Effective field theory for dilute Fermi systems at fourth order

TL;DR

This paper performs high-order perturbative calculations for dilute Fermi gases using effective field theory, demonstrating convergence and resummation techniques up to fourth order, with implications for ultracold atoms and neutron matter.

Contribution

It extends the perturbative expansion of the ground-state energy to fourth order and compares regularization schemes, providing convergence analysis and resummation methods for dilute Fermi systems.

Findings

Expansion converges well for |k_F a_s| ≤ 0.5

Padé-Borel resummation improves convergence up to |k_F a_s| ≤ 1

Results constrain nonperturbative calculations in ultracold atoms and neutron matter

Abstract

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or $k_{\rm F} a_s$ expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well-converged at this order for ${| k_{\rm F} a_s | \lesssim 0.5}$. Further, we show that Pad{\'e}-Borel resummations can improve the convergence for ${| k_{\rm F} a_s | \lesssim 1}$. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.