The authors calculate the imaginary part of the response function (Im chi ) and the imaginary part of the electron self-energy (Im Sigma ) for a two-dimensional energy band with a saddle point close to the Fermi energy EF, using lowest-order perturbation theory in the screened Coulomb interaction. They find that Im chi (q, omega ) remains finite for arbitrarily small frequencies omega for certain directions of q if the saddle point is at EF, leading to a rich behavior of Im Sigma . For an electron far from the saddle point, Im Sigma (k, E(k)) approximately (E(k)-EF)1.5, except in specific directions of k where the power is only 4/3. For an electron close to a saddle point, a linear dependence on the energy is obtained. These results are compared with numerical calculations for the Emery model of the CuO2 planes in high-Tc superconductors.
 

Physical Review B, 46 11798-806, 1992.