Direct test of time reversal symmetry in the entangled neutral kaon system at a ϕ-factory

We present a novel method to perform a direct T (time reversal) symmetry test in the neutral kaon system, independent of any CP and/or CPT symmetry tests. This is based on the comparison of suitable transition probabilities, where the required interchange of in ↔ out states for a given process is obtained exploiting the Einstein–Podolski–Rosen correlations of neutral kaon pairs produced at a ϕ-factory. In the time distribution between the two decays, we compare a reference transition like the one defined by the time-ordered decays (ℓ−,ππ) with the T-conjugated one defined by (3π0,ℓ+). With the use of this and other T-conjugated comparisons, the KLOE-2 experiment at DAΦNE could make a statistically significant test.