Probing CPT in transitions with entangled neutral kaons

In this paper we present a novel CPT symmetry test in the neutral kaon system based, for the first time, on the direct comparison of the probabilities of a transition and its CPT reverse. The required interchange of in $leftrightarrow$ out states for a given process is obtained exploiting the Einstein-Podolsky-Rosen correlations of neutral kaon pairs produced at a $phi$-factory. The observable quantities have been constructed by selecting the two semileptonic decays for flavour tag, the $pipi$ and $3pi^0$ decays for CP tag and the time orderings of the decay pairs. The interpretation in terms of the standard Weisskopf-Wigner approach to this system, directly connects CPT violation in these observables to the violating $Redelta$ parameter in the mass matrix of $K^0$-$bar{K^0}$, a genuine CPT violating effect independent of $Delta Gamma$ and not requiring the decay as an essential ingredient. Possible spurious effects induced by CP violation in the decay and/or a violation of the $Delta S= Delta Q$ rule have been shown to be well under control. The proposed test is thus fully robust, and might shed light on possible new CPT violating mechanisms, or further improve the precision of the present experimental limits. It could be implemented at the DA$Phi$NE facility in Frascati, where the KLOE-2 experiment might reach a statistical sensitivity of $mathcal{O}(10^{-3})$ on the newly proposed observable quantities.