Constraints to Lorentz violation and ultrahigh-energy electrons in D-foamy space-times

TL;DR

The paper investigates whether the absence of vacuum Cherenkov radiation from ultrahigh-energy electrons constrains Lorentz-violating (LV) physics, using both general LV dispersions and specifically string/brane-inspired D-foam models. It shows that, in a broad LV framework, Cherenkov rates above threshold are rapid, justifying threshold-based bounds, but that this conclusion does not hold in D-foam scenarios where photons experience refractive effects while electrons remain effectively unaffected. Two D-foam realizations are analyzed: (i) stretched-string foam, which yields photon delays without modifying local electron dispersion, and (ii) isotropic stochastic recoil foam, where energy losses can push Cherenkov thresholds to very high energies or infinity, suppressing emission. Consequently, the stringent Cherenkov bounds derived for universal LV do not universally apply, and D-foam models can accommodate both potential light-speed variations and compatibility with LHAASO observations, with implications for future neutrino and gamma-ray multi-messenger tests.

Abstract

We entertain the constraints that the absence of vacuum Cherenkov radiation of ultrahigh-energy electrons inferred from LHAASO observations of the Crab Nebula can impose on generic models in which Lorentz symmetry of the particle vacuum is violated, as established by some recent studies in \href{https://doi.org/10.1016/j.physletb.2022.137034}{\emph{Phys. Lett. B} {\bf 829} (2022) 137034}; \href{https://doi.org/10.1016/j.physletb.2022.137536}{{\bf 835} (2022) 137536}; \href{https://doi.org/10.1103/PhysRevD.108.063006}{\emph{Phys. Rev. D} {\bf108} (2023) 063006}. We demonstrate in the present paper, that implementing a phenomenological approach to the Lorentz violation, the rates of this vacuum process are substantial such that one is justified in deriving bounds on the violation scales from simple threshold analysis just as these works did. Albeit such results are likely effective then, they do not apply in the same form among scenarios. Specifically, we show that these Cherenkov constraints are naturally evaded in models of space-time foam inspired from~(supercritical) string theory, involving D-branes as space-time defects in a brane-world scenario, in which subluminous energy-dependent refractive indices of light have been suggested. We examine here two specific foam situations and find for both cases~(though, for different reasons) the potentiality that charged quanta such as electrons do \emph{not} radiate as they pass through the gravitational vacuum `medium' despite moving faster than photons.