The Operator Product Expansion Beyond Leading Order for Spin-1/2 Fermions

Strongly interacting systems of ultracold, two-component fermions have been studied using various techniques for many years. One technique that has been applied is a quantum field theoretical formulation of the zero-range model. In this framework, the Operator Product Expansion was used to derive universal relations for systems with a large scattering length[1]. This corroborated and extended the work of Tan[2-4]. We calculate finite range corrections to the momentum distribution using the OPE framework and demonstrate the utility of including the $1/k^6$ tail from the OPE for the momentum distribution. Corrections to the universal relations for the system are calculated and expressed in terms of the S-wave effective range and an additional quantity D similar to Tan's contact which, in addition to the contact, relates various physical observables. We compare our results with quantum Monte Carlo calculations for the two-component Fermi gas with large scattering length. \\References: \\1. E. Braaten and L. Platter, Phys. Rev. Lett. 100, 205301 (2008) \\2. S. Tan, Annals of Physics 323, 2971 (2008), ISSN 0003-4916 \\3. S. Tan, Annals of Physics 323, 2952 (2008), ISSN 0003-4916 \\4. S. Tan, Annals of Physics 323, 2987 (2008), ISSN 0003-4916