Effective Field Theory Interactions Research Articles

Neutron matter from chiral effective field theory interactions

The neutron-matter equation of state constrains the properties of many physical systems over a wide density range and can be studied systematically using chiral effective field theory (EFT). In chiral EFT, all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We present details and additional results of the first complete N3LO calculation of the neutron-matter energy, which includes the subleading three-nucleon as well as the leading four-nucleon forces, and provides theoretical uncertainties. In addition, we discuss the impact of our results for astrophysics: for the supernova equation of state, the symmetry energy and its density derivative, and for the structure of neutron stars. Finally, we give a first estimate for the size of the N3LO many-body contributions to the energy of symmetric nuclear matter, which shows that their inclusion will be important in nuclear structure calculations.

Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions

We present the first quantum MonteCarlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion MonteCarlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide nonperturbative benchmarks with theoretical uncertainties. For the softer interactions, perturbative calculations are in excellent agreement with the AFDMC results. This work paves the way for QMC calculations with systematic chiral EFT interactions for nuclei and nuclear matter, for testing the perturbativeness of different orders, and allows for matching to lattice QCD results by varying the pion mass.

Neutron matter based on consistently evolved chiral three-nucleon interactions

We present the first results for the neutron matter equation of state (EOS) using nucleon-nucleon and three-nucleon chiral effective field theory interactions that are consistently evolved in the framework of the similarity renormalization group (SRG). The dependence of the EOS on the SRG resolution scale is greatly reduced when induced three-nucleon forces (3NF) are included, and the residual variation, which in part is from missing induced four-body interactions, is comparable to estimated many-body perturbation theory truncation errors. The relative growth with decreasing resolution of the 3NF contributions to the energy per neutron is of natural size, but it accelerates at the lowest resolutions where strong renormalization of the long-range 3NF matrix elements is also observed.

NEUTRINO PROCESSES IN PARTIALLY DEGENERATE NEUTRON MATTER

We investigate neutrino processes for conditions reached in simulations of core-collapse supernovae. Where neutrino-matter interactions play an important role, matter is partially degenerate, and we extend earlier work that addressed the degenerate regime. We derive expressions for the spin structure factor in neutron matter, which is a key quantity required for evaluating rates of neutrino processes. We show that, for essentially all conditions encountered in the post-bounce phase of core-collapse supernovae, it is a very good approximation to calculate the spin relaxation rates in the nondegenerate limit. We calculate spin relaxation rates based on chiral effective field theory interactions and find that they are typically a factor of two smaller than those obtained using the standard one-pion-exchange interaction alone.

Hyperon–Nucleon and Hyperon–Hyperon Interactions in Chiral Effective Field Theory

Current activities in the description of baryon–baryon systems with strangeness S = −1 and −2 within chiral effective field theory are reviewed. In particular, results for the hyperon–nucleon and hyperon–hyperon interactions obtained to leading order are presented. Preliminary results for Λ N and Σ N scattering at next-to-leading order are discussed. Some comments on the H dibaryon are made.

Renormalization Group Invariance in Pionless Effective Field Theory for the NN System

We consider the NN interaction in pionless effective field theory (EFT) up to next-to-next-to-leading order (NNLO) and use a recursive subtractive renormalization scheme to describe NN scattering in the 1S0 channel. We fix the strengths of the contact interactions at a reference scale, chosen to be the one that provides the best fit for the phase-shifts, and then slide the renormalization scale by evolving the driving terms of the subtracted Lippmann-Schwinger equation through a non-relativistic Callan-Symanzik equation. The results show that such a systematic renormalization scheme with multiple subtractions is fully renormalization group invariant.

Constraints on Neutron Star Radii Based on Chiral Effective Field Theory Interactions

We show that microscopic calculations based on chiral effective field theory interactions constrain the properties of neutron-rich matter below nuclear densities to a much higher degree than is reflected in commonly used equations of state. Combined with observed neutron star masses, our results lead to a radius R=9.7-13.9 km for a 1.4M⊙ star, where the theoretical range is due, in about equal amounts, to uncertainties in many-body forces and to the extrapolation to high densities.

Baryon-baryon interactions in effective field theory

Current activities in the description of baryon-baryon systems are reviewed. In particular, recent results for the hyperon-nucleon and hyperon-hyperon interactions as well as for strangeness S = − 3 to −4 baryon-baryon systems, obtained to leading order within the framework of chiral effective field theory, are presented. Preliminary results for the hyperon-nucleon interaction to next-to-leading order are reported.

Similarity Renormalization Group Evolution of Nucleon-Nucleon Interactions in the Subtracted Kernel Method Approach

In this work we study the Similarity Renormalization Group (SRG) evolution of effective nucleon-nucleon ( N N ) interactions derived using the Subtracted Kernel Method (SKM) approach. We present the results for the phaseshifts in the S 0 1 channel calculated using a SRG potential evolved from an initial effective potential obtained by implementing the SKM scheme for the leading-order NN interaction in chiral effective field theory (ChEFT).

Predictions for the strangeness [formula omitted] and −4 baryon–baryon interactions in chiral effective field theory

The leading order strangeness S=−3 and −4 baryon–baryon interactions are analyzed within chiral effective field theory. The chiral potentials consist of contact terms without derivatives and of one-pseudoscalar-meson exchanges. Assuming SU(3) flavor symmetry those contact terms and the couplings of the pseudoscalar mesons to the baryons are related to the corresponding quantities of the S=−1 hyperon–nucleon channels. Specifically, the values of the pertinent five low-energy constants related to the contact terms are already fixed from our preceding study of the ΛN and ΣN systems and thus genuine predictions for the ΞΛ, ΞΣ, and ΞΞ interactions can be made. Strong attraction is found in some of the S=−3 and −4 channels, suggesting the possible existence of bound states.

Δ contribution to the parity-violating nucleon-nucleon force**Supported by National Natural Science Foundation of China (10625521, 10721063, 10775146), China Postdoctoral Science Foundation (20070420526) and Ministry of Education of China

Because the nucleon may be excited and transformed into a virtual Δ resonance easily, we consider the decuplet contribution to the parity-violating (PV) nucleon-nucleon interaction in the chiral effective field theory. The effective PV nucleon-nucleon potential is derived without introducing any unknown coupling constants.

Strangeness [formula omitted] baryon–baryon interactions using chiral effective field theory

We derive the leading order strangeness S=−2 baryon–baryon interactions in chiral effective field theory. The potential consists of contact terms without derivatives and of one-pseudoscalar-meson exchanges. The contact terms and the couplings of the pseudoscalar mesons to the baryons are related via SU(3)f symmetry to the S=−1 hyperon–nucleon channels. We show that the chiral effective field theory predictions with natural values for the low-energy constants agree with the experimental information in the S=−2 sector.

Low-momentum interactions with smooth cutoffs

Nucleon–nucleon potentials evolved to low momentum, which show great promise in few- and many-body calculations, have generally been formulated with a sharp cutoff on relative momenta. However, a sharp cutoff has technical disadvantages and can cause convergence problems at the 10–100 keV level in the deuteron and triton. This motivates using smooth momentum-space regulators as an alternative. We generate low-momentum interactions with smooth cutoffs both through energy-independent renormalization group methods and using a multi-step process based on the Bloch–Horowitz approach. We find greatly improved convergence for calculations of the deuteron and triton binding energies in a harmonic oscillator basis compared to results with a sharp cutoff. Even a slight evolution of chiral effective field theory interactions to lower momenta is beneficial. The renormalization group preserves the long-range part of the interaction, and consequently the renormalization of long-range operators, such as the quadrupole moment, the radius and 〈 1 / r 〉 , is small. This demonstrates that low-energy observables in the deuteron are reproduced without short-range correlations in the wave function.

ΛN→NNweak interaction in effective-field theory

The nonleptonic weak $|\Delta S|=1$ $\Lambda N$ interaction, responsible for the dominant nonmesonic decay of all but the lightest hypernuclei, is studied in the framework of an effective field theory. The long-range physics is described through tree-level exchange of the SU(3) Goldstone bosons, while the short-range potential is parametrized in terms of the lowest-order contact terms. We obtain reasonable fits to available weak hypernuclear decay rates and quote the values for the parity-violating asymmetry as predicted by the present effective field theory.

Three-body interactions in many-body effective field theory

Three-body interactions in many-body effective field theory

Three-body interactions in many-body effective field theory

This contribution is an adverstisement for applying effective field theory (EFT) to many-body problems, including nuclei and cold atomic gases. Examples involving three-body interactions are used to illustrate how EFT's quantify and systematically eliminate model dependence, and how they make many-body calculations simpler and more powerful.