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

In this work, we use a Hořava-Lifshitz scaling to rewrite a Lorentz-violating higher-order derivative electrodynamics controlled by a background 4-vector $n_{\mu }$. The photon propagator is obtained, and we analyze the dispersion relation, and the observational results of gamma-ray burst (GRB) experiments are used. The limits of the critical exponent are discussed in light of the GRB data, and the physical implications are compared with the current GRB-Lorentz-invariance-violation literature. We show that the bound for the Lorentz-violating coupling for dimension-6 operators, obtained from a Hořava-Lifshitz scaling, is 8 orders of magnitude better than the result found without considering a Hořava-Lifshitz scaling and also that this bound is near to 1, which is expected to be relevant phenomenologically.

Figure 1

The behavior of constraints on LIV for the following values: $z=1$, $z=3/2$, and $z=2$.