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We introduce a new approach for solving quantum many-body systems called wave function matching. Wave function matching transforms the interaction between particles so that the wave functions at short distances match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible due to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations of light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. We use interactions at next-to-next-to-next-to-leading order in the framework of chiral effective field theory and find good agreement with empirical data. These results are accompanied by new insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii, and nuclear matter saturation in ab initio calculations., 24 pages, 10 figues, 13 tables

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program., Perspective pieces of the virtual INT program 21-1b "Nuclear Forces for Precision Nuclear Physics", 107 pages

We present a calculation of radiative pion photoproduction in the framework of covariant chiral perturbation theory with explicit $\Delta(1232)$ degrees of freedom. The analysis is performed employing the small scale expansion scheme adjusted for the $\Delta$ region. Depending on the channel, we include contributions up to next-to-next-to-leading order. We fit the available experimental data for the reaction $ \gamma p\to\gamma p\pi^0 $ and extract the value of the $\Delta^+$ magnetic moment. Errors from the truncation of the small scale expansion are estimated using the Bayesian approach. We compare our results both with the previous studies within the $\delta$-expansion scheme and with the $\Delta$-less theory. We also give predictions for radiative charged-pion photoproduction., Comment: 50 pages, 35 figures. Treatment of the $\Delta$-resonance is improved by means of a more consistent choice of its renormalized mass in the complex mass scheme. The results have been updated accordingly

We compute various nucleon polarizabilities in chiral perturbation theory implementing the $\Delta$-full ($\Delta$-less) approach up to order $\epsilon^3 + q^4$ ($q^4$) in the small-scale (chiral) expansion. The calculation is carried out using the covariant formulation of $\chi$PT by utilizing the extended on-mass shell renormalization scheme. Except for the spin-independent dipole polarizabilities used to fix the values of certain low-energy constants, our results for the nucleon polarizabilities are pure predictions. We compare our calculations with available experimental data and other theoretical results. The importance of the explicit treatment of the $\Delta$ degree of freedom in the effective field theory description of the nucleon polarizabilities is analyzed. We also study the convergence of the $1/m$ expansion and analyze the efficiency of the heavy-baryon approach for the nucleon polarizabilities., Comment: 67 pages, 10 figures

We present a comprehensive analysis of the deuteron charge and quadrupole form factors based on the latest two-nucleon potentials and charge density operators derived in chiral effective field theory. The single- and two-nucleon contributions to the charge density are expressed in terms of the proton and neutron form factors, for which the most up-to-date empirical parametrizations are employed. By adjusting the fifth-order short-range terms in the two-nucleon charge density operator to reproduce the world data on the momentum-transfer dependence of the deuteron charge and quadrupole form factors, we predict the values of the structure radius and the quadrupole moment of the deuteron: $r_{\rm str}=1.9729\substack{+0.0015\\ -0.0012}\ \text{fm},\ Q_d=0.2854\substack{+0.0038\\ -0.0017}\ \text{fm}^2. $ A comprehensive and systematic analysis of various sources of uncertainty in our predictions is performed. Following the strategy advocated in our recent publication Phys. Rev. Lett. 124, 082501 (2020), we employ the extracted structure radius together with the accurate atomic data for the deuteron-proton mean-square charge radii difference to update the determination of the neutron charge radius, for which we find: $r_n^2=-0.105\substack{+0.005\\ -0.006} \, \text{fm}^2$. Given the observed rapid convergence of the deuteron form factors in the momentum-transfer range of $Q \simeq 1-2.5$ fm$^{-1}$, we argue that this intermediate-energy domain is particularly sensitive to the details of the nucleon form factors and can be used to test different parametrizations., Comment: 39 pages, 9 figures

We apply a recently developed momentum-space semilocally regularized chiral potential to the $^{2}\mathrm{H}$ and $^{3}\mathrm{He}$ photodisintegration processes and to the (anti)neutrino induced deuteron breakup reactions. Specifically, the differential cross section, the photon analyzing power, and the final proton polarization have been calculated for deuteron photodisintegration at photon energies of 30 and 100 MeV. For $^{3}\mathrm{He}$ photodisintegration, predictions for the semi-inclusive and exclusive differential cross sections are presented for photon energies up to 120 MeV. The total cross section is calculated for (anti)neutrino disintegration of the deuteron for (anti)neutrino energies below 200 MeV. Predictions based on the Argonne V18 potential and on an older chiral force with regularization applied in coordinate space are used for comparison. Using the fifth-order chiral nucleon-nucleon potential supplemented with dominant contributions from the sixth order allows us to obtain converged predictions for observables in the investigated reactions. Our results based on the newest semilocal chiral potentials show even smaller cutoff dependence and a somewhat faster convergence for the considered electroweak observables than the previously reported ones with a coordinate-space regulator, which make them a promising tool to study electroweak processes.

We present a systematic investigation of few-nucleon systems and light nuclei using the current LENPIC interactions comprising semilocal momentum-space regularized two- and three-nucleon forces up to third chiral order (N$^2$LO). Following our earlier study utilizing the coordinate-space regularized interactions, the two low-energy constants entering the three-body force are determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. Predictions are made for selected observables in elastic nucleon-deuteron scattering and in the deuteron breakup reactions, for properties of the $A=3$ and $A=4$ nuclei, and for spectra of $p$-shell nuclei up to $A = 16$. A comprehensive error analysis is performed including an estimation of correlated truncation uncertainties for nuclear spectra. The obtained predictions are generally found to agree with experimental data within errors. Similar to the coordinate-space regularized chiral interactions at the same order, a systematic overbinding of heavier nuclei is observed, which sets in for $A \sim 10$ and increases with $A$., Comment: 21 pages, 13 figures, 5 tables, added reference

The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, $N_c$. However this large-$N_c$ symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call $\Lambda_{{\rm large-}N_c}$. We show that the large-$N_c$ derivation requires a momentum resolution scale of $\Lambda_{{\rm large-}N_c} \sim 500$ MeV. We derive a set of spin-isospin exchange sum rules and discuss implications for the spectrum of $^{30}$P and applications to nuclear forces, nuclear structure calculations, and three-nucleon interactions., Comment: 5 pages (main) + 3 pages (supplemental materials), 1 figure (main) + 4 figures (supplemental materials), final version to appear in Phys. Rev. Lett

We examine a description of available cross section data for symmetric space star (SST) configurations in the neutron-deuteron (nd) and proton-deuteron (pd) breakup reaction using numerically exact solutions of the three-nucleon (3N) Faddeev equation based on two- and three-nucleon (semi)phenomenological and chiral forces. The predicted SST cross sections are very stable with respect to the underlying dynamics for incoming nucleon laboratory energies below $\approx 25$ MeV. We discuss possible origins of the surprising discrepancies between theory and data found in low-energy nd and pd SST breakup measurements., Comment: 30 pages, 12 figures

The pion-nucleon coupling constants determine the strength of the long-range nuclear forces and play a fundamental part in our understanding of nuclear physics. While the charged- and neutral-pion couplings to protons and neutrons are expected to be very similar, owing to the approximate isospin symmetry of the strong interaction, the different masses of the up- and down-quarks and electromagnetic effects may result in their slightly different values. Despite previous attempts to extract these coupling constants from different systems, our knowledge of their values is still deficient. In this Letter we present a precision determination of these fundamental observables with fully controlled uncertainties from neutron-proton and proton-proton scattering data using chiral effective field theory. To achieve this goal, we use a novel methodology based on the Bayesian approach and perform, for the first time, a full-fledged partial-wave analysis of nucleon-nucleon scattering up to the pion production threshold in the framework of chiral effective field theory, including a complete treatment of isospin-breaking effects and our own determination of mutually consistent data. The resulting values of the pion-nucleon coupling constants are accurate at the percent level and show no significant charge dependence. These results mark an important step towards developing a precision theory of nuclear forces and structure., 15 pages (including Supplementary Material), 5 figures, 5 tables. Version published in Physical Review Letters

In this article, we review the status of the calculation of nuclear currents within chiral effective field theory. After formal discussion of the unitary transformation technique and its application to nuclear currents we will give all available expressions for vector, axial-vector currents. Vector and axial-vector currents will be discussed up to order $Q$ with leading-order contribution starting at order $Q^{-3}$. Pseudoscalar and scalar currents will be discussed up to order $Q^0$ with leading-order contribution starting at order $Q^{-4}$. This is a complete set of expressions in next-to-next-to-next-to-leading-order (N$^3$LO) analysis for nuclear scalar, pseudoscalar, vector and axial-vector current operators. Differences between vector and axial-vector currents calculated via transfer-matrix inversion and unitary transformation techniques are discussed. The importance of consistent regularization is an additional point which is emphasized: lack of consistent regularization of axial-vector current operators is shown to lead to a violation of the chiral symmetry in the chiral limit at order $Q$. For this reason, a hybrid approach at order $Q$, discussed in various publications, is non-applicable. To respect the chiral symmetry the same regularization procedure needs to be used in the construction of nuclear forces and current operators. Although full expressions of consistently regularized current operators are not yet available an isoscalar part of the electromagnetic charge operator up to order $Q$ has a very simple form and can be easily regularized in a consistent way. As an application, we review our recent high accuracy calculation of the deuteron charge form factor with a quantified error estimate., 54 pages, 2 figures, 7 tables

We extend our recent analyses of the nuclear vector, axial-vector and pseudoscalar currents and derive the leading one-loop corrections to the two-nucleon scalar current operator in the framework of chiral effective field theory using the method of unitary transformation. We also show that the scalar current operators at zero momentum transfer are directly related to the quark mass dependence of the nuclear forces., 14 pages, 6 figures

The internal spin structure of the nucleon is described by structure functions in deep inelastic lepton-hadron scattering which are related to real, virtual and double virtual Compton scattering amplitudes by various sum rules connecting information at all energy scales. In this proceeding I concentrate on theoretical description of spin polarizabilities of double virtual Compton scattering. We use chiral perturbation theory to describe low energy QCD dynamics in a model independent way. I briefly review chiral perturbation theory activities in this field and show that the Jefferson Lab experimental data at low virtuality are in fair agreement with ChPT calculations with explicit delta-resonance degrees of freedom. Though, preliminary experimental data indicate a disagreement with existing ChPT predictions. There are also discrepancies between two different calculations of generalized polarizabilities which use different power counting for delta degrees of freedom which will be discussed.

We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. The proposed method combines a spherical wall boundary condition and a channel-mixing auxiliary potential to extract the full-rank S-matrix from the radial wave functions. We consider the scattering problem of two spin-1 bosons interacting with a test potential involving up to four coupled channels. For this benchmark system, the phase shifts and mixing angles are shown to agree on the lattice and in the continuum. Our method should allow to extend previous two-channel nuclear lattice EFT simulations to mixing of more than two partial waves.

We present new momentum-space regularized nucleon-nucleon (NN) potentials up to fifth order in chiral effective field theory, whose adjustable parameters have been determined from experimental NN scattering data. The resulting N\(^4\)LO\(^+\) potential achieves the same precision as high-quality phenomenological forces while the new momentum-space regulator paves the way for the implementation of consistently regularized three-nucleon forces and current operators.

Propagation of uncertainties from two-nucleon potential parameters to three-nucleon observables, that is statistical errors for the neutron-deuteron elastic scattering and the deuteron breakup reaction at neutron laboratory energies up to 200 MeV is investigated. To that end we use the chiral nucleon-nucleon interaction with the semi-local momentum-space regularization at various orders of the chiral expansion, exploiting knowledge of the covariance matrix of its parameters. For both reactions we compare statistical uncertainties for chiral predictions with the uncertainties obtained in the same way but for the semi-phenomenological One-Pion-Exchange two-nucleon force. In addition for the elastic scattering we show also the truncation errors arising from restriction to a given order of chiral predictions, estimated among others within the Bayesian method, and the cutoff dependence of chiral predictions. We find that the resulting statistical uncertainty is smaller than the truncation errors for the chiral force at lower orders of the chiral expansion. At the higher orders of the chiral expansion and at low energies the statistical errors exceed the truncation ones but at intermediate and higher energies truncation errors are more important. Overall, magnitudes of the theoretical uncertainties are small and amount up to 0.5\%-4\%, depending on the observable and energy. We also find that the magnitudes of statistical uncertainties for the chiral and semi-phenomenological potentials are similar and that the dependence of predictions on the regularization parameter values is important at all investigated energies., Comment: 18 pages, 14 figures in 29 eps files

Recently, we have worked out the axial two-nucleon current operator to leading one-loop order in chiral effective field theory using the method of unitary transformation. Our final expressions, however, differ from the ones derived by the JLab-Pisa group using time-ordered perturbation theory (Phys. Rev. C 93, no. 1, 015501 (2016) Erratum: [Phys. Rev. C 93, no. 4, 049902 (2016)] Erratum: [Phys. Rev. C 95, no. 5, 059901 (2017)]). In this paper we consider the box diagram contribution to the axial current and demonstrate that the results obtained using the two methods are unitary equivalent at the Fock-space level. We adjust the unitary phases by matching the corresponding two-pion exchange nucleon-nucleon potentials and rederive the box diagram contribution to the axial current operator following the approach of the JLab-Pisa group, thereby reproducing our original result. We provide a detailed information on the calculation including the relevant intermediate steps in order to facilitate a clarification of this disagreement., Comment: 13 pages, 1 figure

Results presented in this contribution are obtained within the Low Energy Nuclear Physics International Collaboration (LENPIC). LENPIC aims to develop chiral nucleon-nucleon and many-nucleon interactions complete through at least the fourth order in the chiral expansion. These interactions will be used together with consistently derived current operators to solve the structure and reactions of light and medium-mass nuclei including electroweak processes. In this contribution the current status of the chiral nuclear forces and current operators will be briefly discussed. A special role played by the calculations of nucleon-deuteron scattering will be explained.

We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation., Comment: 72 pages, 21 figures, 3 tables

We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. Previous nuclear lattice effective field theory simulations were restricted to mixing of up to two partial waves for scattering of two spin-$1/2$ particles, which is insufficient for analyzing nucleon-nucleus or nucleus-nucleus scattering processes. In the proposed method, the phase shifts and mixing angles are extracted from the radial wave functions obtained by projecting the three-dimensional lattice Hamiltonian onto the partial wave basis. We use a spherical wall potential as a boundary condition along with a channel-mixing auxiliary potential to construct the full-rank $S$ matrix. Our method can be applied to particles with any spin, but we focus here on scattering of two spin-$1$ bosons involving up to four coupled channels. For a considered test potential, the phase shifts and mixing angles extracted on the lattice are shown to agree with the ones calculated by solving the Schr\"odinger equation in the continuum., Comment: 14 pages, 9 figures, 1 table, corresponds to the published version in Phys. Rev. C

We present a high-accuracy calculation of the deuteron structure radius in chiral effective field theory. Our analysis employs the state-of-the-art semilocal two-nucleon potentials and takes into account two-body contributions to the charge density operators up to fifth order in the chiral expansion. The strength of the fifth-order short-range two-body contribution to the charge density operator is adjusted to the experimental data on the deuteron charge form factor. A detailed error analysis is performed by propagating the statistical uncertainties of the low-energy constants entering the two-nucleon potentials and by estimating errors from the truncation of the chiral expansion as well as from uncertainties in the nucleon form factors. Using the predicted value for the deuteron structure radius together with the very accurate atomic data for the difference of the deuteron and proton charge radii we, for the first time, extract the charge radius of the neutron from light nuclei. The extracted value reads $r_n^2 = - 0.106 \substack{ +0.007\\ -0.005\\} \, \text{fm}^2$ and its magnitude is about $1.7\sigma$ smaller than the current value given by the Particle Data Group. In addition, given the high accuracy of the calculated deuteron charge form factor and its careful and systematic error analysis, our results open the way for an accurate determination of the nucleon form factors from elastic electron-deuteron scattering data measured at the Mainz Microtron and other experimental facilities., Comment: 5 pages, 1 figure, supplementary material available in source package

In this proceeding I briefly review current status of the construction of nuclear electro-weak currents within chiral effective field theory. I show that gauge and chiral symmetry requirements lead to the well-known continuity equations for the current and charge operators which, however, get modified at higher orders. Regularization of the current will be also discussed. I demonstrate that implementation of a cutoff regulator in a naive way leads to violation of chiral symmetry. To respect the underlying symmetries I propose to use higher derivative regularization in the nuclear forces and currents., 10 pages, 4 tables, Contribution to the proceedings of the 9th International workshop on Chiral Dynamics (PoS CD18)

We discuss the current status of chiral effective field theory in the three-nucleon sector and present selected results for nucleon-deuteron scattering observables based on semilocal momentum-space-regularized chiral two-nucleon potentials together with consistently regularized three-nucleon forces up to third chiral order. Using a Bayesian model for estimating truncation errors, the obtained results are found to provide a good description of the experimental data. We confirm our earlier findings that a high-precision description of nucleon-deuteron scattering data below pion production threshold will require the theory to be pushed to fifth chiral order. This conclusion is substantiated by an exploratory study of selected short-range contributions to the three-nucleon force at that order, which, as expected, are found to have significant effects on polarization observables at intermediate and high energies. We also outline the challenges that will need to be addressed in order to push the chiral expansion of three-nucleon scattering observables to higher orders., 14 pages, 12 figures, 1 table; contribution to the EPJA topical issue on "The tower of effective (field) theories and the emergence of nuclear phenomena"

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 gauge symmetries after regularization., Comment: 44 pages, 14 figures, 2 tables, Submitted to Frontiers in Physics (Research topic) The Long-Lasting Quest for Nuclear Interactions: The Past, the Present and the Future

We solve three-nucleon (3N) Faddeev equations with nucleon–nucleon (NN) and three-nucleon forces (3NF) derived consistently in the framework of chiral perturbation theory, taking the semilocal coordinate-space regularized chiral N $$^4$$ LO NN potential supplemented by the chiral N $$^2$$ LO 3NF regularized in the same way. Based on these solutions the nucleon–deuteron (Nd) elastic scattering and deuteron breakup reactions are studied. We checked that the elastic Nd scattering cross section can be used as an alternative observable to the doublet neutron–deuteron (nd) scattering length to fix, together with the $$^3$$ H binding energy, the strengths of the contact terms of the N $$^2$$ LO 3NF. We investigated the predicted 3NF effects in 3N continuum reactions putting an emphasis on the $$A_y$$ puzzle in low energy nd elastic scattering and on cross sections in the symmetrical-space-star and quasi-free-scattering breakup configurations. We found that the N $$^2$$ LO 3NF provides effects comparable to those of standard, (semi-)phenomenological $$2\pi $$ -exchange Tucson-Melbourne 3NF.

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 $\mathrm{\ensuremath{\Delta}}$(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 $\mathrm{\ensuremath{\Delta}}$-less theory at next-to-next-to-next-to-next-to leading order (${\mathrm{N}}^{4}\mathrm{LO}$), we find effects of the $\mathrm{\ensuremath{\Delta}}$ isobar for this particular topology to be rather well represented in terms of resonance saturation of various low-energy constants in the $\mathrm{\ensuremath{\Delta}}$-less approach.

We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of the chiral expansion and estimate the achievable theoretical accuracy at various chiral orders using the novel approach to quantify truncation errors of the chiral expansion without relying on cutoff variation. We also address the robustness of this method and explore alternative ways to estimate the theoretical uncertainty from the truncation of the chiral expansion., Comment: 34 pages, 15 figures, 11 tables

We present a complete calculation of nucleon-deuteron scattering as well as ground and low-lying excited states of light nuclei in the mass range A=3-16 up through next-to-next-to-leading order in chiral effective field theory using semilocal coordinate-space regularized two- and three-nucleon forces. It is shown that both of the low-energy constants entering the three-nucleon force at this order can be reliably determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. The inclusion of the three-nucleon force is found to improve the agreement with the data for most of the considered observables., Comment: 15 pages, 9 figures, 1 table

Recent ab initio lattice studies have found that the interactions between alpha particles (4He nuclei) are sensitive to seemingly minor details of the nucleon-nucleon force such as interaction locality. In order to uncover the essential physics of this puzzling phenomenon without unnecessary complications, we study a simple model involving two-component fermions in one spatial dimension. We probe the interaction between two bound dimers for several different particle-particle interactions and measure an effective potential between the dimers using external point potentials which act as numerical tweezers. We find that the strength and range of the local part of the particle-particle interactions play a dominant role in shaping the interactions between the dimers and can even determine the overall sign of the effective potential., Final version to be published in Physical Review Letters. Main text: 5 pages, 5 figures. Supplemental material: 2 pages, 2 figures

The chiral nucleon–nucleon interaction with semi-local regularization up to the fifth order of chiral expansion is applied to the nucleon–deuteron radiative capture process. Our theoretical approach is based on the formalism of Faddeev equations and the Siegert theorem is exploited to construct the electromagnetic current operator. The very weak dependence of the differential cross section on values of the regularization parameter is observed. This suggests that the improved chiral two-body interaction is a promising starting point to study electromagnetic processes at low energies.

Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $\Delta(1232)$ as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $\Delta$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $\Delta$-less theory the resummation of $1/m_N$ corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation., Comment: 10 pages, 4 tables, Mathematica notebook with the analytic expressions for threshold and subthreshold parameters included as supplementary material; journal version

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (4He nuclei) within the interior of a larger nucleus. While clustering is important for several well-known examples, much remains to be discovered about the general nature of clustering in nuclei. In this letter we present lattice Monte Carlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the shape of the alpha clusters and the entanglement of nucleons comprising each alpha cluster with the outside medium. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field Monte Carlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in 12C, 14C, and 16C. The structural similarities among the carbon isotopes suggest that 14C and 16C have excitations analogous to the well-known Hoyle state resonance in 12C., Comment: Version to appear in Physical Review Letters. 5 + 12 pages (main + supplemental materials), 3 + 12 figures (main + supplemental materials)

We review the achievements of the project C.9 . Topics addressed include the magnetic moment of the ρ -meson, elastic pion-nucleon scattering in various settings of chiral perturbation theory, the reaction πN → ππN as well as new directions in chiral perturbation theory.

We extend our previous study of elastic pion-nucleon scattering in the framework of chiral perturbation theory by performing a combined analysis of the reactions $\pi N \to \pi N$ and $\pi N \to \pi \pi N$. The calculation is carried out to fourth order in the chiral expansion using the heavy baryon approach and the covariant formulation supplemented with a modified version of the extended on-mass-shell renormalization scheme. We demonstrate that a combined fit to experimental data in both channels leads to a reduced amount of correlations between the low-energy constants. A satisfactory description of the experimental data in both channels is obtained, which is further improved upon including tree-level contributions of the $\Delta$(1232) resonance. We also explore a possibility of using the empirical information about $\pi N$ subthreshold parameters obtained recently by means of the Roy-Steiner equations to stabilize the fits., Comment: 45 pages, 21 figures

We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is implemented in momentum space and (iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the redundant contact terms results in a drastic simplification of the fits to scattering data and leads to interactions which are much softer (i.e. more perturbative) than our recent semilocal coordinate-space regularized potentials. Using the pion-nucleon low-energy constants from matching pion-nucleon Roy-Steiner equations to chiral perturbation theory, we perform a comprehensive analysis of nucleon-nucleon scattering and the deuteron properties up to fifth chiral order and study the impact of the leading F-wave two-nucleon contact interactions which appear at sixth order. The resulting chiral potentials lead to an outstanding description of the proton-proton and neutron-proton scattering data from the self-consistent Granada-2013 database below the pion production threshold, which is significantly better than for any other chiral potential. For the first time, the chiral potentials match in precision and even outperform the available high-precision phenomenological potentials, while the number of adjustable parameters is, at the same time, reduced by about ~40%. Last but not least, we perform a detailed error analysis and, in particular, quantify for the first time the statistical uncertainties of the fourth- and the considered sixth-order contact interactions., Comment: 57 pages, 17 figures, 19 tables

How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (4He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei. Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length., Published version to appear in Physical Review Letters. Main: 5 pages, 3 figures. Supplemental material: 13 pages, 6 figures

We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the $D$ and $F$ waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation., Comment: 41 pages, 12 figures, 7 tables

The reaction $NN \to NN \pi$ 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 $\Delta(1232)$ degrees of freedom. In this paper we calculate the near threshold cross section for the $pp \to d \pi^{+}$ reaction by performing the convolution of the obtained operators with nuclear wave functions based on modern phenomenological and chiral potentials. The available chiral $NN$ wave functions are constructed with a cutoff comparable with the momentum transfer scale inherent in pion production reactions. Hence, a significant portion of the dynamical intermediate-range physics is thereby cut off by them. On the other hand, the NNLO amplitudes evaluated with phenomenological wave functions appear to be largely independent of the $NN$ model used and give corrections to the dominant leading order contributions as expected from dimensional analysis. The result gives support to the counting scheme used to classify the pion production operators, which is a precondition for a reliable investigation of the chirally suppressed neutral pion production. The explicit inclusion of the $\Delta(1232)$ is found to be important but smaller than expected due to cancellations., Comment: 25 pages, 7 figures, 2 tables

The recently developed semi-local improved chiral nucleon-nucleon interaction is used for the first time to study several electromagnetic and weak processes at energies below the pion production threshold. Cross sections and selected polarization observables for deuteron photodisintegration, nucleon-deuteron radiative capture, three-body $^3$He photodisintegration as well as capture rates for decays of the muonic $^2$H and $^3$He atoms are calculated. The Lippmann-Schwinger and Faddeev equations in momentum space are solved to obtain nuclear states. The electromagnetic current operator is taken as a single nucleon current supplemented by many-body contributions induced via the Siegert theorem. For muon capture processes the nonrelativistic weak current together with the dominant relativistic corrections is used. Our results compare well with experimental data, demonstrating the same quality as is observed for the semi-phenomenological AV18 potential. Compared to the older version of the chiral potential with a nonlocal regularization, a much smaller cut-off dependence is found for the state-of-art chiral local interaction employed in this paper. Finally, estimates of errors due to the truncation of the chiral expansion are given., Comment: 23 pages, 12 eps figures, improved version accepted to Phys. Rev. C. Note, the title of the manuscript is changed

Nucleon-nucleon scattering in the 1 S 0 partial wave is considered in chiral effective field theory within the recently suggested renormalizable formulation based on the Kadyshevsky equation. Contact interactions are taken into account beyond the leading-order approximation. The subleading contact terms are included non-perturbatively by means of subtractive renormalization. The dependence of the phase shifts on the choice of the renormalization condition is discussed. Perturbative inclusion of the subleading contact interaction is found to be justified only very close to threshold. The low-energy theorems are reproduced significantly better compared with the leading order results.

We present recent results for 4 He and 6 Li obtained with improved NN interactions derived from chiral effective field theory up to N4 LO. The many-body calculations are performed order-by-order in the chiral expansion. At N3 LO and N4 LO additional renormalization using the Similarity Renormalization Group is adopted to improve numerical convergence of the many-body calculations. We discuss results for the ground state energies, as well as the magnetic moment and the low-lying spectrum of 6 Li.

Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant $\ensuremath{\beta}$ functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the $\mathrm{\ensuremath{\Delta}}$ resonance. The explicit inclusion of the leading contributions of the $\mathrm{\ensuremath{\Delta}}$ isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the predictions from the recent Roy--Steiner-equation analysis of pion-nucleon scattering.

We discuss the role of the three-nucleon isospin T=3/2 amplitude in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon-nucleon potential and is driven by the difference between neutron-neutron (proton-proton) and neutron-proton forces. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the locally regularized chiral N4LO nucleon-nucleon potential supplemented by the chiral N2LO three-nucleon force. For comparison we employ also the Av18 nucleon-nucleon potential combined with the Urbana IX three-nucleon force. We find that the isospin T=3/2 component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the 1S0 state with isospin T=3/2. For neutron-deuteron elastic scattering the T=3/2 contributions are insignificant and charge-independence breaking can be accounted for by using the effective t-matrix generated with the so-called "2/3-1/3" rule., Comment: 24 pages, 8 figures, 3 Tables