Gapless superconductivity and the Fermi arc in the cuprates

We argue that the Fermi arc observed in angle resolved photoemission measurements in underdoped cuprates can be understood as a consequence of inelastic scattering in a d-wave superconductor. We analyze this phenomenon in the context of strong coupling Eliashberg theory, deriving a `single lifetime' model for describing the temperature evolution of the spectral gap as measured by single particle probes such as photoemission and tunneling.