Theory of Neutron Scattering in the Normal and Superconducting States ofYBa2Cu3O6+x

We analyze neutron experiments on $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ at various stoichiometries in the superconducting state, within the context of a bilayer theory that yields good agreement with the normal state Cu NMR and neutron data as a function of $\omega$, q, and $T$. A $d$-wave superconducting state exhibits peaks at $\mathrm{q}=(\pi , \pi , \pi )$ and sharp maxima as a function of $\omega$, at twice the gap frequency. This behavior may have been observed experimentally. The counterpart behavior for other choices of order parameter symmetry, as well as for another cuprate ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_4$, is discussed.