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

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