Masud Chaichian, Kazuo Fujikawa, Anca Tureanu
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 proposed in Ref. [Chaichian et al., Phys. Lett. B 699 (2011) 177, arXiv:1103.0168 [hep-th]]. 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.
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http://arxiv.org/abs/1205.0152
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