Symmetry Be Tested With K 0 vs K̄ 0 → π + π − π 0 Decays ?

We show that the CP-violating effect in K vs K̄ → πππ decays differs from that in KL → π π, KL → π π or the semileptonic KL transitions, if there exists CPT violation in K-K̄ mixing. A delicate measurement of this difference in the KTeV experiment and at the φ factory will provide a new test of CPT symmetry in the neutral kaon system. PACS number(s): 11.30. Er, 13.25. Es, 14.40. Aq Typeset using REVTEX 1 The K-K̄ mixing system has been playing an important role in particle physics for testing fundamental symmetries (such as CP, T and CPT) and examining conservation laws (such as ∆S = ∆Q). The existing experimental evidence for CPT invariance in the mixing and decays of neutral kaon mesons remains rather poor [1]: it is not excluded that the strength of CPT-violating interactions could be as large as about ten percentage of that of CP-violating interactions. This unsatisfactory situation will be improved in the near future, in particular after a variety of more delicate measurements are carried out in the KTeV experiment [2] and at the φ factory [3]. There are several possibilities to pin down CPT violation in K-K̄ mixing with the decays of KS and KL mesons into the two-pion and (or) the semileptonic states [4]. Recently a new possibility to test CPT symmetry, with the help of neutral kaon decays into the threepion states, has been pointed out in Ref. [5]. The idea is simply that the CP-violating effect induced by K-K̄ mixing in K vs K̄ → πππ transitions should not be identical to that in KL → π π, KL → π π or the semileptonic KL decays, if CPT symmetry is also violated. Thus a careful comparison between these two types of CP-violating effects may provide a robust test of CPT invariance in K-K̄ mixing. This paper aims at elaborating the preliminary idea proposed in Ref. [5] and presenting the time-dependent CP asymmetry between K(t) → πππ and K̄(t) → πππ decays. Our result is expected to be useful for the forth-coming experiments of kaon physics. Let us explain the main idea concisely. The mass eigenstates of K and K̄ mesons can in general be written as |KS〉 = 1