Phenomenology of Planck-scale Lorentz-symmetry test theories

In the recent quantum-gravity literature, there has been considerable interest in exploring the possibility of Planck-scale departures from Lorentz symmetry, including possible modifications of the energy/momentum dispersion relation. I stress that a meaningful characterization of the progress of experimental bounds on these Planck-scale effects requires the analysis of some reference test theories, and I propose to focus on two 'minimal' test theories, a pure-kinematics test theory and an effective-field-theory-based test theory. I illustrate some features of the phenomenology based on these test theories considering some popular strategies for constraining Planck-scale effects, and in particular I observe that sensitivities that are already in the Planck-scale range for some parameters of the two test theories can be achieved using observations of TeV photons from blazars, both using the so-called 'gamma-ray time-of-flight analyses' and using the now robust evidence of absorption of TeV photons. Instead, the Crab-nebula synchrotron-radiation analyses, whose preliminary sensitivity estimates raised high hopes, actually do not lead to any bound on the parameters of the two 'minimal' test theories. The Crab-nebula synchrotron-radiation analyses do however constrain some possible generalizations of one of the minimal test theories. As an example of forthcoming data which could provide extremely stringent (beyond-Planckian) limits on the two minimal test theories, I consider the possibility of studies of the GZK cutoff for cosmic rays.