DSR, if it can eventually be made mathematically consistent in its current incarnation, has one phenomenological advantage - it does not have a preferred frame. Therefore it evades most of the threshold constraints from astrophysics as well as any terrestrial experiment that looks for sidereal variations, while still modifying the usual action of the Lorentz group. Since these experiments provide almost all of the tests of Lorentz violation that we have, DSR becomes more phenomenologically attractive as a Lorentz violating/deforming theory.
So what is DSR? At the level we need for phenomenology, DSR is a set of assumptions that the Lorentz group acts in such a way that the usual speed of light and a new momentum scale are invariant. Usually is taken to be the Planck energy - we also make this assumption. All we will need for this review are the Lorentz boost expressions and the conservation laws, which we will postulate as true in the DSR framework. For brevity we only detail the Magueijo-Smolin version of DSR , otherwise known as DSR2 - the underlying conclusions for DSR1  remain the same. The DSR2 boost transformations are most easily derived from the relations. Similarly, the and for particles are conserved as energy and momentum normally are for a scattering problem.3 Given this set of rules, for any measured particle momentum and energy, we can solve for and and calculate interaction thresholds, etc. The invariant dispersion relation for the DSR2 boosts is given by [186, 21, 14, 95]. We discuss the threshold behavior of DSR theories in Section 6.6.1.
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