Theory of the CP-violating parameter epsilon '/epsilon

The real part of epsilon'/epsilon measures direct CP violation in the decay s of neutral kaons into two pions. This is a fundamental quantity that has justly attracted a great deal of theoretical as well as experimental work. Determination of its value may answer the question of whether CP violation is present only in the mass matrix of neutral kaons (the superweak scenario ) or whether it is also at work directly in the decay amplitudes. After a b rief historical summary, the present and expected experimental sensitivitie s are discussed. In light of these, the authors address the problem of esti mating epsilon'/epsilon in the standard model and review the status of the theoretical predictions of epsilon'/epsilon as of the beginning of 1999. Th e short-distance part of the computation is now known to the next-to-leadin g order in QCD and QED and is therefore well under control. On the other ha nd, the evaluation of the hadronic matrix elements of the relevant operator s is where most of the theoretical uncertainty still resides. The authors a nalyze the results of the most extensive calculations to date. The values o f the matrix-element parameters in the various approaches are discussed, to gether with the allowed range of quark mixing angles in the Cabibbo-Kobayas hi-Maskawa matrix. All recent predictions of epsilon'/epsilon are summarize d and compared. Because of the intrinsic uncertainties of the long-distance computations, values ranging from 10(-4) to a few times 10(-3) can be acco unted for in the standard model. Since this range covers most of the presen t experimental uncertainty, it is unlikely that new-physics effects can be disentangled from the standard-model prediction.