Resonant neutron scattering on the high Tc cuprates and π and η excitations of the t-J and Hubbard models

We review the explanation for resonant neutron scattering experiments in YBa2Cu3O6+δ and Bi2Sr2Ca2O8+δ materials from the point of view of triplet excitation in the particle-particle channel, the π excitation. Relation of these resonances to the superconducting condensation energy and their role in stabilizing the superconducting state is discussed. Due to the superconducting fluctuations, the π resonance may appear as a broad peak above Tc. The analogue problem to the π excitation for the case of s-wave pairing, the η excitation, is considered in the strong coupling limit with an emphasis on the resonance precursors in a state with no long range order.