Direct Test of T and CPT Symmetries with Entangled Neutral Mesons

Abstract

In general any theoretical connection among the parameters describing T, CP or CPT violation, as given by the CPT theorem, does not imply a corresponding connection among the experimental results of the T, CP or CPT tests. In this paper the possibility to perform a direct test of time-reversal T symmetry in the neutral kaon system is discussed. It requires the exchange of in and out states of a transition process. The only existing result [1] for neutral kaons showing a non-zero asymmetry comparing the rates of a reference process (K → K) and its T conjugated one (K → K) cannot be considered a direct test, because the T and CP conjugated processes are identical in this case, and cannot be distinguished. In fact here direct test means a test whose outcome is independent of the result of any other discrete symmetry test, as discussed in detail in Refs. [3 7]. In order to implement such a direct test of the T symmetry, and also of the CPT symmetry which requires as well the inversion of in and out states, it has been suggested to exploit the Einstein-Podolsky-Rosen (EPR) entanglement of neutral mesons produced at a φ-factory (or B-factory) [4 7]. In fact in this case the initial state of the neutral kaon pair produced in φ → KK decay can be rewritten in terms of any pair of orthogonal states |K+〉 and |K−〉: |i〉 = 1 √ 2 {|K〉|K〉 − |K〉|K〉} =