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Theoretical status of ǫ ′ /ǫ ∗

I give a detailed introduction into the theoretical formalism for ǫ ′ /ǫ , which measures direct CP-violation in K → ππ decays. The current status of hadronic matrix elements and the strange quark mass is discussed. Several possible explanations of the unexpectedly high experimental results for ǫ ′ /ǫ are pointed out: A small strange quark mass, an enhancement of the hadronic parameter B (1 / 2) 6 from the σ resonance, an underestimate of isospin breaking and possible new physics contributions in the sdZ -vertex and the sd -gluon-vertex.