Ultra-high-energy physics is about to enter a new era thanks to the impressive results of experiments such as the Large High Altitude Air Shower Observatory (LHAASO), detecting photons of up to 1.4 PeV (10 15 eV). These new results could be used to test deviations with respect to special relativity. While this has been already explored within the approach of Lorentz invariance violation (LIV) theories, in this work we consider, for the first time, modifications of a relativistic deformed kinematics (which appear in doubly special relativity, or DSR, theories). In particular, we study the mean free path of very high-energy photons due to electron-positron pair creation when interacting with low-energy photons of the cosmic microwave background. Depending on the energy scale of the relativistic deformed kinematics, present (or near future) experiments can be sensitive enough to be able to identify deviations from special relativity.

Doubly special relativity considers a deformation of the special relativistic kinematics parametrized by a high-energy scale, in such a way that it preserves a relativity principle. When this deformation is assumed to be applied to any interaction between particles one faces some inconsistencies. In order to avoid them, we propose a new perspective where the deformation affects only the interactions between elementary particles. A consequence of this proposal is that the deformation cannot modify the special relativistic energy-momentum relation of a particle.