Vector meson exchange contributions to K --> pi gamma gamma and K(L) -> gamma lepton+ lepton-

We have studied in the framework of Chiral Perturbation Theory (ChPT) the O(p^6) Vector Meson contributions to K -> pi gamma gamma and K(L) -> gamma gamma^*. We construct the most general ChPT lagrangian for the weak Vector-Pseudoscalar-Photon (VPgamma) vertex for K -> pi gamma gamma and K(L) -> gamma gamma^* and consequently we get the full structure of the O(p^6) local contributions generated by Vector Meson exchange. Then we compute new factorizable contributions to the weak VPgamma vertex generated by the odd-intrinsic parity violating lagrangian with no additional couplings. We find in fact a very nice agreement with the phenomenology of K -> pi gamma gamma and K(L) -> gamma gamma^*, more predictive power and a deeper understanding of the O(p^6) local operators. A novel interpretation of the K(L) -> gamma gamma^* data is given. Also a comparison with the existing models is presented.