Invariance Tests in Neutral Kaon

The time evolution of a neutral kaon state state is described by d dt Ψ = −iΛΨ , Λ ≡ M − i 2 Γ (1) where M and Γ are Hermitian 2 × 2 matrices known as the mass and decay matrices. The corresponding eigenvalues are λ L,S = m L,S − i 2 γ L,S. CPT invariance requires the diagonal elements of Λ to be equal. The CPT-violation complex parameter δ is defined as δ = Λ K 0 K 0 − Λ K 0 K 0 2(λ L − λ S) = δ exp iφ SW + δ ⊥ exp i(φ SW + π 2) (2) where we have introduced the projections δ and δ ⊥ respectively parallel and perpendicular to the superweak direction φ SW = tan −1 (2∆m/∆γ), where ∆m = m L − m S and ∆γ = γ S − γ L , the positive mass and width differences between K L and K S. These projections are linked to the mass and width difference between K 0 and K 0 : δ = 1 4 γ K 0 − γ K 0 ∆m 2 + ∆γ 2 2 , δ ⊥ = 1 2 m K 0 − m K 0 ∆m 2 + ∆γ 2 2. (3) Re(δ) can be directly measured by studying the time evolution of the strangeness content of initially pure K 0 and K 0 states, for example through the asymmetry A CP T = P [K 0 → K 0 (t)] − P [K 0 → K 0 (t)] P [K 0 → K 0 (t)] + P [K 0 → K 0 (t)] = 4Re(δ) (4) where P [a → b(t)] is the probability that the pure initial state a is seen as state b at proper time t. This method has been used by tagging the initial strangeness with strong interactions and the final strangeness with the semileptonic decay (a more appropriate combination of semileptonic rates allows to be independent of any direct CPT violation in the decay itself)