Instability of a dilute Fermi liquid in the presence of forward scattering

The stability of a Fermi liquid is analyzed by summing series of diagrams with an interaction mediated by a system close to quantum criticality. The critical temperature and the gap are derived in terms of an effective coupling constant and do not depend on the density of states at the Fermi surface. The forward scattering process is identified as the main pairing mechanism for the case of low, or vanishing, levels of doping.