Evolution of the pairing pseudogap in the spectral function with interplane anisotropy

We study the pairing pseudogap in the spectral function as a function of in terplane coupling. The analytical expressions for the self-energy in the cr itical regime are obtained for any degree of anisotropy. The frequency depe ndence of Sigma(omega) is found to be qualitatively different in two and th ree dimensions, and the crossover from two to three dimensional behavior is discussed. In particular, by considering the anisotropy of the Fermi veloc ity and gap along the Fermi surface, we can qualitatively explain recent ph otoemission experiments on high temperature superconductors concerning the temperature dependent Fermi arcs seen in the pseudogap phase. [S0163-1829(9 9)00302-1].