Collective Modes and the Superconducting State Spectral Function of Bi2212

Photoemission spectra of the high temperature superconductor Bi2212 near (pi,0) show a dramatic change when cooling below Tc: the broad peak in the normal state turns into a sharp low energy peak followed by a higher binding energy hump. Recent experiments find that this low energy peak persists over a significant range in momentum space. We show in this paper that these data are well described by a simple model of electrons interacting with a collective mode which appears only below Tc.