Differential sum rule for the relaxation rate in the cuprates

Motivated by recent experiments by Basov et al., we study the differential sum rule for the effective scattering rate 1/tau(omega) . We show that, in a dirty BCS superconductor, the area under 1/tau(omega) does not change between the normal and the superconducting states. For magnetically mediated pairing, a similar result holds between T