Spectra for the Vacuum Cherenkov Effect in Astrophysical Electromagnetic Cascades with Lorentz Invariance Violation

TL;DR

Lorentz invariance violation can enable vacuum Cherenkov radiation, altering high-energy electron propagation in astrophysical environments. The authors develop a full kinematic and rate framework for VC under second-order LIV terms, deriving the differential emission spectrum and a piecewise total rate, and validate it with Monte Carlo simulations of VC cascades. They show four distinct spectral morphologies and demonstrate that a full cascade treatment is necessary rather than the commonly used binary approximation. The results provide actionable VC spectra as inputs for electromagnetic cascade modeling and LIV constraint studies, with plans to integrate into the CRPropa framework and extend the analysis to other LIV processes and species-dependent effects.

Abstract

Lorentz invariance violation is a feature of several quantum gravity models in which Lorentz symmetry is broken at high energies, possibly leading to changes in particle behavior and interactions. In this work, we investigate vacuum Cherenkov radiation, a reaction in which an electron spontaneously emits a photon. This process, forbidden when Lorentz symmetry is unbroken, is a phenomenological consequence of some quantum gravity models. We derive, for the first time, the spectra for the vacuum Cherenkov reaction, and confirm our results numerically. These results can be used to derive limits on Lorentz invariance violation.

Figures (3)

• Figure 1: VC kinetics formalism used in Rubtsov:2012kb and in the present work for the momenta of the incoming electron, outgoing photon and outgoing electron labeled $p_{{\rm in},e}$, $k_{{\rm out},\gamma}$ and $p_{{\rm out},e}$, respectively.
• Figure 2: Differential probability distribution ($\frac{{\rm d}P_{\rm VC}}{{\rm d}x}$) for various combinations of $\chi_{2}^{e}$ and $\chi_{2}^{\gamma}$, with $\left| \chi_{2}^{\gamma} \chi_{2}^{e} \right| = 10^{-10}$. Each panel corresponds to different regimes, based on the signs of $\chi_{2}^{\gamma}$ and $\chi_{2}^{e}$, according to Eq. (\ref{['eq:cases']})
• Figure 3: Results of Monte Carlo simulations for various $\chi_2^e$ and $\chi_2^\gamma$ combinations. Dashed lines refer to the corresponding threshold energies. Spectra are energy-weighted to highlight the ${\rm d}N/{\rm d}E \propto E^{-1}$ behaviour. The normalization of the distributions is arbitrary.