Deformation-induced CPT violation in entangled pairs of neutral kaons

In this paper we consider description of kaon – anti-kaon interference in the context of a theory with deformed $\mathcal{C}\mathcal{P}\mathcal{T}$ symmetry. In the case of such theoretical models, deviations from the standard $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance is related to the momentum carried by the particles; in particular the rest masses of particles and antiparticles are equal. We find that the decay intensity of kaon – anti-kaon pair has three contributing terms: the correct-parity, the wrong-parity, and the interference between them, all of which are affected by deformation. Using the fact that the presence of such terms were not observed we estimate the magnitude of deformation parameter $\kappa \gtrsim {10}^{18}$ GeV, very close to the expected Planck mass scale. This raises hopes that the effect, if exists, could be detected in a near future accelerator experiments. An uncertainty of the energy measurement is crucial for accuracy of these predictions.