Photon Decay into Neutrinos: New Frontiers of Lorentz Invariance ✦
We consider the vacuum decay of a photon into a neutrino-antineutrino pair under Lorentz invariance violation (LIV). LIV corrections to the photon dispersion are set by an effective invariant mass, which kinematically allows the normally forbidden γ→νν̄. The decay proceeds through a one-loop electromagnetic neutrino vertex in the Standard Model and is highly suppressed. Using the anapole form factor (small q²), the rate is computed for TeV-PeV photons. Results: below the e⁺e⁻ threshold, the neutrino channel is open but too rare to improve constraints. Above the threshold, if e⁺e⁻ production is suppressed by the relative photon-electron LIV parameter, the neutrino decay gives an independent bound on the photon-neutrino LIV coupling parameters.
Context
Recent detections of cosmic gamma rays with energies up to 1.4 PeV by the LHAASO observatory from sources like the Crab Nebula (a supernova remnant with a pulsar at its center), once studied by gamma-ray astronomy pioneer Rashid Sunyaev, have raised the question of the validity of the principle of the constancy of the speed of light on extreme scales. According to Einstein’s special relativity, the speed of light in a vacuum is invariant, but quantum-gravity effects could break this Lorentz invariance, making photons slightly superluminal. Such a modification opens up kinematically forbidden decay channels, and decay into a neutrino pair is among the most intriguing, as it does not rely on charged leptons.
Methods
To calculate the decay probability, the authors used the photon’s effective mass, which parameterizes deviations from the standard dispersion relation. The photon-neutrino interaction vertex is absent in classical electrodynamics but arises from loop corrections in the Standard Model via W-boson and charged-lepton exchange. At low photon virtuality, the neutrino’s anapole moment—a specific form factor computed long ago in quantum field theory—dominates. Taking this vertex factor, they summed over all three neutrino flavors and obtained an analytic decay rate as a function of effective mass and photon energy within a phenomenological approach to Lorentz invariance violation.
Results
The calculated decay rate of a photon into neutrinos turned out to be extremely small due to the quadratic dependence on the anapole moment (~10⁻³⁴ cm²). With an effective mass around 1 MeV and a photon energy of 1 TeV, the lifetime is about a thousand years—comparable to the propagation time from galactic sources. However, if the effective mass drops to 10 keV (typical for a constant speed shift δ~10⁻²²), the lifetime stretches to millions of years, making the decay unobservable. Interestingly, for PeV photons, the threshold effective mass of 3 MeV already lies above the electron-positron pair production threshold, but if the latter channel is suppressed due to a fine-tuned violation parameter for electrons, the neutrino channel provides independent constraints. In particular, for a quadratic dispersion modification, the suppression scale M₂ must be at least 3×10¹⁴ GeV.
Implications
The significance of this work lies in demonstrating the fundamental possibility of probing relative Lorentz invariance violation between the photon and neutrino sectors, not just the standard photon-electron difference. Although current limits are weaker than existing ones (e.g., for a constant speed shift δ, the limit is ~9×10⁻¹⁸ versus ~10⁻²¹ from the photon-electron channel), this method could become decisive if future data point to a specific suppression pattern in the electron channel. Moreover, it links high-energy physics to neutrino properties, potentially opening a path to test predictions of Lorentz-violating theories, including some string models and loop quantum gravity.
Future development
This topic could advance with improved sensitivity of neutrino telescopes and gamma-ray observatories. If an anomalously large absorption of PeV photons is detected alongside the absence of electron-positron showers, that would hint at the neutrino channel. Progress in measuring the arrival time of gamma-ray bursts, such as GRB 221009A, will also help pinpoint the energy dependence of photon dispersion, narrowing the allowed range of effective masses. Theorists could refine the anapole moment calculation near the electron threshold, where resonant enhancements may occur.
Impact
The results impact high-energy photometry and the interpretation of data from observatories like LHAASO, as well as the theory of neutrino interactions.
Next steps
Direct observation of the decay would require either a dramatic (orders of magnitude) increase in sensitivity, or the discovery of a new class of sources with anomalously strong Lorentz invariance violation in the neutrino sector.
Key open problems
The article is directly connected to the problem of quantum gravity and the search for Lorentz invariance violations as a low-energy trace of Planck-scale physics. It also touches on the nature of neutrino masses and possible additional interactions beyond the Standard Model.
🎯 For a PeV photon with a typical speed shift, the effective mass is only about 10 keV—a hundred times less than the electron rest mass, but millions of times greater than the lightest neutrino mass. Such a 'heavier' photon could decay, but due to the weakness of the neutrino coupling, its lifetime is comparable to Earth's geological history.
Key numbers
- Effective mass for a PeV photon with δ~10⁻²²: 10 keV
- Threshold effective mass for a 1000-year lifetime: 3.1 MeV (for 1 PeV)
- Limit on parameter δ from the neutrino channel: 9×10⁻¹⁸ (for 1 PeV)
- Limit on the scale M₂ (quadratic suppression): > 3.3×10¹⁴ GeV
- Anapole moment of the electron neutrino: 6.8×10⁻³⁴ cm²