A dynamical mean-field theory analysis of the attractive Hubbard model in the normal phase is carried out upon restricting to solutions where superconducting order is not allowed. A clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half filling between a Fermi liquid, stable for U<U(c), and an insulating bound pairs phase for U>U(c), and it is accompanied by phase separation. The spectral function in the metallic phase is constituted by a low-energy structure around the Fermi level, which disappears discontinuously at U = U(c), and two high-energy features (Hubbard bands), which persist in the insulating phase.
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Capone et al. (2002) studied this question.