Analyzing the Fierz Rearrangement Freedom for Local Chiral Two-Nucleon Potentials

TL;DR

This paper investigates how local regulators in chiral effective field theory affect the Fierz rearrangement freedom of two-nucleon potentials, analyzing its impact on nuclear observables and the restoration of this freedom at higher orders.

Contribution

It provides a detailed analysis of the violation of Fierz rearrangement freedom in local chiral potentials and explores its partial restoration at NLO, with implications for three-nucleon interactions.

Findings

Fierz rearrangement freedom is violated at LO with local regulators.

Partial restoration of Fierz freedom occurs at NLO due to subleading interactions.

Impacts on phase shifts, helium ground state, and neutron matter energy are analyzed.

Abstract

Chiral effective field theory is a framework to derive systematic nuclear interactions. It is based on the symmetries of quantum chromodynamics and includes long-range pion physics explicitly, while shorter-range physics is expanded in a general operator basis. The number of low-energy couplings at a particular order in the expansion can be reduced by exploiting the fact that nucleons are fermions and therefore obey the Pauli exclusion principle. The antisymmetry permits the selection of a subset of the allowed contact operators at a given order. When local regulators are used for these short-range interactions, however, this "Fierz rearrangement freedom" is violated. In this paper, we investigate the impact of this violation at leading order (LO) in the chiral expansion. We construct LO and next-to-leading order (NLO) potentials for all possible LO-operator pairs and study their reproduction of phase shifts, the ${}^4$He ground-state energy, and the neutron-matter energy at different densities. We demonstrate that the Fierz rearrangement freedom is partially restored at NLO where subleading contact interactions enter. We also discuss implications for local chiral three-nucleon interactions.