The rare K and B semileptonic decays into neutrino pairs are well-known to be
extremely sensitive to non-standard physics in the quark sector. In this talk,
their capabilities to signal New Physics in the leptonic sector, or even to
reveal entirely new invisible sectors, are analyzed.Comment: Talk given at CKM2010, 6th International Workshop on the CKM
Unitarity Triangle, University of Warwick, UK, 6-10 September 201