On calculation of cross sections in Lorentz violating theories

Abstract

We develop a systematic approach to the calculation of scattering cross sections in theories with violation of the Lorentz invariance taking into account the whole information about the theory Lagrangian. As an illustration we derive the Feynman rules and formulas for sums over polarizations in spinor electrodynamics with Lorentz violating operators of dimensions four and six. These rules are applied to compute the probabilities of several astrophysically relevant processes. We calculate the rates of photon decay and vacuum Cherenkov radiation along with the cross sections of electron-positron pair production on background radiation and in the Coulomb field. The latter process is essential for detection of photon-induced air showers in the atmosphere.

23 pages, 1 figure

References in corpus (20)

• Quantum Gravity at a Lifshitz Point
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• Neutrinos with Lorentz-violating operators of arbitrary dimension
• Renormalization of Lorentz violating theories
• Renormalization group in Lifshitz-type theories
• Lorentz Violation for Photons and Ultra-High Energy Cosmic Rays
• Weighted power counting and Lorentz violating gauge theories. I: General properties
• Limits on isotropic Lorentz violation in QED from collider physics
• Search for ultra-high energy photons using air showers
• Massive photons and Lorentz violation
• Classification of Dimension 5 Lorentz Violating Interactions in the Standard Model
• Weighted power counting and Lorentz violating gauge theories. II: Classification
• Lorentz Violation and Ultrahigh-Energy Photons
• Planck-scale Lorentz violation constrained by Ultra-High-Energy Cosmic Rays
• Lorentz Invariance Violation and Chemical Composition of Ultra High Energy Cosmic Rays
• Model dependence of the bremsstrahlung effects from the superluminal neutrino at OPERA
• Have we tested Lorentz invariance enough?
• Vacuum Cherenkov Radiation In Quantum Electrodynamics With High-Energy Lorentz Violation
• Uncertainties in Constraints from Pair Production on Superluminal Neutrinos
• Non-Standard Neutrino Propagation and Pion Decay

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