Theory of the Resonant Neutron Scattering of High-TcSuperconductors

Recent polarized neutron scattering experiments on Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ have revealed a sharp spectral peak at the ($\pi$, $\pi$) 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.