1 Introduction

The state produced in the decay of the resonance is odd under charge conjugation and is therefore an antisymmetric state. This characteristic makes a factory very suitable to study CP violation and to test CPT symmetry in K meson decays [1,2].

For a long time it has been stressed that the presence in the same detector of and beams, produced without regeneration and thus with the relative fluxes perfectly known, will allow a very clean determination of the ratio [3]. A non-zero value for is an unambiguous signal of the existence of direct CP violation, which is naturally expected in the Standard Model. The present experimental situation is:

still consistent with . The theoretical calculation of in the Standard Model is strongly affected by QCD corrections and, for large values of the top mass, large cancellations are expected [6]. The present estimate is , [7] thus a fundamental goal of DANE is certainly to reach the sensitivity of in the measurement of this ratio. Independent information about direct CP violation could be obtained also by charge asymmetries in [8] and [9] decays.

Beyond the study of direct CP violation, the presence of a pure beam will allow the observation at DANE of some suppressed decays, such as the semileptonic and the three-pion ones. The theoretical predictions for semileptonic decays are not strongly affected by QCD corrections and, as we will discuss later, the measurement of the semileptonic rates and charge asymmetries in decays can give many interesting tests of CPT and of the rule. Moreover, due to the coherence of the initial state, T and CPT symmetries can be directly tested in events with two leptons in the final state [10,11].

Some time ago it was pointed out that the radiative decay could have a non-negligible branching ratio [12] and therefore a dangerous background, namely a component even under charge conjugation, could be present. New determinations of the branching ratio [13] turn out to be much smaller, then, as we will show, the inclusion of the C-even background does not sensibly affect the measurements of and suppressed decays.

It has been suggested that quantum mechanics violations may be generated by non-local theories at the Planck scale [14]. As a consequence CP- and CPT-violating effects of non quantum-mechanical origin could be induced [15,16]. In [16] it was proposed to investigate such effects in quantum correlated particle systems, such as the system. The coherence of the -factory initial state will help in disentangling these effects, and quite stringent bounds could be obtained for the quantum mechanics violating parameters [17,18]. It is worth while to note that the quantum mechanics violation induces a loss of the initial state coherence which can somehow simulate the effect of a C-even background.

The plan of the paper is the following: in section 2 we recall the time evolution of the initial state. In section 3 we report its implications on the determination of real and imaginary parts of . In section 4 the semileptonic decays, with possible direct tests of T and CPT symmetry, are discussed. Sections 5 and 6 are devoted, respectively, to and decays. In section 7 we study the effect of the C-even background. In section 8 we discuss the implications of possible quantum mechanics violations. Finally, in the appendix, the relation between time and distance measurements are discussed.