Ghostly Duet: Neutrino Decay of a Superluminal Photon ✦
In the Standard Model, photons are stable, but if Lorentz symmetry is broken (LIV), they gain an effective mass and can decay into a neutrino pair. The decay proceeds through the weak force and is heavily suppressed. For TeV–PeV photons, the rate is calculated. Below the electron-positron pair threshold, the neutrino channel opens up but is too rare to improve limits. Above the threshold, if pair creation is suppressed, neutrino decay offers an independent probe of photon–neutrino symmetry.
In 2021, the LHAASO observatory registered gamma quanta with energies above a petaelectronvolt from sources like the Crab Nebula — a supernova remnant with a pulsating neutron star at its heart. These particles traveled thousands of years, and their very arrival challenges the immutability of Lorentz invariance — the principle that the speed of light in a vacuum is absolute and identical for all observers. According to special relativity of Albert Einstein, a photon cannot have mass, thus it cannot decay. But if quantum fluctuations of spacetime make light slightly superluminal, the photon gains an effective mass — and with it, the ghostly possibility to turn into a pair of neutrinos. It's like a shadow theater: the photon-actor casts a silent neutrino silhouette, carrying its energy off the stage.
Forbidden in the Standard Model, the decay becomes possible through quantum corrections: via virtual W-boson exchange, an anapole moment emerges — a specific form factor, computed within quantum field theory. This moment, like a microscopic loop in the fabric of electrodynamics, connects the photon to a neutrino pair. Pioneer of gamma-ray astronomy Rashid Sunyaev studied the emission of the Crab Nebula, never suspecting that decades later its photons would become a testing ground for Lorentz-violations. The key parameter is the effective photon mass, proportional to the energy and speed shift δ: m_eff² = δ E_γ². The decay probability catastrophically collapses with decreasing mass — proportional to the sixth power! For a typical shift δ~10⁻²², the effective mass of a PeV photon is around 10 keV, and its lifetime is comparable to Earth's geological history. For the photon to decay within a thousand years, its mass must reach ~3 MeV — above the threshold for electron-positron pair production.
The derived constraints — for example, a suppression scale M₂ > 3×10¹⁴ GeV for quadratic models — don’t break records, but the method is unique. It probes the relative violation between the photon and neutrino sectors, not just the absolute deviation of the speed of light. That’s what makes it indispensable for scenarios where the electron channel is locked. Precise photometry of the gamma-ray sky is already helping refine dispersion relations, and future data from gamma-ray bursts like the record-breaking GRB 221009A will allow searching for anomalous absorption without electron showers — a direct shadow of neutrino decay. Improved neutrino telescopes may even catch the twin particles themselves. Ultimately, we are touching the structure of spacetime: violations of Lorentz invariance could be echoes of quantum gravity, string theory, or Planck-scale physics. And perhaps these ghostly shadows are the only way to peer into the epochs when the universe was so dense that even light was learning to decay.
🎯 The effective mass of a PeV photon at a typical speed shift is only about 10 keV — a hundred times lighter than an electron, yet millions of times heavier than the lightest neutrino. Due to the feebleness of the neutrino interaction, its lifetime stretches billions of years, comparable to the age of Earth. Such a long-lived photon could have existed since the planet formed, never once decaying.
🎬 Imagine a neutrino telescope capturing the shadows of photons: it predicts gamma-ray bursts before the light arrives, working as a cosmic detector of hidden symmetries.