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

## TL;DR

This paper investigates the stability of a dilute Fermi liquid near quantum criticality, highlighting forward scattering as the main pairing mechanism and deriving critical temperature and gap expressions independent of the Fermi surface density of states.

## Contribution

It introduces a new analysis of Fermi liquid stability considering forward scattering near quantum criticality, deriving key physical quantities.

## Key findings

- Forward scattering dominates pairing in low doping regimes.
- Critical temperature and gap are independent of the Fermi surface density of states.
- Theoretical framework sums series of diagrams to analyze stability.

## Abstract

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.