Dispersion of the neutron resonance in cuprate superconductors

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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-wave superconductor. The reduction of the resonant frequency away from the antiferromagnetic wave vector is a direct consequence of the momentum dependence of the d-wave superconducting gap. When the magnetic correlation length becomes large, the dispersion should become magnon-like, i.e., curve upwards from (pi,pi).