Abstract
We review recent work on CPT and Lorentz violation in the context of the Standard-Model Extension. In particular, we show that, when CPT and Lorentz violation is present in the kinetic terms of any particle in the gauge boson or the lepton sector, this will generally lead to proton decay at sufficiently high energy. Using observational data from ultra-high energy cosmic rays, this has allowed to derive new bounds on the corresponding CPT and Lorentz-violation parameters.
Highlights
We show that, when CPT and Lorentz violation is present in the kinetic terms of any particle in the gauge boson or the lepton sector, this will generally lead to proton decay at sufficiently high energy
Lorentz symmetry is a fundamental ingredient of both quantum field theory and General Relativity
Suggestions that Lorentz invariance violation (LV) might be originate at the Planck scale come from a number of candidate theories for quantum gravity that have been shown to involve LV as a possible effect
Summary
Lorentz symmetry is a fundamental ingredient of both quantum field theory and General Relativity. We will see that in the presence of LV, threshold values exist for the momentum of the protons above which Cherenkov-like emission of such gauge bosons, or of leptons, acquires a nonzero rate. The four-vector e(μ+)(p) is the gauge-boson polarization vector that corresponds to the dispersion relation Λ+(p) = 0 It can be shown from formula (5) that in order to have a nonzero decay rate, the incoming fermion momentum has to exceed a threshold value:. We conclude that the threshold value for W emission by a proton to occur is still given by formula (7), while the decay rate will depend on the details of the PDFs, but its order of magnitude value is the same as for the elementary fermion case (at least for values of a not very close to 1)
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