Modification of the mean free path of very high-energy photons due to a relativistic deformed kinematics

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