Lorentz-invariant CPT violation

TL;DR

This paper explores a Lorentz-invariant form of CPT violation based on non-local interactions, analyzing its theoretical consistency, effects on particle-antiparticle properties, and potential for inducing mass splitting.

Contribution

It introduces a consistent framework for Lorentz-invariant CPT violation via non-local interactions, examining its implications on unitarity, mass equality, and T violation.

Findings

Lorentz covariant $T^{ullet}$-product is well-defined in this non-local theory.

Energy-momentum conservation holds in perturbation theory despite unitarity loss.

Mass equality of particles and antiparticles can be preserved or broken depending on the Lagrangian.

Abstract

A Lorentz-invariant CPT violation, which may be termed as long-distance CPT violation in contrast to the familiar short-distance CPT violation, has been recently proposed. This scheme is based on a non-local interaction vertex and characterized by an infrared divergent form factor. We show that the Lorentz covariant $T^{\star}$-product is consistently defined and the energy-momentum conservation is preserved in perturbation theory if the path integral is suitably defined for this non-local theory, although unitarity is generally lost. It is illustrated that T violation is realized in the decay and formation processes. It is also argued that the equality of masses and decay widths of the particle and anti-particle is preserved if the non-local CPT violation is incorporated either directly or as perturbation by starting with the conventional CPT-even local Lagrangian. However, we also explicitly show that the present non-local scheme can induce the splitting of particle and anti-particle mass eigenvalues if one considers a more general class of Lagrangians.