Lorentz violating kinematics: Threshold theorems

TL;DR

This paper develops general threshold theorems for Lorentz-violating kinematics, revealing that at threshold all final particles share the same velocity and initial particles are aligned, despite complex momentum behaviors.

Contribution

It introduces threshold theorems that require only an energy-momentum relation, avoiding assumptions like isotropy or monotonicity, thus broadening the analysis of Lorentz violation effects.

Findings

At threshold, all final particles have the same 3-velocity.

Initial particles' velocities are parallel or anti-parallel to final particles.

3-momenta can behave counter-intuitively despite velocity constraints.

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.