One-electron spectral functions of the attractive Hubbard model for intermediate coupling

We calculate the one-electron spectral function of the attractive (negative-$U)$ Hubbard model. We work in the intermediate-coupling and low-density regime and obtain the self-energy in an approximate analytical form. The excitation spectrum is found to consist of three branches. The results are obtained in a framework based on the self-consistent $T$-matrix approximation, which is compatible with the Mermin-Wagner theorem.