Phenomenology of doubly special relativity

Investigations of the possibility that some novel "quantum" properties of space-time might induce a Planck-scale modification of the energy/momentum dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry, with an associated reduced n-parameter (n < 6) rotation-boost symmetry group. More recently several studies have also 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 6-parameter group of rotation-boost symmetry transformations (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. Here we show that the analysis of the experimental limits could be significantly different in a doubly-special-relativity framework. We find that the study 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, should not provide significant constraints on a doubly-special-relativity parameter space. However, certain types of analyses of gamma-ray bursts should be 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 frame,work and the framework of kappa-Poincare Hopf algebras, two frameworks which are often confused with each other in the literature.