Vertex corrections in a non-fermi liquid with a 2d patched Fermi Surface

We consider vertex correction effects in the self-energy Sigma from a 2d mo del composed of Landan quasiparticles states with a patched Fermi Surface ( FS) sandwiched by states with flat (1d) dispersion to simulate the "cold" s pot regions found in the underdoped cuprates. We calculate Sigma up to 3-lo op order. We show that the interaction with the single-particle states with the if at FS turn the cold spots into non-Fermi liquid states.