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Theory of the Resonant Neutron Scattering of High $T_c$ Superconductors

Recent polarized neutron scattering experiments on $YBa_2 Cu_3 O_7$ have revealed a sharp spectral peak at the $(π,π)$ in reciprocal lattice centered around the energy transfer of $41\ meV$. We offer a theoretical explanation of this remarkable experiment in terms of a new collective mode in the particle particle channel of the Hubbard model. This collective mode yields valuable information about the symmetry of the superconducting gap.