Direct tests of T, CP, CPT symmetries in transitions of neutral K mesons with the KLOE experiment

Tests of the T, CP and CPT symmetries in the neutral kaon system are performed by the direct comparison of the probabilities of a kaon transition process to its symmetry-conjugate. The exchange of in and out states required for a genuine test involving an anti-unitary transformation implied by time-reversal is implemented exploiting the entanglement of $K^0\bar{K}{}^0$ pairs produced at a $\phi$-factory. A data sample collected by the KLOE experiment at DA$\mathrm{\Phi }$NE corresponding to an integrated luminosity of about 1.7 fb${}^{-1}$ is analysed to study the $\mathrm{\Delta }$t distributions of the $\phi \to K_S{K}_L\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }{e}^{\mp }\nu$ and $\phi \to K_S{K}_L\to {\pi }^{\pm }{e}^{\mp }\nu 3{\pi }^0$ processes, with $\mathrm{\Delta }$t the difference of the kaon decay times. A comparison of the measured $\mathrm{\Delta }$t distributions in the asymptotic region $\mathrm{\Delta }t\gg {\tau }_S$ allows to test for the first time T and CPT symmetries in kaon transitions with a precision of few percent, and to observe CP violation with this novel method.