Threshold Effects and Lorentz Symmetry

Abstract

Evidence on the violation of Lorentz symmetry arises from the observation of cosmic rays with energies beyond the GZK cutoff, $E_{GZK} \simeq 4 \times 10^{19} eV$, from the apparent transparency of the Universe to the propagation of high energy gamma radiation and from the stability of pions in air showers. These three paradoxes can be explained through deformations of the relativistic dispersion relation. Theoretical ideas aimed to understand how Lorentz symmetry may be broken and phenomenologically interesting deformations of the relativistic dispersion relation may arise are briefly discussed.Comment: 7 pages. Talk presented at the ``Decoherence, Information, Complexity and Entropy 2002'', Piombino, Italy, September 200

Quantum-Spacetime Phenomenology

“…It has been established (see, e.g., Refs. [305, 59, 334, 115]) that when Lorentz symmetry is broken at the Planck scale, there can be significant implications for certain decay processes. At the qualitative level, the most significant novelty would be the possibility for massless particles to decay.…”

“…At the qualitative level, the most significant novelty would be the possibility for massless particles to decay. And certain observations in astrophysics, which allow us to establish that photons of energies up to ∼ 10 14 eV are stable, can then be used [305, 59, 334, 115] to set limits on schemes for departures from Lorentz symmetry.…”

“…In particular, there has been strong interest [327, 38, 73, 463, 305, 59, 115, 35, 431] in the analysis of the “photopion production” process, pγ → pπ . As already stressed in Section 1.5, interest in the photopion-production process originates from its role in our description of the high-energy portion of the cosmic-ray spectrum.…”

“…While in some cases departures from Lorentz symmetry allow the decay of otherwise stable particles (as in the case of γ → e + e − , discussed above, for appropriate choice of values of parameters), it is indeed also possible for departures from Lorentz symmetry to either introduce a threshold value of the energy of the particle, above which a certain decay channel for that particle is totally forbidden [179, 81], or introduce some sort of suppression of the decay probability that increases with energy and becomes particularly effective above a certain threshold value of the energy of the decaying particle [59, 115, 244]. This may be relevant [81, 59] for the description of the air showers produced by cosmic rays, whose structure depends rather sensitively on certain decay probabilities, particularly the one for the decay π → γγ .…”

“…The possibility of suppression at ultrahigh energies of the decay π → γγ has been considered from the quantum-gravity-phenomenology perspective primarily adopting PKV0-type frameworks [59, 115]. Using the kinematics of the PKV0 test theory one easily arrives [59] at the following relationship between the opening angle ϕ of the directions of the momenta of the outgoing photons, the energy of the pion ( E π ) and the energies ( E and E ′ = E π − E ) of the outgoing photons: This relation shows that, for positive η , at high energies the phase space available to the decay is anomalously reduced: for a given value of E π certain values of E that would normally be accessible to the decay are no longer accessible (they would require cos θ > 1).…”