1 Introduction

The observation of CP violation in decays would greatly enrich our understanding of this, still mysterious, phenomenon.

CP violation in , even at the level where mass-mixing effects only are observed, is very interesting, because any deviation of from is a direct signal of CPT violation. On the other side, CP-odd charge asymmetries in decays would give a univocal sign of the milliweak nature of CP violation. If current Standard Theory estimates are correct, the direct CP violation parameter for , , tends to be quite small because of a cancellation of the dominant gluon penguin diagram contribution with the one arising from the electroweak penguin diagrams, made competitive by the large value of the t quark mass [1]. The same two classes of contributions do not cancel in the asymmetry of decays, which then could provide the crucial test of the scheme. Furthermore, while is essentially suppressed by the rule as being proportional to the small ratio of the to the amplitude, in there are two independent amplitudes whose CP-violating interference can avoid this suppression, and in principle could be expected to produce an enhanced effect.

Unfortunately, in general the predicted Dalitz-plot slope asymmetries are in the order of few units per million (subject to a theoretical error which could be perhaps of a factor ten). In particular, the interference between the two amplitudes turns out to occur only in higher orders in the chiral perturbation theory expansion (), and the corresponding enhancement is therefore somewhat reduced. On purely statistical grounds, DANE experiments can reach the level of a few units in and therefore are rather far from the crucial region, with presently foreseen luminosities. Concerning neutral kaon decays, DANE experiments can observe a few decays [2], enough to establish the effect, but to a precision unlikely to reveal any CPT anomaly in .

Nonetheless, since DANE should significantly improve presently existing data and/or bounds on decays, it is appropriate to discuss in this Handbook the present status-of-the-art of this field.