Lorentz violating kinematics: threshold theorems Article

First Online: 27 March 2012 Received: 06 December 2011 Revised: 23 February 2012 Accepted: 10 March 2012 DOI :
10.1007/JHEP03(2012)087

Cite this article as: Baccetti, V., Tate, K. & Visser, M. J. High Energ. Phys. (2012) 2012: 87. doi:10.1007/JHEP03(2012)087
Abstract Recent tentative experimental indications, and the subsequent theoretical speculations, regarding possible violations of Lorentz invariance have attracted a vast amount of attention. An important technical issue that considerably complicates detailed calculations in any such scenario, is that once one violates Lorentz invariance the analysis of thresholds in both scattering and decay processes becomes extremely subtle, with many new and naively unexpected effects. In the current article we develop several extremely general threshold theorems that depend only on the existence of some energy momentum relation E (p), eschewing even assumptions of isotropy or monotonicity. We shall argue that there are physically interesting situations where such a level of generality is called for, and that existing (partial) results in the literature make unnecessary technical assumptions. Even in this most general of settings, we show that at threshold all final state particles move with the same 3-velocity, while initial state particles must have 3-velocities parallel/anti-parallel to the final state particles. In contrast the various 3-momenta can behave in a complicatedand counter-intuitive manner.

Keywords Space-Time Symmetries Beyond Standard Model Neutrino Physics Global Symmetries

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Authors and Affiliations 1. School of Mathematics, Statistics, and Operations Research Victoria University of Wellington Wellington New Zealand