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

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.

11 pages, 5 figures

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• Chiral effective field theory and nuclear forces
• Accurate nuclear radii and binding energies from a chiral interaction
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Local three-nucleon interaction from chiral effective field theory
• Local chiral effective field theory interactions and quantum Monte Carlo applications
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• Local nucleon-nucleon and three-nucleon interactions within chiral effective field theory
• Dispersion relations applied to double-folding potentials from chiral EFT
• Chiral Effective Field Theory's Impact on Advancing Quantum Monte Carlo Methods
• Local chiral EFT potentials in nuclei and neutron matter: results and issues