Effective theory and universal relations for Fermi gases near a $d$-wave interaction resonance

TL;DR

This paper develops an effective field theory for two-component Fermi gases near a $d$-wave resonance, revealing universal properties and additional correlation contacts, and extends the theory to higher partial waves.

Contribution

It introduces a renormalizable effective field theory for $d$-wave resonant Fermi gases and uncovers new universal relations involving extra contacts.

Findings

Derived universal properties using operator product expansion.

Identified additional contacts in momentum distribution and spectroscopy.

Generalized the formalism to higher partial wave resonances.

Abstract

In this work, we present an effective field theory to describe a two-component Fermi gas near a $d$-wave interaction resonance. The effective field theory is renormalizable by matching with the low energy $d$-wave scattering phase shift. Based on the effective field theory, we derive universal properties of the Fermi gas by the operator product expansion method. We find that beyond the contacts defined by adiabatic theorems, the asymptotic expressions of the momentum distribution and the Raman spectroscopy involve two extra contacts which provide additional information of correlations of the system. Our formalism sets the stage for further explorations of many-body effects in a $d$-wave resonant Fermi gas. Finally we generalise our effective field theory for interaction resonances of arbitrary higher partial waves.