required violations.
• Theoretical models suggest that laboratory tests with precision approaching 10⁻²⁵ could detect the necessary Lorentz-violating parameters.
• The absence of a detectable GZK cutoff in cosmic-ray data may thus be evidence for Lorentz violation, rather than a flaw in astrophysical models.