Abstract
Chiral Effective Field Theory (EFT) two- and three-nucleon forces are now widely employed. Since they were originally formulated in momentum space, these interactions were non-local, making them inaccessible to Quantum Monte Carlo (QMC) methods. We have recently derived a local version of chiral EFT nucleon-nucleon and three-nucleon interactions, which we also used in QMC calculations for neutron matter and light nuclei. In this contribution I go over the basics of local chiral EFT and then summarize recent results.
Highlights
Chiral Effective Field Theory (EFT) nuclear forces were designed to provide a connection with the symmetries of QCD [1,2,3]
Such interactions contain pion exchanges as well as shorter-range phenomenological terms. These include consistently predicted three-nucleon (3N) forces, which first enter at next-to-next-to-leading order (N2LO) [4, 5]. (The expansion parameter here is Q/Λb where Q is the soft scale—typically a nucleon momentum or the pion mass—and Λb ∼ Mρ is the hard scale where the chiral EFT expansion breaks down.) These interactions are critical for neutron and nuclear matter [6,7,8,9,10,11,12,13,14]
Given the accuracy and precision of Quantum Monte Carlo (QMC) calculations for strongly interacting systems [19, 20], this state of affairs was problematic, a direct consequence of chiral EFT potentials being non-local. (It’s worth noting that Monte Carlo methods have, been used to study neutron matter based on lattice techniques [21] and with momentum-space QMC approaches [22, 23].) The main reason for chiral EFT interactions being non-local was that they are naturally formulated in momentum space, so they were historically constructed without considering their locality or non-locality
Summary
Chiral EFT nuclear forces were designed to provide a connection with the symmetries of QCD [1,2,3]. Such interactions contain pion exchanges as well as shorter-range phenomenological terms. These include consistently predicted three-nucleon (3N) forces, which first enter at next-to-next-to-leading order (N2LO) [4, 5]. Given the accuracy and precision of QMC calculations for strongly interacting systems [19, 20], this state of affairs was problematic, a direct consequence of chiral EFT potentials being non-local. We have been constructing local chiral potentials, at the NN and 3N level, and using them to calculate properties of neutron matter and light nuclei. [24,25,26,27,28] Here we briefly summarize basic aspects of local chiral EFT, before discussing NN+3N results for neutron matter and light nuclei
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