Eur. Phys. J. C (2013) 73: 2349
https://doi.org/10.1140/epjc/s10052-013-2349-2

Regular Article - Theoretical Physics

Lorentz-invariant CPT violation

¹ Department of Physics, University of Helsinki, P.O. Box 64, 00014, Helsinki, Finland
² Mathematical Physics Laboratory, RIKEN Nishina Center, Wako, 351-0198, Japan

^* e-mail: masud.chaichian@helsinki.fi

Received: 14 September 2012
Published online: 23 March 2013

Abstract

A Lorentz-invariant CPT violation, which may be termed 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 ^⋆-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 antiparticle 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 antiparticle mass eigenvalues if one considers a more general class of Lagrangians.