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DOE OSTI2022

Magnetic structure of few-nucleon systems at high momentum transfers in a chiral effective field theory approach

The five low-energy constants (LECs) in the electromagnetic current derived in chiral effective field theory ( χ EFT ) up to one loop are determined by a simultaneous fit to the A = 2 – 3 nuclei magnetic moments and to the deuteron magnetic form factor and threshold electrodisintegration at backward angles over a wide range of momentum transfers. The resulting parametrization then yields predictions for the 3 He/ 3 H magnetic form factors in excellent accord with the experimental values for momentum transfers ranging up to ≈0.8 GeV/c, beyond the expected regime of validity of the χEFT approach. The calculations are based on last-generation two-nucleon interactions including high orders in the chiral expansion and derived by Entem, Machleidt, and Nosyk [Phys. Rev. C 96, 024004 (2017)] and by Piarulli et al. [Phys. Rev. C 94, 054007 (2016)], using different χEFT formulations. In the A = 3 calculations, (chiral) three-nucleon interactions are also accounted for. The model dependence resulting from these different formulations of the interactions is found to be mild for momentum transfer below ≈0.8 GeV/c . Further, an analysis of the convergence of the chiral expansion is also provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Nucleon-Nucleon Scattering Up to N5LO in Chiral Effective Field Theory

During the past few decades a large effort has been made toward describing the NN interaction in the framework of chiral Effective Field Theory (EFT). The main idea is to exploit the symmetries of QCD to obtain an effective theory for low energy nuclear systems. In 2003, the first accurate charge-dependent NN potential in this scheme was developed and it has been applied to many ab-initio calculations, opening the possibility to study nuclear systems in a systematic and accurate way. It was shown that the fourth order (N3LO) was necessary and sufficient to describe the NN scattering data with a χ 2 /d.o.f on the order of so-called high precision potentials. However the systematics of chiral EFT also allow to relate two- and many-body interactions in a well-defined way. Since many-body forces make their first appearance at higher order, they are substantially smaller than their two-body counterparts, but may never-the-less be crucial for some processes. Thus, there are observables where they can have a big impact and, for example, there are indications that they solve the long standing Ay puzzle of N-d scattering. The last few years, have also seen substantial progress toward higher orders of chiral EFT which was motivated by the fact that only three-body forces of rather high order may solve some outstanding issues in microscopic nuclear structure and reactions. In this chapter we will review the latest contributions of the authors to development of chiral EFT based potentials up to N4LO as well as first calculations conducted for NN scattering at N5LO.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Renormalization of one-pion exchange in chiral effective field theory for antinucleon-nucleon scattering

The renormalization of iterated one-pion exchange (OPE) is studied in Chiral Effective Field Theory ($\chi$EFT) for the antinucleon-nucleon ($\overline{N}N$) system. The OPE potential is cut off at a certain distance and contact interactions are represented by a complex spherical well with the same radius. We investigate the dependence on the cutoff radius of the phase shifts, inelasticities, and mixing angles for the low partial waves in $\overline{N}N$ scattering. We show that renormalization requires additional contact interactions compared to the expectation based on naive dimensional analysis. Results after renormalization are compared with the state-of-the-art energy-dependent partial-wave analysis of $\overline{N}N$ data. We compare our conclusions with applications of $\chi$EFT to the nucleon-nucleon system.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Proton pairing in neutron stars from chiral effective field theory

Here, we study the 1 S 0 proton pairing gap in beta-equilibrated neutron star matter within the framework of chiral effective field theory. We focus on the role of three-body forces, which strongly modify the effective proton-proton spin-singlet interaction in dense matter. We find that three-body forces generically reduce both the size of the pairing gap and the maximum density at which proton pairing may occur. The pairing gap is computed within BCS theory using a single-particle dispersion relation calculated up to second order in perturbation theory. Model uncertainties are estimated by varying the nuclear potential (its order in the chiral expansion and high-momentum cutoff) and the choice of single-particle spectrum in the gap equation. We find that a second-order perturbative treatment of the single-particle spectrum suppresses the proton 1 S 0 pairing gap relative to the use of a free spectrum. We estimate the critical temperature for the onset of proton superconductivity to be T c = (3:2–5:1) 10 9 K, which is consistent with previous theoretical results in the literature and marginally within the range deduced from a recent Bayesian analysis of neutron star cooling observations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Nuclear multipole responses from chiral effective field theory interactions

We probe nuclear multipole resonances in the framework of the random-phase approximation by using the interaction obtained from the chiral effective field theory. The three-nucleon force is included in a form of the in-medium two-nucleon interaction, which was derived from the chiral three-nucleon force. The isoscalar monopole, isoscalar dipole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell 56,68,78 Ni have been investigated. The calculations reasonably reproduce the experimental multipole resonances of 56,68 Ni, and well describe the pygmy dipole resonance and dipole polarizability measured in 68 Ni. The multipole resonances of 78 Ni, including pygmy dipole resonance and dipole polarizability, are predicted. The detailed effects of the tensor force and three-body force are analyzed by dissecting the chiral interaction. In this work, we find that in general the tensor force effect on electric giant resonances is not as significant as the effect from the three-body force, although the tensor force provides more than half of the binding energy. The effect from three-body force is strong in light nuclei. Particularly, three-body force is crucial for the formation of the pygmy resonance in calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables

We explore the constraints on the three-nucleon force (3NF) of chiral effective field theory (χ EFT) that are provided by bound-state observables in the A = 3 and A = 4 sectors. Our statistically rigorous analysis incorporates experimental error, computational method uncertainty, and the uncertainty due to truncation of the χ EFT expansion at next-to-next-to-leading order. A consistent solution for the 3 H binding energy, the 4 He binding energy and radius, and the 3 H β-decay rate can only be obtained if χ EFT truncation errors are included in the analysis. Here, the β-decay rate is the only one of these that yields a nondegenerate constraint on the 3NF low-energy constants, which makes it crucial for the parameter estimation. We use eigenvector continuation for fast and accurate emulation of no-core shell model calculations of the few-nucleon observables. This facilitates sampling of the posterior probability distribution, allowing us to also determine the distributions of the parameters that quantify the truncation error. We find a χ EFT expansion parameter of Q = 0.33 ± 0.06 for these observables.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Three-nucleon lepton-number-violating potentials in chiral effective field theory and their matrix elements in light nuclei

Here, we derive the three-nucleon neutrinoless double-𝛽 decay potential in a Δ-full chiral effective field theory through next-to-next-to-next-to leading order in Weinberg's power counting. The matrix elements of the resulting operators are computed in light nuclei using variational Monte Carlo with wave functions constructed from the Norfolk family of nuclear interactions. We find that three-nucleon corrections induce a modest quenching of the total nuclear matrix elements. We discuss model dependencies and the potential impact of these corrections on the sensitivity of experimental programs to probe lepton number violating parameters. These results provide a benchmark for many-body methods capable of reaching heavier nuclei of experimental interest.

Chambers-Wall, Graham [Washington University, St. ↗
DOE OSTI2022

Two-pion exchange as a leading-order contribution in chiral effective field theory

Pion exchange is the central ingredient to nucleon-nucleon interactions used in nuclear structure calculations, and one-pion exchange (OPE) enters at leading order in chiral effective field theory. In the 2S+1 L J = 1 S 0 partial wave, however, OPE and a contact term needed for proper renormalization fail to produce the qualitative, and quantitative, features of the scattering phase shifts. Cutoff variation also revealed a surprisingly low breakdown momentum Λ b ≈ 330 MeV in this partial wave. Here we show that potentials consisting of OPE, two-pion exchange (TPE), and a single contact address these problems and yield accurate and renormalization group (RG) invariant phase shifts in the 1 S 0 partial wave. Here, we demonstrate that a leading-order potential with TPE can be systematically improved by adding a contact quadratic in momenta. For momentum cutoffs Λ ≲ 500 MeV, the removal of relevant physics from TPE loops needs to be compensated by additional contacts to keep RG invariance. Inclusion of the Δ isobar degree of freedom in the potential does not change the strong contributions of TPE.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Constraining Hamiltonians from chiral effective field theory with neutron-star data

Multi-messenger observations of neutron stars (NSs) and their mergers have placed strong constraints on the dense-matter equation of state (EOS). The EOS, in turn, depends on microscopic nuclear interactions that are described by nuclear Hamiltonians. These Hamiltonians are commonly derived within chiral effective field theory (EFT). Ideally, multi-messenger observations of NSs could be used to directly inform our understanding of EFT interactions, but such a direct inference necessitates millions of model evaluations. This is computationally prohibitive because each evaluation requires us to calculate the EOS from a Hamiltonian by solving the quantum many-body problem with methods such as auxiliary-field diffusion Monte Carlo (AFDMC), which provides very accurate and precise solutions but at a significant computational cost. Additionally, we need to solve the stellar structure equations for each EOS which further slows down each model evaluation by a few seconds. In this work, we combine emulators for AFDMC calculations of neutron matter, built using parametric matrix models, and for the stellar structure equations, built using multilayer perceptron neural networks, with the PyCBC data-analysis framework to enable a direct inference of coupling constants in an EFT Hamiltonian using multi-messenger observations of NSs. We find that astrophysical data can provide informative constraints on two-nucleon couplings despite the high densities probed in NS interiors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Neutron matter from local chiral effective field theory interactions at large cutoffs

Neutron matter is an important many-body system that provides valuable constraints for the equation of state (EOS) of neutron stars. Neutron-matter calculations employing chiral effective field theory (EFT) interactions have been extensively used for this purpose. Among the various many-body methods, quantum Monte Carlo (QMC) methods stand out due to their nonperturbative nature and the achievable precision. However, QMC methods require local interactions as input, which leads to the appearance of stronger regulator artifacts compared to nonlocal interactions. To circumvent this, we employ large-cutoff interactions derived within chiral EFT (400 MeV ≤ Λ 𝑐 ≤ 700MeV) for studies of pure neutron matter. These interactions have been adjusted to nucleon-nucleon scattering phase shifts, the triton binding energy, as well as the triton 𝛽-decay half-life. We find that regulator artifacts significantly decrease with increasing cutoff, leading to a significant reduction of uncertainties in the neutron-matter EOS. We discuss implications for the symmetry energy and demonstrate how our new calculations lead to a reduction in the theoretical uncertainty of predicted neutron-star radii by up to 30% for low-mass stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

From chiral effective field theory to perturbative QCD: A Bayesian model mixing approach to symmetric nuclear matter

Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory (𝜒⁢EFT ) can describe the EOS between the typical densities of nuclei and those in the outer cores of neutron stars, while perturbative QCD (pQCD) can be applied to properties of deconfined quark matter, both with quantified theoretical uncertainties. However, describing the full range of densities in between with a single EOS that has well-quantified uncertainties is a challenging problem. Bayesian multimodel inference from 𝜒⁢EFT and pQCD can help bridge the gap between the two theories. In this work, we introduce a correlated Bayesian model mixing framework that uses a Gaussian process (GP) to assimilate different information into a single QCD EOS for symmetric nuclear matter. The present implementation uses a stationary GP to infer this mixed EOS solely from the EOSs of 𝜒⁢EFT and pQCD while accounting for the truncation errors of each theory. The GP is trained on the pressure as a function of number density in the low- and high-density regions where 𝜒⁢EFT and pQCD are, respectively, valid. We impose priors on the GP kernel hyperparameters to suppress unphysical correlations between these regimes. This, together with the assumption of stationarity, results in smooth 𝜒⁢EFT-to-pQCD curves for both the pressure and the speed of sound. We show that using uncorrelated mixing requires uncontrolled extrapolation of at least one of 𝜒⁢EFT or pQCD into regions where the perturbative series breaks down and leads to an acausal EOS. Here, we also discuss extensions of this framework to nonstationary and less differentiable GP kernels, its future application to neutron-star matter, and the incorporation of additional constraints from nuclear theory, experiment, and multimessenger astronomy.

Bayesian methods↗
DOE OSTI2024

Constraining the Dense Matter Equation of State with New NICER Mass–Radius Measurements and New Chiral Effective Field Theory Inputs

Pulse profile modeling of X-ray data from the Neutron Star Interior Composition Explorer is now enabling precision inference of neutron star mass and radius. Combined with nuclear physics constraints from chiral effective field theory (χEFT), and masses and tidal deformabilities inferred from gravitational-wave detections of binary neutron star mergers, this has led to a steady improvement in our understanding of the dense matter equation of state (EOS). Here, we consider the impact of several new results: the radius measurement for the 1.42 M ⊙ pulsar PSR J0437−4715 presented by Choudhury et al., updates to the masses and radii of PSR J0740+6620 and PSR J0030+0451, and new χEFT results for neutron star matter up to 1.5 times nuclear saturation density. Using two different high-density EOS extensions—a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS)—we find the radius of a 1.4 M ⊙ (2.0 M ⊙ ) neutron star to be constrained to the 95% credible ranges ${12.28}_{-0.76}^{+0.50}$ km (${12.33}_{-1.34}^{+0.70}$ km) for the PP model and ${12.01}_{-0.75}^{+0.56}$ km (${11.55}_{-1.09}^{+0.94}$ km) for the CS model. The maximum neutron star mass is predicted to be ${2.15}_{-0.16}^{+0.14}$M ⊙ and ${2.08}_{-0.16}^{+0.28}$M ⊙ for the PP and CS models, respectively. We explore the sensitivity of our results to different orders and different densities up to which χEFT is used, and show how the astrophysical observations provide constraints for the pressure at intermediate densities. Moreover, we investigate the difference R 2.0 − R 1.4 of the radius of 2 M ⊙ and 1.4 M ⊙ neutron stars within our EOS inference.

gravitational wave sources↗
DOE OSTI2023

Auxiliary field diffusion Monte Carlo calculations of magnetic moments of light nuclei with chiral effective field theory interactions

We calculate the magnetic moments of light nuclei $( A < 20 )$ using the auxiliary field diffusion Monte Carlo method and local two- and three-nucleon forces with electromagnetic currents from chiral effective field theory. For all nuclei under consideration, we also calculate the ground-state energies and charge radii. We generally find a good agreement with experimental values for all of these observables. For the electromagnetic currents, we explore the impact of employing two different power counting schemes, and study theoretical uncertainties stemming from the truncation of the chiral expansion order by order for select nuclei within these two approaches. In conclusion, we find that it is crucial to employ consistent power counting schemes for interactions and currents to achieve a systematic order-by-order convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Order-by-order uncertainties of nucleon-nucleon Wolfenstein amplitudes in chiral effective field theory

Quantum mechanical invariance principles dictate the most general operator structure that can be present in the nucleon-nucleon (NN) interaction. Five independent operators appear in the on-shell NN amplitude together with five corresponding coefficient functions. The usual choice for these coefficient functions is known as the NN Wolfenstein amplitudes. We analyze the order-by-order convergence of each of the five NN Wolfenstein amplitudes predicted by a semilocal coordinate space potential implementation of chiral effective field theory (𝜒⁢EFT). We do this at laboratory kinetic energies between 25 and 200 MeV for both neutron-proton and proton-proton scattering. Our analysis uses the Gaussian-process methods developed by the BUQEYE Collaboration to describe the contributions of each 𝜒⁢EFT order, and so yields truncation uncertainties for each Wolfenstein amplitude that are correlated across scattering angles. We combine information on the size of different orders in the EFT to infer the 𝜒⁢EFT breakdown scale for each amplitude, finding, on average, Λ 𝑏 between 750 and 800 MeV. Furthermore, with this choice of Λ 𝑏 , the EFT truncation uncertainties cover both higher-order results and empirical Wolfenstein amplitudes well for all orders other than the leading order.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Direct astrophysical tests of chiral effective field theory at supranuclear densities

Recent observations of neutron stars with gravitational waves and X-ray timing provide unprecedented access to the equation of state (EoS) of cold dense matter at densities difficult to realize in terrestrial experiments. At the same time, predictions for the EoS equipped with reliable uncertainty estimates from chiral effective field theory ( x EFT) allow us to bound our theoretical ignorance. In this work, we analyze astrophysical data using a nonparametric representation of the neutron-star EoS conditioned on x EFT to directly constrain the underlying physical properties of the compact objects without introducing modeling systematics. We discuss how the data alone constrain the EoS at high densities when we condition on x EFT at low densities. Here, we also demonstrate how to exploit astrophysical data to directly test the predictions of x EFT for the EoS up to twice nuclear saturation density, in order to estimate the density at which these predictions might break down. We nd that the existence of massive pulsars, gravitational waves from GW170817, and NICER observations of PSR J0030+0451 favor x EFT predictions for the EoS up to nuclear saturation density over a more agnostic analysis by as much as a factor of 7 for the quantum Monte Carlo (QMC) calculations used in this work. While x EFT predictions using QMC are fully consistent with gravitational-wave data up to twice nuclear saturation density, NICER observations suggest that the EoS stiffens relative to these predictions at or slightly above nuclear saturation density. Additionally, for these QMC calculations, we marginalize over the uncertainty in the density at which x EFT begins to break down, constraining the radius of a 1.4M $\bigodot$ neutron star to R 1.4 = $11.40^{+1.38}_{–1.04}$ ($12.54^{+0.71}_{–0.63}$) km and the pressure at twice nuclear saturation density to p(2n sat ) = $14.2^{+18.1}_{–8.4}$ ($28.7^{+15.3}_{–15.0}$) MeV=fm 3 with massive pulsar and gravitational-wave (and NICER) data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Calculations of the $np→dγ$ reaction in chiral effective field theory

Here, we present a calculation of the radiative capture cross section of the $np→dγ$ reaction in the low-energy range, where the M⁢1 reaction channel dominates. Employing the LENPIC nucleon-nucleon interaction up to the fifth order (N4LO) that is regularized by the semilocal coordinate space regulators, we obtain the initial and final state wave functions, and evaluate the phase shifts of the scattering state and deuteron properties. We derive the transition operator from the chiral effective field theory up to the next-to-next-to leading order (N2LO), where we also regularize the transition operator using regulators consistent with those of the interactions. We compute the capture cross sections, and the results show a converging pattern with the chiral-order expansion of the nucleon-nucleon interaction, where the regulator dependence of the results is weak when higher-order nucleon-nucleon interactions are employed. We quantify the uncertainties of the cross-section results due to the chiral-order truncation. The chirally complete and consistent cross-section results are calculated up to N2LO and they compare well with the experiments and other theoretical predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Densities and momentum distributions in A ≤ 12 nuclei from chiral effective field theory interactions

Current and future electron and neutrino scattering experiments will be greatly aided by a better understanding of the role played by short-range correlations in nuclei. Two-body physics, including nucleon-nucleon correlations and two-body electroweak currents, is required to explain the body of experimental data for both static and dynamical nuclear properties. In this work, we focus on examining nucleon-nucleon correlations from a chiral effective field theory perspective and provide a comprehensive set of new variational Monte Carlo calculations of one- and two-body densities and momentum distributions based on the Norfolk many-body nuclear Hamiltonians for A ≤ 12 systems. Here, online access to detailed tables and figures is available.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Studying electroweak few-body observables in chiral effective field theory

The use of nuclei to study electroweak probes is becoming increasingly relevant experimentally. The success of dark matter and neutrino experiments strongly depends on the ability to control nuclear effects in order to extract the fundamental parameters associated with external probes. Therefore, reliable theoretical calculations of nuclear structure and reactions, with well-controlled errors, are crucial for the success of experimental efforts. Currently, chiral effective field theory ($\chi$EFT) coupled with {\it ab-initio} methods represents one of the best approaches that fulfills these requirements. To use this approach as a tool for studying fundamental physics, it is essential to validate it against experimental data for which the calculations are well under control, such as the elastic scattering of electrons on nuclei. In this proceeding, I will present recent developments in the fitting of electromagnetic currents derived using $\chi$EFT and the calculation of electromagnetic form factors of light nuclei. The results of these calculations demonstrate the strength of the theory in describing the interaction of nuclei with electromagnetic probes over a broad range of momentum transfers and highlight the robustness of $\chi$EFT for analyzing future experimental data aimed at extracting fundamental parameters.

Gnech, Alex [Old Dominion Univ., Norfolk, VA (Unit↗