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We derive the universal high momentum factorization of the fermionself-energy in the BCS-BEC crossover of ultracold atoms using nonperturbativequantum field theoretical methods. This property is then employed to computethe Tan contact as a function of interaction strength, temperature, chemicalpotential and Fermi momentum. We clarify the mechanism of the factorizationfrom an analysis of the self-consistent Schwinger-Dyson equation for thefermion propagator, and compute the perturbative contact on the BCS and BECsides within this framework. A Functional Renormalization Group approach isthen put forward, which allows to determine the contact over the wholecrossover and, in particular, for the Unitary Fermi gas. We present numericalresults from an implementation of the Renormalization Group equations within abasic truncation scheme.

Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover