Dispersion of the neutron resonance in cuprate superconductors

We argue that recently measured downward dispersion of the neutron resonance peak in cuprate superconductors is naturally explained if the resonance is viewed as a spin-1 collective mode in a $d-\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}$ superconductor. The reduction of the resonant frequency away from the antiferromagnetic wave vector is a direct consequence of the momentum dependence of the $d-\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}$ superconducting gap. When the magnetic correlation length becomes large, the dispersion should become magnonlike, i.e., curve upwards from $(\pi ,\pi ).\mathrm{}$