Phenomenology of Doubly Special Relativity

TL;DR

This paper analyzes the phenomenology of doubly special relativity, examining how it differs from Lorentz symmetry violations and assessing experimental constraints, especially from gamma-ray burst observations.

Contribution

It provides a detailed analysis of experimental constraints on doubly special relativity and clarifies its distinction from Lorentz symmetry breaking frameworks.

Findings

Photon stability and synchrotron radiation do not strongly constrain the framework.

Gamma-ray burst analyses are sensitive to symmetry deformations.

Clarifies the sign ambiguity in the doubly-special-relativity framework.

Abstract

Investigations of the possibility that some novel ``quantum" properties of spacetime might induce a modification dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry. More recently several studies have considered the possibility of a ``doubly special relativity", in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a deformation of the Lorentz transformations. For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. We provide here a corresponding analysis for the doubly-special-relativity framework. We find that the analyses of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, cannot provide significant constraints on doubly-special-relativity parameter space. However, certain types of analyses of gamma-ray bursts are sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-special-relativity framework. This result also allows us to characterize more sharply the differences between the doubly-special-relativity framework and the framework of k-Poincare Hopf algebras, two frameworks which are often confused with each other in the literature.