Kaons and Hyperons rare decays by the NA48 experiment at CERN

Neutral Kaons were the place where CP violation was discovered for the first time [1]. Forty years after that discovery, kaons are still a privileged system where quarks coupling can be studied. The CKM quark mixing matrix [2] structure is usually addressed through the so-called unitarity triangle [3]. The very popular picture of this triangle based on measurements coming from B mesons decays and mixing can be replaced by an analogous one based on Kaons decays. It is evident that the possibility to compare the theoretical prediction in two independent system (the B system and the K system) with comparable experimental and theoretical uncertainties is very promising in the view of any signal of new physics or of the possible failure of the present Standard Model of particle interactions. The Kaon version of the unitarity triangle is mainly identified by the branching ratio of the K → πνν decay and of the (direct CP-violating) KL → πνν, which are theoretically very clean even if very demanding from an experimental point of view. The less theoretically clean KL → πee and KL → πμμ decays can be used in place of the KL → πνν decay, but the different physical contributions to the decay must be disentangled. The CP conserving part of KL → πll can be calculated from the branching ratio of the KL → πγγ decay measured by NA48 [4]: BR(KL → πee)CPcons. = 0.47 −0.18 × 10 (1)