Theoretical status of ε ′ / ε

The present theoretical status of the parameter for direct CP violation ε/ε in the Standard Model is reviewed and compared with most recent experimental measurements of the same quantity. After collecting the basic expressions for ε/ε, the situation of hadronic matrix element calculations is summarised. The matrix elements constitute the dominant source of uncertainty for theoretical determinations of ε/ε. For central values of the input parameters, the numerical analysis then yields results which are generally below the experimental data. Possible reasons for these findings are discussed. T his year has experienced a revived strong interest in the parameter ε/ε which quantifies direct CP violation in the neutral kaon system, due to the recent experimental measurements by the KTeV and NA48 collaborations: Re (ε/ε) = (28.0± 4.1) · 10 KTeV [1] , Re (ε/ε) = (18.5± 7.3) · 10 NA48 [2] . Both measurements confirm the large value found previously by the NA31 collaboration [5] and give rise to the new world average [3] Re (ε/ε) = (21.4± 4.0)× 10 . (1) Experimentally, the signature for direct CP violation is a deviation of the ratio |η+−/η00| 2 from unity, where η+− ≡ A(KL → ππ) A(KS → π+π−) , (2) η00 ≡ A(KL → ππ) A(KS → π0π0) . (3) Theoretically, it is more convenient to consider quantities were the final state pions are in a definite isospin state: ε ≡ A(KL → (ππ)I=0) A(KS → (ππ)I=0) , (4) ω ≡ A(KS → (ππ)I=2) A(KS → (ππ)I=0) . (5) Heisenberg fellow. The parameter ε measures indirect CP violation in the neutral kaon system which displays the fact that the physical mass eigenstates KL and KS are not eigenstates of CP, but have small admixtures of the order of ε from the opposite CP parity. The second parameter ω has nothing to do with CP violation, but is introduced for convenience. It parametrises the so called ∆I = 1/2 rule which states that the isospin zero final state is much enhanced over the isospin two final state. In other words, the ∆I = 1/2 transition is strongly enhanced over the ∆I = 3/2 transition. With the help of these quantities, the parameter ε can be defined as ε ≡ 1 √ 2 [ A(KL → (ππ)I=2) A(KS → (ππ)I=0) − ε · ω ]