Lifshitz-scaling to Lorentz-violating high derivative operator and gamma-ray busts

TL;DR

This paper uses Hořava-Lifshitz scaling to analyze Lorentz-violating electrodynamics, deriving tighter bounds on Lorentz violation from gamma-ray burst data, significantly improving previous limits.

Contribution

It introduces a novel approach applying Hořava-Lifshitz scaling to Lorentz-violating electrodynamics, leading to more stringent experimental bounds.

Findings

Bound for Lorentz-violating coupling improved by eight orders of magnitude.

Derived photon dispersion relations consistent with gamma-ray burst observations.

Results suggest near-phenomenological relevance of the bounds.

Abstract

In this work we have used a Ho\v{r}ava-Lifshitz scaling to rewrite a Lorentz-violating higher-order derivative electrodynamics controlled by a background four-vector $n_{\mu}$. The photon propagator was obtained and we have analyzed the dispersion relation and the observational results of gamma-ray burst (GRB) experiments were used. The limits of the critical exponent were discussed in the light of the GRB data and the physical implications were compared with the current GRB-Lorentz-invariance-violation literature. We show that the bound for the Lorentz-violating coupling for dimension-six operators, obtained from a Ho\v{r}ava-Lifshitz scaling, is eight orders of magnitude better than the result found without considering a Ho\v{r}ava-Lifshitz scaling, also this bound is nearby one, which is expected to be relevant phenomenologically.