Weak Matrix Elements and K-meson Physics

Kaon Physics is a very complicated blend of Ultraviolet and Infrared effects which still defies complete physical understanding. The problem consists in the large enhancement (≈ 20) of the ∆I = 12 amplitude with respect to the ∆I = 32 one. Being a process involving hadrons, Kdecay must be treated non-perturbatively, so that lattice discretization is the ideal tool to deal with this problem. In fact lattice regularization is the only convergent (as a → 0) approximation scheme to QCD. Due to the difficulties of putting the Standard Model on the lattice, one can use weak interaction perturbation theory, which, together with Asymptotic Freedom of Strong Interactions, allows the definition of an effective low energy actions for non-leptonic decays: