We explain recent experimental results on the superconducting state spectral function as obtained by angle resolved photoemission, as well as by tunneling, in high-T-c cuprates. In our model, electrons are coupled to the resonant spin-fluctuation mode observed in inelastic neutron-scattering experiments, as well as to a gapped continuum. We show that, although the weight of the resonance is small, its effect on the electron self-energy is large, and can explain various dispersion anomalies seen in the data. In agreement with the experiment, we find that these effects are a strong function of doping. We contrast our results to those expected for electrons coupled to phonons.
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