High-Energy Tests of Lorentz Invariance

High-Energy Tests of Lorentz Invariance

20 Jan 1999 | Sidney Coleman and Sheldon L. Glashow
The paper by Sidney Coleman and Sheldon L. Glashow explores the implications of small, non-invariant terms in the standard model Lagrangian on Lorentz invariance. These terms are assumed to be renormalizable (dimension ≤ 4), invariant under $SU(3) \otimes SU(2) \otimes U(1)$ gauge transformations, and rotationally and translationally invariant in a preferred frame. There are 46 independent CPT-even perturbations, all of which preserve anomaly cancellation. These perturbations define the energy-momentum eigenstates and their maximal attainable velocities in the high-energy limit, with effects increasing rapidly with energy in the preferred frame. The authors discuss several new phenomena relevant to cosmic-ray physics and neutrino physics, such as the GZK cutoff being undone and novel types of neutrino oscillations. These phenomena may lead to new and sensitive high-energy tests of special relativity. The paper also examines the kinematics of particle decays, showing that a decay can be kinematically allowed at both low and high energies but forbidden for intermediate energies. This analysis is applied to charged leptons and neutrinos, providing constraints on Lorentz-violating parameters through observations of cosmic rays and neutrino oscillations.The paper by Sidney Coleman and Sheldon L. Glashow explores the implications of small, non-invariant terms in the standard model Lagrangian on Lorentz invariance. These terms are assumed to be renormalizable (dimension ≤ 4), invariant under $SU(3) \otimes SU(2) \otimes U(1)$ gauge transformations, and rotationally and translationally invariant in a preferred frame. There are 46 independent CPT-even perturbations, all of which preserve anomaly cancellation. These perturbations define the energy-momentum eigenstates and their maximal attainable velocities in the high-energy limit, with effects increasing rapidly with energy in the preferred frame. The authors discuss several new phenomena relevant to cosmic-ray physics and neutrino physics, such as the GZK cutoff being undone and novel types of neutrino oscillations. These phenomena may lead to new and sensitive high-energy tests of special relativity. The paper also examines the kinematics of particle decays, showing that a decay can be kinematically allowed at both low and high energies but forbidden for intermediate energies. This analysis is applied to charged leptons and neutrinos, providing constraints on Lorentz-violating parameters through observations of cosmic rays and neutrino oscillations.
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Understanding High-energy tests of Lorentz invariance