⚛️ phenomenology

Revisiting Very High Energy Gamma-Ray Absorption in Cosmic Propagation under the Combined Effects of Axion-Like Particles and Lorentz Invariance Violation

This paper proposes that the unexpected survival of very-high-energy gamma rays from GRB 221009A can be explained by a combined scenario of photon-axion-like particle oscillations and subluminal quadratic Lorentz invariance violation, which together enhance photon transparency more effectively than either mechanism alone.

Original authors: Longhua Qin, Jiancheng Wang, Chuyuan Yang, Huaizhen Li, Quangui Gao, Ju Ma, Ao Wang, Weiwei Na, Ming Zhou, Zunli Yuan, Chunxia Gu, Guangbo Long

Published 2026-03-03

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Longhua Qin, Jiancheng Wang, Chuyuan Yang, Huaizhen Li, Quangui Gao, Ju Ma, Ao Wang, Weiwei Na, Ming Zhou, Zunli Yuan, Chunxia Gu, Guangbo Long

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Mystery: The "Ghost" Photons

Imagine the universe is a giant, crowded hallway filled with invisible fog. This fog is made of old starlight (called the Extragalactic Background Light or EBL).

When a very high-energy gamma-ray photon (a particle of light) tries to run through this hallway, it usually crashes into the fog. When it hits the fog, it explodes into an electron and a positron (a pair of particles), effectively disappearing. Physics tells us that if a photon travels a long distance, it should almost certainly crash and vanish.

The Problem:
Recently, scientists detected a massive explosion in space called GRB 221009A. It was so bright and energetic that it sent photons flying toward Earth. Some of these photons were incredibly fast and heavy (up to 300 TeV). According to the standard rules of physics, these photons should have been completely stopped by the "fog" long before they reached us.

But they didn't. They arrived at Earth like ghosts, passing right through the fog that should have stopped them. The universe seemed to be much more "transparent" (clear) than it should be.

The Suspects: Two New Physics Ideas

Scientists needed a new explanation. They looked at two famous "suspects" from theoretical physics that could help photons sneak past the fog:

The Chameleon (Axion-Like Particles or ALPs):
Imagine a photon is a human trying to walk through a crowded room. An ALP is like a magical cloak. If the photon wears this cloak, it turns into a different particle (an ALP) that the fog can't see. It walks through the crowd safely, then takes the cloak off and turns back into a photon just before reaching Earth.
- The Catch: This works well for medium-high energies, but maybe not for the super-heavy 300 TeV photons.
The Speed Limit Breaker (Lorentz Invariance Violation or LIV):
Einstein said the speed of light is the ultimate speed limit and that the rules of physics are the same for everyone. But what if, at extremely high energies, those rules change? Imagine the "fog" in the hallway suddenly becomes thinner or the walls move further apart for super-fast runners. This is LIV. It changes the rules of the game so that the high-energy photons don't crash into the fog as easily.
- The Catch: This helps the super-fast photons, but it doesn't explain the "wiggles" or specific patterns seen in the lower-energy data.

The Solution: The "Tag-Team" Strategy

The authors of this paper realized that trying to solve the mystery with just the "Chameleon" or just the "Speed Breaker" wasn't working perfectly.

The Chameleon alone couldn't explain the 300 TeV photon.
The Speed Breaker alone messed up the data for the lower-energy photons.

So, they proposed a Tag-Team Strategy: ALPs + LIV working together.

Think of it like a video game level where you need two power-ups to win:

The ALP Power-up: As the photon travels through space, it occasionally swaps into an ALP to dodge the fog in the host galaxy and our own Milky Way.
The LIV Power-up: Because the rules of physics are slightly tweaked at the highest energies, the "fog" itself becomes less dense for the 300 TeV photon, allowing it to survive the long journey.

The Results: A Perfect Fit

The scientists ran the numbers using a supercomputer model. They tested three scenarios:

Standard Physics: Failed miserably (The photons should have died).
ALPs Only: Saved the lower-energy photons, but the 300 TeV one still died.
LIV Only: Saved the 300 TeV one, but the lower-energy ones didn't look right.
The Hybrid (ALP + LIV): Bingo!

When they combined both effects, the model perfectly matched the observations. The photons survived the journey, explaining both the 18 TeV data from the LHAASO telescope and the massive 300 TeV event reported by the Carpet-3 detector.

Why This Matters

This isn't just about one explosion. It suggests that our current understanding of the universe is missing a piece of the puzzle.

It hints that Axion-Like Particles (a form of dark matter candidate) might actually exist.
It hints that Einstein's rules might have a tiny exception at the highest energies, pointing toward a theory of Quantum Gravity.

In short: The universe is a bit more magical than we thought. Photons are using a "Chameleon" trick and a "Speed Limit" loophole to survive a journey that should have been impossible. This paper proves that you need both tricks to explain what we saw.

1. Problem Statement

Very-high-energy (VHE) gamma rays ( $E \gtrsim 100$ GeV) are theoretically expected to undergo significant attenuation during cosmological propagation due to electron-positron pair production ( $\gamma\gamma \to e^+e^-$ ) on the Extragalactic Background Light (EBL). However, recent observations of GRB 221009A ( $z = 0.151$ ) present a paradox:

LHAASO detected photons up to $\sim 18$ TeV.
Carpet-3 reported a candidate event at $\sim 300$ TeV (updated to $300^{+42}_{-38}$ TeV).

Standard EBL absorption models cannot explain the survival of these photons without invoking unphysical intrinsic spectral upturns. Furthermore, neither Axion-Like Particles (ALPs) (via photon-ALP oscillations) nor Lorentz Invariance Violation (LIV) (via modified pair-production thresholds) considered in isolation can simultaneously reproduce the broadband spectrum from 10 TeV to 300 TeV without conflicting with independent constraints or failing to fit specific data points.

2. Methodology

The authors propose a unified hybrid framework that simultaneously incorporates photon-ALP mixing and subluminal quadratic LIV corrections.

A. Physical Framework

Photon-ALP Oscillation:
- Modeled using a Schrödinger-like evolution equation for the state vector $\psi = (A_x, A_y, a)^T$ in external magnetic fields.
- The mixing matrix $M$ includes terms for plasma effects, QED vacuum birefringence, and the photon-ALP coupling ( $\Delta_{a\gamma} \propto g_{a\gamma} B_T$ ).
- The authors focus on oscillations in the source host galaxy and the Milky Way, neglecting oscillations in the Intergalactic Magnetic Field (IGMF) due to weak field strength ( $B_{IGMF} \lesssim 1$ nG) and dephasing effects at high energies.
Lorentz Invariance Violation (LIV):
- The authors adopt a subluminal quadratic LIV scenario ( $n=2$ ), which modifies the photon dispersion relation.
- This modification raises the energy threshold for $\gamma\gamma \to e^+e^-$ pair production, effectively reducing the optical depth ( $\tau_{\gamma\gamma}$ ) for ultra-high-energy photons.
- The LIV effect is implemented by replacing the soft-photon energy in the optical depth calculation with an effective energy term derived from the modified dispersion relation.
Joint Propagation Model:
- The total photon survival probability $P_{\gamma \to \gamma}$ is calculated by combining the survival probabilities in the source ( $S$ ), intergalactic medium ( $I$ ), and Milky Way ( $M$ ).
- The model assumes $P^I_{\gamma \to \gamma} = e^{-\tau_{LIV, \gamma\gamma}}$ (no ALP mixing in IGMF) and calculates $P^S$ and $P^M$ using the mixing matrix formalism.
- The LIV correction enters the mixing matrix via the modified mean free path and threshold shifts.

B. Data and Analysis

Target: GRB 221009A.
Data Sources:
- LHAASO: KM2A and WCDA data (300–900 s post-trigger) covering 200 GeV to 20 TeV.
- Carpet-3: A single event at $\sim 300$ TeV. Due to lack of explicit differential flux, the authors estimated flux limits assuming burst durations of 1 hour and 1 day.
Statistical Approach: Bayesian parameter inference using UltraNest to obtain posterior distributions. Model performance is evaluated using the Akaike Information Criterion (AIC) to balance goodness-of-fit against model complexity.
EBL Model: The Finke et al. (2022) model was used for EBL density.

3. Key Contributions

Novel Hybrid Scenario: The paper is the first to systematically apply a joint ALP-LIV propagation model to the specific broadband data of GRB 221009A, moving beyond previous studies that treated these mechanisms independently.
Resolution of the "300 TeV Puzzle": The study demonstrates that while LIV alone can raise the transparency threshold for 300 TeV photons, it fails to shape the spectrum correctly in the 10–30 TeV range. Conversely, ALPs alone cannot explain the 300 TeV survival. The synergy of both mechanisms is required.
Quantitative Constraints: The authors derive specific best-fit parameters for the ALP sector within the context of a fixed, literature-supported LIV scale.

4. Results

The authors compared four scenarios: Standard EBL only, ALP-only, LIV-only, and the Hybrid ALP-LIV model.

Model	Best-Fit Parameters	AIC Value	Performance
EBL Only	Standard	192.46	Fails to explain 18 TeV and 300 TeV data.
ALP Only	$g_{a\gamma} = 1.489 \times 10^{-10}$ GeV $^{-1}$ $m_a = 4.191 \times 10^{-7}$ eV	85.86	Explains 18 TeV but fails to reproduce the 300 TeV flux (underestimates survival).
LIV Only	Fixed quadratic LIV ( $\eta_2 = 1.30 \times 10^{-15}$ )	135.33	Allows 300 TeV survival but overproduces flux in the 10–30 TeV range; fails to fit 18 TeV.
Hybrid (ALP-LIV)	$g_{a\gamma} = 1.685 \times 10^{-10}$ GeV $^{-1}$ $m_a = 9.545 \times 10^{-8}$ eV $\eta_2 = 1.30 \times 10^{-15}$ (Fixed)	25.63	Best Fit. Simultaneously reproduces the 18 TeV LHAASO data and the $\sim$ 300 TeV Carpet-3 event.

Survival Probability: In the hybrid model, at least 70% of photons at both 18 TeV and 300 TeV survive the host galaxy and intergalactic propagation.
Parameter Compatibility: The derived ALP coupling ( $g_{a\gamma} \sim 10^{-10}$ GeV $^{-1}$ ) and mass ( $m_a \sim 10^{-7}$ eV) are consistent with current astrophysical bounds (e.g., Fermi-LAT blazar spectra, CAST), particularly when the LIV contribution relaxes the constraints that would apply in a pure ALP scenario.

5. Significance

Physics Beyond the Standard Model: The results provide strong evidence that the anomalous transparency of the Universe to VHE gamma rays may require a combination of new physics (ALPs) and quantum gravity effects (LIV).
Synergistic Mechanism: The study highlights that ALP oscillations (which provide spectral modulation and hardening in the 10–30 TeV range) and LIV (which monotonically increases transparency at $>100$ TeV) are complementary rather than degenerate.
Future Probes: The paper establishes a testable paradigm for future observatories like the Cherenkov Telescope Array (CTA) and the International Axion Observatory (IAXO). It suggests that distinguishing between ALP-induced oscillatory features and LIV-induced monotonic transparency will be crucial for validating this hybrid model.
Methodological Advance: By utilizing time-resolved differential fluxes and carefully handling the uncertainty of the 300 TeV event, the authors provide a more robust statistical foundation than previous integrated fluence studies.

In conclusion, the paper argues that the extreme-energy observations of GRB 221009A cannot be explained by standard physics or single-new-physics mechanisms, but are naturally resolved by a unified ALP-LIV framework, offering a viable path to understanding the transparency of the Universe at the highest energies.