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 phase-disordered 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.
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