Threshold anomalies of ultra-high energy cosmic photons due to Lorentz invariance violation

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

“…Thanks to experiments like LHAASO, which recently detected photons around this energy, the possible deviations with respect to special relativity could be studied in the near future. In the present work we have considered, for the first time, possible consequences from a perspective of a deformed kinematics that is relativistic invariant, in contrast to the alternative, already explored [56][57][58][59][60], LIV case.…”

“…The present study is motivated by the recent observations of the Large High Altitude Air Shower Observatory (LHAASO), which was able to report the detection of more than 530 photons with energies between 10 14 eV and 1.4 × 10 15 eV from 12 sources of ultra-high energy gamma rays within our galaxy, called PeVatrons, with a statistical significance greater than 7 standard deviations [55]. The consequences of these results for LIV models have already been examined [56][57][58][59][60]. The LHAASO results severely constrain the superluminal scenario, since pair-emission (γ → e + e − ) and photon splitting (γ → 3γ ) processes force the energy scale characterizing the modification of the dispersion relation to be at least five orders of magnitude above the Planck energy ≈ 1.22 × 10 28 eV in the case of a linear correction [58,60].…”

Lorentz Symmetry Violation of Cosmic Photons

“…We assume that the 4-momentum of the high-energy photon γ is p 1 = (ω(k), 0, 0, k) with LV effects, and that of the low-energy photon γ b is still p 2 = (ε b , 0, 0, −ε b ) 19 . According to the threshold configuration of this reaction 20 , the energy-momentum conservation and the on-shell condition of the outgoing electron-positron pair, we get [128]:…”

“…A function f (k) is defined in the above formula [128]. Then we consider a simplified case (n = 3), which corresponds to the linear modification.…”

“…Now studying the threshold behavior is equivalent to studying the solution of Equation ( 27), and we can acquire the number and locations of solutions of Equation ( 27) by studying the relationship between the value of ξ and the function f (k). Finally, according to the three kinds different values of the LV parameter ξ, the threshold of the annihilation reaction γ + γ b → e + + e − has three different cases [128]: 27) has no solution. No solution means that there is not even a lower threshold, and all photons can freely traverse the background of low-energy photons.…”