Phase Space Factor for Two-Body Decay if One Product is a Stable Tachyon

TL;DR

This paper derives the phase space factor for two-body decay involving a stable tachyon, revealing threshold conditions and contrasting with Lorentz-invariant approaches, thus advancing tachyon quantum field theory.

Contribution

It introduces a consistent quantum field theory framework for tachyons with spontaneous Lorentz symmetry breaking and calculates the decay phase space with new threshold conditions.

Findings

Derived lower and upper threshold conditions for tachyon decay

Contrasted with Lorentz-invariant calculations showing no thresholds

Established a framework for tachyon quantum field theory

Abstract

We calculate the phase space factor for a two-body decay in which one of the products is a tachyon. Two threshold conditions, a lower and an upper one, are derived in terms of the masses of the particles and the speed of a preferred frame. Implicit in the derivation is a consistently formulated quantum field theory of tachyons in which spontaneous Lorentz symmetry breaking occurs. The result is to be contrasted with a parallel calculation by Hughes and Stephenson, which, however, implicitly adheres to strict Lorentz invariance of the underlying quantum field theory and produces the conclusion that there is no threshold for this process.