Effective Field Theory Interactions Research Articles

Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions

Local chiral effective field theory interactions have recently been developed and used in the context of quantum Monte Carlo few- and many-body methods for nuclear physics. In this work, we go over detailed features of local chiral nucleon-nucleon interactions and examine their effect on properties of the deuteron, paying special attention to the perturbativeness of the expansion. We then turn to three-nucleon interactions, focusing on operator ambiguities and their interplay with regulator effects. We then discuss the nuclear Green's function Monte Carlo method, going over both wave-function correlations and approximations for the two- and three-body propagators. Following this, we present a range of results on light nuclei: Binding energies and distribution functions are contrasted and compared, starting from several different microscopic interactions.

Recent development in theoretical studies of hyperon-nucleon interaction

Hypernuclear physics is the study of hypernuclei, their decays and productions, and the role they play in other related fields. It has always been at the frontier of experimental and theoretical nuclear physics since the quantum number strangeness was introduced and the first Λ hypernuclus was discovered in 1953. In recent years, open questions such as the large change symmetry breaking in A =4 Λ hypernuclei, the overbinding problem of A =5 Λ hypernucleus, the existence of the H-dibaryon and the hyperon puzzle in neutron stars have attracted a lot of attention. Today facilities like J-PARC, KEK, JLab, MAMI and COSY allow one to study the properties of hypernuclei with a precision and scope hitherto impossible. The experiments focus not only on the spectroscopy and weak decays of hypernuclei with strangeness S= − 1 and S = − 2, but also on the fundamental ΣN cross sections. In the meantime, theoretical techniques of few- and many-body calculations for hypernuclei have made steady progress, such as the Gaussian expansion method, the lattice QCD simulations and the Dirac-Brueckner-Hartree-Fock approach. Hyperon-nucleon interaction is the key input of the hypernuclear few- and many-body calculations. It plays a fundamental role in the microscopic understanding of hypernuclear physics. Meanwhile, it can also help improve our understanding of the role of strangeness in particle and nuclear physics, as well as the SU(3) symmetry and its breaking. In this paper, we first review the origin of hypernuclear physics and enmumerrate the aforementioned open questions of current interest. These outstanding issues reflect that the hyerpon-nucleon interaction is not fully understood so far. Then we discuss at length the history and current status of theoratical studies of hyperon-nucleon interaction, which are mainly performed in phenomenological models, lattice quantumchromo dynamics (lattice QCD) simulations and chiral effective field theory. The construction of phenomenological models, such as meson exchange models and quark models, has a rather long history. However, they predict very different results even for some of the low-energy phase shifts and scattering lengths, owing to the rather loose constraint from the small number of hyperon-nucleon scattering data. Lattice QCD simulations have made impressive progress since the 21st century, which provide an ab-initio numerical solution to QCD from first principles. With the ever-growing computing power and evolving numerical algorithms, lattice QCD simulations are getting close to the physical point (but still with large error bars). As the effective theory of low-energy QCD, chiral effective field theory has proven to be a useful tool in studies of low-energy strong interaction phenomena. The main feature of this approach is that by using a proper power counting scheme, one can improve calculations systematically by going to higher orders in powers of external momenta and light quark masses, and meantime the uncertainties of any given order. Furthermore, three- and four-body forces can be derived in a consistent manner. Studies of hadron-hadron interaction in chiral effective field theory have made remarkable progress in the past two decades and in the last part of this article we discuss the recent construction of hyperon-nucleon interaction in chiral effective field theory in detail.

First-principle calculations of dark matter scattering off light nuclei

We study the scattering of Dark Matter particles off various light nuclei within the framework of chiral effective field theory. We focus on scalar interactions and include one- and two-nucleon scattering processes whose form and strength are dictated by chiral symmetry. The nuclear wave functions are calculated from chiral effective field theory interactions as well and we investigate the convergence pattern of the chiral expansion in the nuclear potential and the Dark Matter-nucleus currents. This allows us to provide a systematic uncertainty estimate of our calculations. We provide results for ${}^2$H, ${}^3$H, and ${}^3$He nuclei which are theoretically interesting and the latter is a potential target for experiments. We show that two-nucleon currents can be systematically included but are generally smaller than predicted by power counting and suffer from significant theoretical uncertainties even in light nuclei. We demonstrate that accurate high-order wave functions are necessary in order to incorporate two-nucleon currents. We discuss scenarios in which one-nucleon contributions are suppressed such that higher-order currents become dominant.

Electric Dipole Polarizability of ^{48}Ca and Implications for the Neutron Skin.

The electric dipole strength distribution in ^{48}Ca between 5 and 25MeV has been determined at RCNP, Osaka from proton inelastic scattering experiments at forward angles. Combined with photoabsorption data at higher excitation energy, this enables the first extraction of the electric dipole polarizability α_{D}(^{48}Ca)=2.07(22) fm^{3}. Remarkably, the dipole response of ^{48}Ca is found to be very similar to that of ^{40}Ca, consistent with a small neutron skin in ^{48}Ca. The experimental results are in good agreement with abinitio calculations based on chiral effective field theory interactions and with state-of-the-art density-functional calculations, implying a neutron skin in ^{48}Ca of 0.14-0.20fm.

Applying the density matrix expansion with coordinate-space chiral interactions

We apply the density matrix expansion (DME) at Hartree-Fock level with long-range chiral effective field theory interactions defined in coordinate space up to next-to-next-to-leading order. We consider chiral potentials both with and without explicit $\mathrm{\ensuremath{\Delta}}$ isobars. The challenging algebra associated with applying the DME to three-nucleon forces is tamed using a new organization scheme, which will also facilitate generalizations. We include local regulators on the interactions to mitigate the effects of singular potentials on the DME couplings and simplify the optimization of generalized Skyrme-like functionals.

Singlet model interference effects with high scale UV physics

One of the simplest extensions of the Standard Model (SM) is the addition of a scalar gauge singlet, S. If S is not forbidden by a symmetry from mixing with the Standard Model Higgs boson, the mixing will generate non-SM rates for Higgs production and decays. In general, there could also be unknown high energy physics that generates additional effective low energy interactions. We show that interference effects between the scalar resonance of the singlet model and the effective field theory (EFT) operators can have significant effects in the Higgs sector. We examine a non-$Z_2$ symmetric scalar singlet model and demonstrate that a fit to the 125 GeV Higgs boson couplings and to limits on high mass resonances, S, exhibit an interesting structure and possible large cancellations of effects between the resonance contribution and the new EFT interactions, that invalidate conclusions based on the renormalizable singlet model alone.

Quantum Monte Carlo calculations of two neutrons in finite volume

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the L\"uscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.

Regulator artifacts in uniform matter for chiral interactions

Regulator functions applied to two- and three-nucleon forces are a necessary ingredient in many-body calculations based on chiral effective field theory interactions. These interactions have been developed recently with a variety of different cutoff forms, including regulating both the momentum transfer (local) and the relative momentum (nonlocal). While in principle any regulator that suppresses high momentum modes can be employed, in practice artifacts are inevitable in current power counting schemes. Artifacts from particular regulators may cause significant distortions of the physics or may affect many-body convergence rates, so understanding their nature is important. Here we characterize the differences between cutoff effects using uniform matter at Hartree-Fock and second-order in the interaction as a testbed. This provides a clean laboratory to isolate phase-space effects of various regulators on both two- and three-nucleon interactions. We test the normal-ordering approximation for three-nucleon forces in nuclear matter and find that the relative size of the residual 3N contributions is sensitive to the employed regularization scheme.

Neutron matter with Quantum Monte Carlo: chiral 3N forces and static response

Neutron matter is related to the physics of neutron stars and that of neutron-rich nuclei. Quantum Monte Carlo (QMC) methods offer a unique way of solving the many-body problem non-perturbatively, providing feedback on features of nuclear interactions and addressing scenarios that are inaccessible to other approaches. In this contribution we go over two recent accomplishments in the theory of neutron matter: a) the fusing of QMC with chiral effective field theory interactions, focusing on local chiral 3N forces, and b) the first attempt to find an ab initio solution to the problem of static response.

Nuclear saturation in lowest-order Brueckner theory with two- and three-nucleon forces in view of chiral effective field theory

The nuclear saturation mechanism is discussed in terms of two-nucleon and three-nucleon interactions in chiral effective field theory (Ch-EFT), using the framework of lowest-order Brueckner theory. After the Coester band, which is observed in calculating saturation points with various nucleon-nucleon (NN) forces, is revisited using modern NN potentials and their low-momentum equivalent interactions, detailed account of the saturation curve of the Ch-EFT interaction is presented. The three-nucleon force (3NF) is treated by reducing it to an effective two-body interaction by folding the third nucleon degrees of freedom. Uncertainties due to the choice of the 3NF low-energy constants $c_D$ and $c_E$ are discussed. The reduction of the cutoff-energy dependence of the NN potential is explained by demonstrating the effect of the 3NF in the $^1$S$_0$ and $^3$S$_1$ states.

Effective Field Theory of Interactions on the Lattice

We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare lattice coupling constants to the continuum coupling constants. Our method constitutes a very simple avenue for the systematic renormalization in effective field theory, and is especially useful as the number of interaction parameters increases.

Local chiral effective field theory interactions and quantum Monte Carlo applications

We present details of the derivation of local chiral effective field theory interactions to next-to-next-to-leading order, and show results for nucleon-nucleon phase shifts and deuteron properties for these potentials. We then perform systematic auxiliary-field diffusion Monte Carlo calculations for neutron matter based on the developed local chiral potentials at different orders. This includes studies of the effects of the spectral-function regularization and of the local regulators. For all orders, we compare the quantum Monte Carlo results with perturbative many-body calculations and find excellent agreement for low cutoffs.

Quantum Monte Carlo calculations of neutron matter with nonlocal chiral interactions.

We present fully nonperturbative quantum MonteCarlo calculations with nonlocal chiral effective field theory (EFT) interactions for the ground-state properties of neutron matter. The equation of state, the nucleon chemical potentials, and the momentum distribution in pure neutron matter up to one and a half times the nuclear saturation density are computed with a newly optimized chiral EFT interaction at next-to-next-to-leading order. This work opens the way to systematic order by order benchmarking of chiral EFT interactions and ab initio prediction of nuclear properties while respecting the symmetries of quantum chromodynamics.

Photon Asymmetries in $${nd\rightarrow}$$ n d → 3 Hγ Using EFT( $${/\!\!\!\pi}$$ / π ) Approach

The parity-violating Lagrangian of the weak nucleon-nucleon ($NN$) interaction in the pionless effective field theory (EFT($//!/!/!/pi$)) approach contains five independent unknown low-energy coupling constants (LECs). The photon asymmetry with respect to neutron polarization in $np\rightarrow$ $d\gamma$ $A^{np}_\gamma$, the circular polarization of outgoing photon in $np\rightarrow$ $d\gamma$ $P^{np}_\gamma$, the neutron spin rotation in hydrogen $\frac{1}{\rho}\frac{d\phi^{np}}{dl}$, the neutron spin rotation in deuterium $\frac{1}{\rho}\frac{d\phi^{nd}}{dl}$ and the circular polarization of $\gamma$-emission in $nd\rightarrow$ $^3H\gamma$ $P^{nd}_\gamma$ are the parity-violating observables which have been recently calculated in terms of parity-violating LECs in the EFT($//!/!/!/pi$) framework. We obtain the LECs by matching the parity-violating observables to the Desplanques, Donoghue, and Holstein (DDH) best value estimates. Then, we evaluate photon asymmetry with respect to the neutron polarization $a^{nd}_\gamma$ and the photon asymmetry in relation to deuteron polarization $A^{nd}_\gamma$ in $nd\rightarrow$ $^3H\gamma$ process. We finally compare our EFT($//!/!/!/pi$) photon asymmetries results with the experimental values and the previous calculations based on the DDH model.

Antinucleon-nucleon interaction in chiral effective field theory

Results of an exploratory study of the antinucleon-nucleon interaction within chiral effective field theory are reported. The antinucleon-nucleon potential is derived up to next-to-next-to-leading order, based on a modified Weinberg power counting, in close analogy to pertinent studies of the nucleon-nucleon interaction. The low-energy constants associated with the arising contact interactions are fixed by a fit to phase shifts and inelasticities provided by a recently published phase-shift analysis of antiproton-proton scattering data. The overall quality of the achieved description of the antinucleon-nucleon amplitudes is comparable to the one found in case of the nucleon-nucleon interaction at the same order. For most S-waves and several P-waves good agreement with the antinucleon-nucleon phase shifts and inelasticities is obtained up to laboratory energies of around 200 MeV.

Symmetry energy, neutron skin, and neutron star radius from chiral effective field theory interactions

We discuss neutron matter calculations based on chiral effective field theory interactions and their predictions for the symmetry energy, the neutron skin of 208 Pb, and for the radius of neutron stars.

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.