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

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