Lorentz violating kinematics: threshold theorems

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 complicated and counter-intuitive manner.

Einstein's special relativity beyond the speed of light

“…In fact, (1.2) is the only possibility if the corresponding energy-momentum equations are be invariant under the new transformations, and formulae such as (1.3) have energymomentum relations that are not invariant under the new transformations. For extensive accounts of modern tests of Lorentz invariance, we refer the reader to Baccetti et al (2012a), Coleman & Glashow (1999), Liberati et al (2001), Mattingly (2005) and Mattingly et al (2003).…”

Inertial frames without the relativity principle

“…We have seen that once one for any reason moves away from Lorentz invariance, and specifically once one discards the relativity principle, then many of the intuitions one has been trained to develop in a special relativistic setting need to be significantly and carefully revised. In a companion article we had considered threshold phenomena [104], which can be studied by picking and working in a particular arbitrary but fixed inertial frame. In the current article we have carefully analyzed what happens to the transformation properties between inertial frames once the relativity principle is abandoned.…”

Testing Lorentz and CPT Invariance with Neutrinos

“…In other words, the Lorentz-violating contribution can open the phase space of conventionally forbidden processes as well as blocking certain processes that would be otherwise allowed. Take for instance the leptonic decay of a charged meson M + of the form M + → l + + ν l , which becomes forbidden above some threshold energy E th [19,[39][40][41][42][43][44][45][46]. The observation of the decay products at a given energy E 0 can then be used to establish the threshold condition E th > E 0 .…”