Shower formation in the presence of a string-inspired foam in space-time

TL;DR

The paper investigates whether string-inspired space-time foam, modeled via D-particle recoil and stochastic energy fluctuations, can produce a subluminal photon dispersion compatible with gamma-ray time delays without disturbing atmospheric electromagnetic showers. It derives the modified photon dispersion $\omega\simeq k[1+\tfrac{1}{2}\sigma^{2}k^{2}/M_{D}^{2}]$ and the corresponding group velocity, incorporating energy fluctuations $\delta E_{D}$ from foam interactions. A formation-length analysis yields a suppression factor $S \simeq \big[1+\tfrac{\omega^{3}g_{s}(2\sigma^{2}-\varsigma_{I})}{8M_{s}m_{e}^{2}}\big]^{-1}$, identifying parameter regions (e.g., $\sigma^{2}=\varsigma_{I}/2$) where shower development is unchanged. The results show that, under appropriate foam parameters, Lorentz-violating effects can evade shower-formation constraints while remaining consistent with light-speed variation hints, though a robust, explicit QG formalism and further dynamical studies are required for definitive constraints.

Abstract

It was recently proposed that predictions of Lorentz-breaking space-time foam models from string theory may be compatible with the suggestion of light-speed variation from gamma-ray burst studies. Our analysis of foam-modified kinematics shows that despite the subluminal photon velocities explaining photon time delays one may, and in certain circumstances does, keep intact the electromagnetic showers essential for the detection and identification of cosmic photons. In contrast to other~(mostly phenomenological) approaches to Lorentz violations with modified dispersions leading to drastic changes on the formation length for the cascade development in the atmosphere and in detectors, there is the possibility that the dispersion effect in the present string foam model avoids such modifications and the theory naturally escapes the shower formation constraints from recent observations.