23 pages, 21 figures; commissioned for the Topical Issue of The European Physical Journal A - Hadrons and Nuclei entitled "The tower of effective (field) theories and the emergence of nuclear phenomena."
We compare nuclear forces derived from chiral effective field theory (EFT) with those obtained from traditional (phenomenological and meson) models. By means of a careful analysis of paralleles and differences, we show that chiral EFT is superior to all earlier approaches in terms of both formal aspects and successful applications in ab initio calculations. However, in spite of the considerable progress made possible by chiral EFT, complete satisfaction cannot be claimed until outstanding problems---the renormalization issue being the most important one---are finally settled.
In spite of the great progress we have seen in recent years in the derivation of nuclear forces from chiral effective field theory (EFT), some important issues are still unresolved. In this contribution, we discuss the open problems which have particular relevance for microscopic nuclear structure, namely, the proper renormalization of chiral nuclear potentials and sub-leading many-body forces.
We are celebrating thirty-years from the seminal papers from Weinberg proposing to use the rules of Chiral Perturbation Theory to nucleon systems. His proposal was to build an Effective Field Theory (EFT) with Chiral symmetry as a key property. A big effort on this line have been made during these three decades, however the issue of renormalization of the theory is not settled. I will briefly review my path on this issue and give my personal view.
I report on recent progress in the description of baryon-baryon systems within chiral effective field theory. In particular, I discuss results for the strangeness S=-3 to -4 baryon-baryon systems, obtained to leading order.
Ever since quantum field theory was first applied to the derivation of nuclear forces in the mid-20th century, the renormalization of pion exchange with realistic couplings has presented a challenge. The implementation of effective field theories (EFTs) in the 1990s promised a solution to this problem but unexpected obstacles were encountered. The response of the nuclear community has been to focus on "chiral potentials" with regulators chosen to produce a good description of data. Meanwhile, a successful EFT without explicit pion exchange --- Pionless EFT --- has been formulated where renorma…
Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schrödinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic interactions and currents. These ab-initio methods have been used to accurately compute properties of light nuclei -- including their spectra, moments, and transitions -- and the equation of state of neutron and nuclear matter. In this work we review selected results obtained by combining quantum Monte Carlo methods and recent Hamiltonians constructed within chir…
The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory ($χ$EFT) up to order $e\, Q$ (or N4LO), where $Q$ denotes the low-momentum scale and $e$ is the electric charge. The specific form of the N3LO and N4LO corrections from, respectively, one-pion-exchange and two-pion-exchange depends on the off-the-energy-shell prescriptions adopted for the non-static terms in the corresponding potentials. We show that different prescriptions lead to unitarily equivalent potentials and accompanying charge operators. Thus, provided a consistent set is adopted, …
In recent years, the combination of advanced quantum Monte Carlo (QMC) methods and local interactions derived from chiral effective field theory (EFT) has been shown to provide a versatile and systematic approach to nuclear systems. Calculations at next-to-next-to-leading order in chiral EFT have lead to fascinating results for nuclei and nucleonic matter. On the one hand, ground-state properties of nuclei are well reproduced up to $A\leq16$, even though these potentials have been fit to nucleon-nucleon scattering and few-body observables only. On the other hand, a reasonable description of ne…
Since the pioneering work of Weinberg, Chiral Effective Field Theory ($χ$EFT) has been widely and successfully utilized in nuclear physics to study many-nucleon interactions and associated electroweak currents. Nuclear $χ$EFT has now developed into an intense field of research and is applied to study light to medium mass nuclei. In this contribution, we focus on the development of electroweak currents from $χ$EFT and present applications to selected nuclear electroweak observables.
Recent developments in nuclear theory allow us to make a connection between quantum chromodynamics (QCD) and low-energy nuclear physics. First, chiral effective field theory (chiEFT) provides a natural hierarchy to define two-nucleon (NN), three-nucleon (NNN), and even four-nucleon interactions. Second, ab initio methods have been developed capable to test these interactions for light nuclei. In this contribution, we discuss ab initio no-core shell model (NCSM) calculations for s-shell and p-shell nuclei with NN and NNN interactions derived within chiEFT.
We analyze the longest-range two-pion exchange contributions to the three-nucleon force at leading-loop order in the framework of heavy-baryon chiral effective field theory with explicit $Δ(1232)$ degrees of freedom. All relevant low-energy constants which appear in the calculation are determined from pion-nucleon scattering. Comparing our results with the ones obtained in the $Δ$-less theory at N4LO, we find effects of the $Δ$ isobar for this particular topology to be rather well represented in terms of resonance saturation of various low-energy constants in the $Δ$-less approach.
We present a determination of optical potentials using the double-folding method based on chiral effective field theory nucleon-nucleon interactions at next-to-next-to-leading order combined with dispersion relations to constrain the imaginary part. This approach is benchmarked on $^{16}$O--$^{16}$O collisions, and extended to the $^{12}$C--$^{12}$C and $^{12}$C--$^{16}$O cases. Predictions derived from these potentials are compared to data for elastic scattering at energies up to 1000 MeV, as well as for fusion at low energy. Without adjusting parameters, excellent agreement with experiment i…
We solve the ab initio no-core shell model (NCSM) in the complete Nmax = 8 basis for A = 7 and A = 8 nuclei with two-nucleon and three-nucleon interactions derived within chiral effective field theory (EFT). We find that including the chiral EFT three-nucleon interaction in the Hamiltonian improves overall good agreement with experimental binding energies, excitation spectra, transitions and electromagnetic moments. We predict states that exhibit sensitivity to including the chiral EFT three-nucleon interaction but are not yet known experimentally.
Neutron matter presents a unique system in chiral effective field theory (EFT), because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We discuss perturbative and first Quantum Monte Carlo (QMC) calculations of neutron matter with chiral EFT interactions and their astrophysical impact for the equation of state and neutron stars.
Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron scattering lengths and the triton binding energy) at the leading and next-to-leading orders of a power counting that ensures order-by-order renormalization in the two-nucleon system. Our results imply that three-body forces are not needed for renormalization of the three-nucleon system up to next-to-leading order, as usually assumed in the literature. (Errat…
A compressible liquid-drop approach adjusted to uniform matter many-body calculations based on chiral EFT interactions and to the experimental nuclear masses is used to investigate the neutron star crust properties. Eight chiral EFT hamiltonians and a representative phenomenological force (SLy4) are confronted. We show that some properties of the crust, e.g. clusters mass, charge, and asymmetry, are mostly determined by symmetric matter properties close to saturation density and are therefore mainly constrained by experimental nuclear masses, while other properties, e.g., energy per particle, …
We review the nuclear forces currently in use, i.e., the high-precision NN potentials of the 1990's and the nuclear two- and many-body forces based upon chiral effective field theory (EFT). We argue that the EFT approach is superior to any of the older schemes. Since accurate chiral forces are available now, the stage is set for microscopic nuclear structure to move into a new exciting era.
We have studied electroweak (EW) interactions in quantum hadrodynamics (QHD) effective field theory (EFT). The Lorentz-covariant EFT contains nucleon, pion, $Δ$, isoscalar scalar ($σ$) and vector ($ω$) fields, and isovector vector ($ρ$) fields. The lagrangian exhibits a nonlinear realization of (approximate) $SU(2)_L \otimes SU(2)_R$ chiral symmetry and incorporates vector meson dominance. First, we discuss the EW interactions at the quark level. Then we include EW interactions in QHD EFT by using the background-field technique. The completed QHD EFT has a nonlinear realization of $SU(2)_L \ot…
The five low-energy constants (LECs) in the electromagnetic current derived in chiral effective field theory ($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 $\approx 0.8$ GeV/c, beyond the expected regime of validity of t…
Recent chiral EFT calculations of nucleon polarizabilities reveal a problem in the current empirical determination of proton's electromagnetic polarizabilities. We also report on the progress in the empirical determination of the $Δ$(1232)-resonance magnetic moment in the process of $γp \to p π^0 γ'$ measured at MAMI.
We compute from chiral two- and three-nucleon interactions the energy per particle of symmetric nuclear matter and pure neutron matter at third-order in perturbation theory including self-consistent second-order single-particle energies. Particular attention is paid to the third-order particle-hole ring-diagram, which is often neglected in microscopic calculations of the equation of state. We provide semi-analytic expressions for the direct terms from central and tensor model-type interactions that are useful as theoretical benchmarks. We investigate uncertainties arising from the order-by-ord…
M. Smoluchowski Institute of Physics, Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University（雅盖隆大学物理、天文学与应用科学学院 M.Smoluchowski 物理研究所）；Doctoral School of Exact and Natural Sciences, Jagiellonian University（雅盖隆大学精确与自然科学研究生院）；Ruhr-Universität Bochum, Fakultät für Physik und Astronomie, Institut für Theoretische Physik II（波鸿鲁尔大学物理与天文学院理论物理第二研究所）
We present a fit of the spin-independent electromagnetic polarisabilities of the proton to low-energy Compton scattering data in the framework of covariant baryon chiral effective field theory. Using the Baldin sum rule to constrain their sum, we obtain $α=[10.6\pm0.25$(stat)$\pm0.2$(Baldin)$\pm0.4$(theory)$]\times10^{-4}$fm$^3$ and $β=[3.2\mp0.25$(stat)$\pm0.2$(Baldin)$\mp0.4$(theory)$]\times10^{-4}$fm$^3$, in excellent agreement with other chiral extractions of the same quantities.
Recent calculations of EDMs of light nuclei in the framework of chiral effective field theory are presented. We argue that they can be written in terms of the leading six low-energy constants encoding CP-violating physics. EDMs of the deuteron, triton, and helion are explicitly given in order to corroborate our claim. An eventual non-zero measurement of these EDMs can be used to disentangle the different sources and strengths of CP-violation.
We present a study of two-nucleon scattering in chiral effective field theory with a finite cutoff to next-to-leading order in the chiral expansion. In the proposed scheme, the contributions of the lowest-order interaction to the scattering amplitude are summed up to an arbitrary order, while the corrections beyond leading order are iterated only once. We consider a general form of the regulator for the leading-order potential including local and non-local structures. The main objective of the paper is to address formal aspects of renormalizability within the considered scheme. In particular, …
Recently, a new generation of nuclear forces has been developed in the framework of chiral EFT. An important feature of these potentials is a novel semi-local regularization approach that combines the advantages of a local regulator for long-range interactions with the convenience of an angle-independent nonlocal regulator for contact interactions. The authors discuss the key features of the semi-local two-nucleon potentials and demonstrate their outstanding performance in the two-nucleon sector by showing selected results up to fifth order in the EFT expansion. Also reviewed are applications …
The reaction $NN \to NN π$ offers a good testing ground for chiral effective field theory at intermediate energies. It challenges our understanding of the first inelastic channel in nucleon-nucleon scattering and of the charge-symmetry breaking pattern in hadronic reactions. In our previous studies, we presented a complete calculation of the pion-production operator for s-wave pions up-to-and-including next-to-next-to-leading order (NNLO) in the formulation of chiral effective field theory, which includes pions, nucleons and $Δ(1232)$ degrees of freedom. In this paper we calculate the near thr…
We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N$^2$LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the nonlocal HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermo…
We compare the predictions of different variants of chiral effective field theory for the gamma-p elastic scattering differential cross section. We pay particular attention to the role of pion loops, and the impact that a heavy-baryon expansion has on the behavior of those loops. We also correct erroneous results for these loops that were published in Phys. Rev. C 67, 055202 (2003) [ arXiv:nucl-th/0212024 ].
Chiral effective field theory has established itself as the method of choice to study nuclear forces and low-energy nuclear dynamics. I review the status and prospects of this approach and discuss ongoing efforts to advance the precision frontier for ab initio description of few-nucleon systems. Special emphasis is put on the precise determination of the two-nucleon force at fifth order in the chiral expansion, role of the chiral symmetry, the convergence pattern of the chiral expansion and the quantification of the theoretical uncertainties. The discussed topics are essential for ongoing stud…
We outline the modified formulation of baryon chiral effective field theory for nucleon-nucleon scattering and discuss the issue of a possible power counting violation by the nucleon mass. We also present the results for the quark mass dependence of the $^1S_0$ and $^3S_1$ scattering lengths and the deuteron binding energy at leading order.
We review a new generation of nuclear forces derived in chiral effective field theory using the recently proposed semilocal regularization method. We outline the conceptual foundations of nuclear chiral effective field theory, discuss all steps needed to compute nuclear observables starting from the effective chiral Lagrangian and consider selected applications in the two- and few-nucleon sectors. We highlight key challenges in developing high-precision tree-body forces, such as the need to maintain consistency between two- and many-body interactions and constraints placed by the chiral and ga…
Chiral effective field theory (EFT) provides a systematic and controlled approach to low-energy nuclear physics. Here, we use chiral EFT to calculate low-energy weak Gamow-Teller transitions. We put special emphasis on the role of two-body (2b) weak currents within the nucleus, and discuss their applications in predicting physical observables.
The complex-mass scheme (CMS) provides a consistent framework for dealing with unstable particles in quantum field theory and has been successfully applied to various loop calculations. As applications of the CMS in chiral effective field theory we consider the form factor of the pion in the time-like region and the magnetic moment of the Roper resonance.
We use chiral effective field theory (EFT) to make predictions for the longitudinal electromagnetic response function of the deuteron, f_L, which is measured in d(e,e'N) reactions. In this case the impulse approximation gives the full chiral EFT result up to corrections that are of O(P^4) relative to leading. By varying the cutoff in the chiral EFT calculations between 0.6 and 1 GeV we conclude that the calculation is accurate to better than 10 % for values of q^2 within 4 fm^{-2} of the quasi-free peak, up to final-state energies E_{np}=60 MeV. In these regions chiral EFT is in reasonable agr…
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective…
To obtain an understanding of the structure and reactions of nuclear systems from first principles has been a long-standing goal of nuclear physics. In this respect, few- and many-body systems provide a unique laboratory for studying nuclear interactions. During the past decades, the development of accurate representations of the nuclear force has undergone substantial progress. Particular emphasis has been devoted to chiral effective field theory (EFT), a low-energy effective representation of quantum chromodynamics (QCD). Within chiral EFT, many studies have been carried out dealing with the…
Using dispersive representations of the nucleon gravitational form factors, the results for their absorptive parts from chiral effective field theory in curved space-time, and the mechanical stability conditions, we obtain a model independent inequality for the value of the gravitational $D(t)$ form factor at zero momentum transfer (Druck-term). In particular, the obtained inequality leads to a conservative bound on the Druck-term in the chiral limit $D \leq -0.95(9)$. This bound implies the restriction on the low-energy constant $c_8$ of the effective chiral action for nucleons and pions in t…
During the past two decades, chiral effective field theory has become a popular tool to derive nuclear forces from first principles. Two-nucleon interactions have been worked out up to sixth order of chiral perturbation theory and three-nucleon forces up to fifth order. Applications of some of these forces have been conducted in nuclear few- and many-body systems---with a certain degree of success. But in spite of these achievements, we are still faced with great challenges. Among them is the issue of a proper uncertainty quantification of predictions obtained when applying these forces in {\i…
We show that chiral effective field theory (EFT) two-body currents provide important contributions to the quenching of low-momentum-transfer Gamow-Teller transitions, and use chiral EFT to predict the momentum-transfer dependence that is probed in neutrinoless double-beta decay. We then calculate for the first time the neutrinoless double-beta decay operator based on chiral EFT currents and study the nuclear matrix elements at successive orders. The contributions from chiral two-body currents are significant and should be included in all calculations.
We review theoretical progress and prospects for determining the nucleon's static dipole polarisabilities from Compton scattering on few-nucleon targets, including new values; see Refs. [1-5] for details and a more thorough bibliography.
Ab initio calculations of nuclear charge radii across and beyond ${}^{132}$Sn: Putting chiral EFT nuclear interactions to the test
KU Leuven（荷语天主教鲁汶大学）；Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles（布鲁塞尔自由大学天文与天体物理研究所）；Brussels Laboratory of the Universe–BLU-ULB（布鲁塞尔宇宙实验室）；Technische Universität Darmstadt（达姆施塔特工业大学）；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心极端物质研究所EMMI）；IRFU, CEA, Université Paris-Saclay（巴黎萨克雷大学CEA IRFU）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）
We discuss the application of an effective field theory (EFT) which incorporates the chiral symmetry of QCD to Compton scattering from the proton and deuteron. We describe the chiral EFT analysis of the proton Compton scattering database presented in our recent review (arXiv:1203.6834), which gives: alpha^{(p)}=10.5 +/- 0.5(stat) +/- 0.8(theory); beta^{(p)}= 2.7 +/- 0.5(stat) +/- 0.8(theory), for the electric and magnetic dipole polarizability of the proton. We also summarize the chiral EFT analysis of the world data on coherent Compton scattering from deuterium presented in arXiv:1203.6834. T…
Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. In previous work, a Bayesian model for truncation errors of perturbative expansions was adapted to EFTs. The model yields posterior probability distribution functions (pdfs) for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. A first application was made to chiral EFT for neutron-proton scattering u…
Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most accurate solutions, but they require as input local potentials. We have recently constructed local chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading order (N$^2$LO). Chiral EFT naturally predicts consistent many-body forces. In this paper, we consider the leading chiral three-nucleon (3N) interactions in local form. These are included i…
Understanding the structure and reactions of nuclei from first principles has been a long-standing goal of nuclear physics. In this respect, few- and many-body systems provide a unique laboratory for studying nuclear interactions. In the past couple of decades, the modeling of nuclear interactions has progressed significantly owing, in particular, to the development of chiral effective field theory ($χ$EFT), a low-energy effective representation of quantum chromodynamics (QCD). Within $χ$EFT, many studies have dealt with the construction of both two- and three-nucleon interactions. The aim of …
We carry out a series of studies on pion and photon productions in neutrino/electron/photon--nucleus scatterings. The low energy region is investigated by using a chiral effective field theory for nuclei. The results for the neutral current induced photon production ($γ$-NCP) are then extrapolated to neutrino energy $E_ν\sim$ GeV region. By convoluting the cross sections with MiniBooNE's beam spectrum and detection efficiency, we estimate its $γ$-NCP, event number, and conclude that such photon production can not fully explain its low energy event excess in both neutrino and antineutrino runs.
We present a simple introduction to the techniques of effective field theory (EFT) and their application to QCD. For problems with more than one energy scale, the EFT approach is a useful alternative to more traditional model-building strategies. The most relevant such problem for this discussion is that of making contact between QCD and the hadronic phase of matter. As a simple example, an EFT calculation of the bound states of hydrogen within QED is sketched. A more significant demonstration of the power of EFTs, the construction of the chiral Lagrangian and chiral perturbation theory, is al…
We recently developed a Bayesian framework for parameter estimation in general effective field theories. Here we present selected results from using that framework to estimate parameters with a nucleon-nucleon (NN) potential derived using chiral effective field theory ($χ$EFT): the semi-local NN potential of Epelbaum, Krebs, and Meißner (EKM). There are many NN scattering data, up to high energies, and with rather small errors, so imposing a penalty for unnatural low-energy constants (LECs) usually has a small effect on the fits. In contrast, we have found that including an estimate of higher …
We present fully non-perturbative quantum Monte Carlo calculations with non-local 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 \emph{ab initio} prediction of nuclear properties while respe…
