After a brief review of the first phase of development of Quantum-Gravity Phenomenology, I argue that this research line is now ready to enter a more advanced phase: while at first it was legitimate to resort to heuristic orderof- magnitude estimates, which were suffcient to establish that sensitivity to Planck-scale effects can be achieved, we should now rely on detailed analyzes of some reference test theories. I illustrate this point in the specific example of studies of Planck-scale modifications of the energy/momentum dispersion relation, for which I consider two test theories. Both the photon-stability analyzes and the Crab-nebula synchrotron-radiation analyzes, which had raised high hopes of “beyond-Plankian” experimental bounds, turn out to be rather ineffective in constraining the two test theories. Examples of analyzes which can provide constraints of rather wide applicability are the so-called “time-of- fight analyzes”, in the context of observations of gamma-ray bursts, and the analyzes of the cosmic-ray spectrum near the GZK scale.
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