Universal One-dimensional Atomic Gases Near Odd-wave Resonance

We show the renormalization of contact interaction for odd-wave scattering in one-dimension(1D). Based on the renormalized interaction, we exactly solve the two-body problem in a harmonic trap, and further explore the universal properties of spin-polarized fermions near odd-wave resonance using the operator product expansion method. It is found that the high-momentum distribution behaves as $C/k^2$, with $C$ the odd-wave contact. Various universal relations are derived. Our work suggests a new universal system emergent in 1D with large odd-wave scattering length.