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Background: Weak interactions between quarks induce a parity-violating (PV) component in the nucleonnucleon potential, whose effects are currently being studied in a number of experiments involving few-nucleon systems. In the present work, we reconsider the derivation of this PV component within a chiral effective field theory (χEFT) framework. Purpose: The objectives of the present work are twofold. The first is to perform a detailed analysis of the PV nucleon-nucleon potential up to next-to-next-to-leading (N2LO) order in the chiral expansion, in particular, by determining the number of independent low-energy constants (LECs) at N2LO. The second objective is to investigate PV effects in a number of few-nucleon observables, including the p-p longitudinal asymmetry, the neutron spin rotation in n-p and n-d scattering, and the longitudinal asymmetry in the ³He(n,p)³H chargeexchange reaction. Methods: The χEFT PV potential includes one-pion-exchange, two-pion-exchange, and contact terms as well as 1/M (M being the nucleón mass) nonstatic corrections. Dimensional regularization is used to renormalize pion loops. The wave functions for the A = 2-4 nuclei are obtained by using strong two- and three-body potentials also derived, for consistency, from χEFT. In the case of the A = 3-4 systems, the wave functions are computed by expanding on a hyperspherical harmonics functions basis. Results: We find that the PV potential at N2LO depends on six LECs: the pion-nucleon PV coupling constant hπ¹ and five parameters multiplying contact interactions. An estimate for the range of values of the various LECs is provided by using available experimental data, and these values are used to obtain predictions for the other PV observables. Conclusions: The χEFT approach provides a very satisfactory framework to analyze PV effects in few-nucleon systems. [ABSTRACT FROM AUTHOR]

We present a detailed study of the effect of different three-nucleon interactions in p-³He elastic scattering at low energies. In particular, two interactions have been considered: one derived from effective field theory at next-to-next-to-leading order and one derived from a more phenomenological point of view—the so-called Illinois model. The four-nucleon scattering observables are calculated by using the Kohn variational principle and the hyperspherical harmonics technique, and the results are compared with available experimental data. We have found that the inclusion of both interactions improves the agreement with the experimental data, in particular, for the proton vector analyzing power. [ABSTRACT FROM AUTHOR]

Bound-state-like wave functions are used to determine the scattering matrix corresponding to low-energy n-d and p-3He collisions. To this end. the coupled-channel form of the integral relations derived from the Kohn variational principle is used. The construction of degenerate bound-state-like wave functions belonging to the continuum spectrum of the Hamiltonian is discussed. Examples are shown using realistic nucleon-nucleon forces. [ABSTRACT FROM AUTHOR]

The n-³H and p-³He elastic phase shifts below the trinucleon disintegration thresholds are calculated by solving the four-nucleon problem with three different realistic nucleon-nucleon interactions (the I-N3LO model by Entem and Machleidt, the Argonne ν18 potential model, a low-k model derived from the CD-Bonn potential). Three different methods--Alt-Grassberger-Sandhas, hyperspherical harmonics, Faddeev-Yakubovsky--have been used and their respective results are compared. For both n-³H and p-³He we observe a rather good agreement between the three different theoretical methods. We also compare the theoretical predictions with the available experimental data, confirming the large underprediction of the p-³He analyzing power. [ABSTRACT FROM AUTHOR]

The large values of the singlet and triplet two-nucleon scattering lengths locate the nuclear system close to the unitary limit. This particular position strongly constrains the low-energy observables in the three-nucleon system as depending on one parameter, the triton binding energy, and introduces correlations in the low-energy sector of light nuclei. Here we analyze the propagation of these correlations to infinite nuclear matter showing that its saturation properties, the equation of state of β-stable nuclear matter, and several properties of neutron stars, as their maximum mass, are well determined solely by a few number of low-energy quantities of the two- and three-nucleon systems. In this way we make a direct link between the universal behavior observed in the low-energy region of few-nucleon systems and fundamental properties of nuclear matter and neutron stars. [ABSTRACT FROM AUTHOR]

p-³H and n-³He scattering in the energy range above the n-³He but below the d-d thresholds is studied by solving the four-nucleon problem with a realistic nucleon-nucleon interaction. Three different methods--Alt, Grassberger, and Sandhas, hyperspherical harmonics, and Faddeev-Yakubovsky--have been employed and their results for both elastic and charge-exchange processes are compared. We observe a good agreement between the three different methods, thus the obtained results may serve as a benchmark. A comparison with the available experimental data is also reported and discussed. [ABSTRACT FROM AUTHOR]

In chiral effective field theory the leading order (LO) nucleon-nucleon potential includes two contact terms, in the two spin channels S=0,1, and the one-pion-exchange potential. When the pion degrees of freedom are integrated out, as in the pionless effective field theory, the LO potential includes two contact terms only. In the three-nucleon system, the pionless theory includes a three-nucleon contact term interaction at LO whereas the chiral effective theory does not. Accordingly arbitrary differences could be observed in the LO description of three- and four-nucleon binding energies. We analyze the two theories at LO and conclude that a three-nucleon contact term is necessary at this order in both theories. In turn this implies that subleading three-nucleon contact terms should be promoted to lower orders. Furthermore, this analysis shows that one single low-energy constant might be sufficient to explain the large values of the singlet and triplet scattering lengths. [ABSTRACT FROM AUTHOR]

General expressions for the breakup cross sections in the laboratory frame for 1 + 2 reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial functions are obtained by solving a set of second order differential equations. The S matrix is computed by using two recently derived integral relations. Even though the method is shown to be well suited to describe 1 + 2 processes, there are particular configurations in the breakup channel (for example, those in which two particles move away close to each other in a relative zero-energy state) that need a huge number of basis states. This pathology manifests itself in the extremely slow convergence of the breakup amplitude in terms of the hyperspherical harmonic basis used to construct the adiabatic channels. To overcome this difficulty the breakup amplitude is extracted from an integral relation as well. For the sake of illustration, we consider neutron-deuteron scattering. The results are compared to the available benchmark calculations [ABSTRACT FROM AUTHOR]

The astrophysical S factor for proton-proton weak capture is calculated in chiral effective field theory over the center-of-mass relative-energy range 0-100 keV. The chiral two-nucleon potential derived up to next-to-next-to-next-to leading order is augmented by the full electromagnetic interaction including, beyond Coulomb, two-photon and vacuum-polarization corrections. The low-energy constants entering the weak current operators are fixed so as to reproduce the A=3 binding energies and magnetic moments and the Gamow-Teller matrix element in tritium β decay. Contributions from S and P partial waves in the incoming two-proton channel are retained. The S factor at zero energy is found to be S(0) = (4.030 ± 0.006) × 10-23 MeV fm², with a P-wave contribution of 0.020×10-23 MeV fm². The theoretical uncertainty is due to the fitting procedure of the low-energy constants and to the cutoff dependence. [ABSTRACT FROM AUTHOR]

The use of the hyperspherical harmonic (HH) basis in the description of bound states in an A-body system composed of identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into account. This preliminary step is not strictly necessary; the direct use of the HH basis is possible, even if the basis does not have a well-defined behavior under particle permutations. In fact, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it. They have well-defined symmetry under particle permutation and identification of the physical states is possible, as shown here in specific cases. The problem related to the large degeneration of the basis is circumvented by constructing the Hamiltonian matrix as a sum of products of sparse matrices. This particular representation of the Hamiltonian is well suited for a numerical iterative diagonalization, where only the action of the matrix on a vector is needed. As an example we compute bound states for systems with A=3-6 particles interacting through a short-range central interaction. We also consider the case in which the potential is restricted to act in relative s waves with and without the inclusion of the Coulomb potential. This very simple model predicts results in qualitative good agreement with the experimental data and it represents the first step in a project dedicated to the use of the HH basis to describe bound and low-energy scattering states in light nuclei. [ABSTRACT FROM AUTHOR]

The muon-capture reactions 2H(μ¯,vμ)nn and 3He(μ¯,vμ)3H are studied with conventional or chiral realistic potentials and consistent weak currents. The initial and final A=2 and A=3 nuclear wave functions are obtained from the Argonne v18 or chiral next-to-next-to-next-to leading order (N3LO) two-nucleon potential, in combination with, respectively, the Urbana IX or chiral next-to-next-to leading order (N2LO) three-nucleon potential in the case of A=3. The weak current consists of polar- and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory (χEFT) framework. There is one parameter (either the N-to-Δ axial coupling constant in the meson-exchange model, or the strength of a contact term in the χEFT model) that is fixed by reproducing the Gamow-Teller matrix element in tritium β decay. The model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the χEFT currents) is weak, resulting in total rates of 392.0±2.3 s-1 for A=2, and 1484±13 s-1 for A=3, where the spread accounts for this model dependence. [ABSTRACT FROM AUTHOR]

The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance, which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. For example, the triton binding energy is correlated with other observables such as the doublet nucleon-deuteron scattering length or the α-particle binding energy. Moreover, the low-energy dynamics of these systems is universal; it does not depend on the details of the nuclear interaction. Instead, it depends on a few control parameters such as the (large) values of the scattering lengths and the triton binding energy. Using a potential model in order to vary the values of the scattering lengths, we study the spectrum of A=2,3,4,6 nuclei in the region between the unitary limit and the point where the scattering lengths get their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels. [ABSTRACT FROM AUTHOR]

We construct accurate models of the three-nucleon (3N) interaction by fitting, in a hybrid phenomenological approach, the low-energy constants parametrizing the subleading 3N contact operators to the triton binding energy, n-d scattering lengths, cross section, and polarization observables of p-d scattering at 2 MeV center-of-mass energy. These models lead to a satisfactory description of polarized p-d scattering data in the whole energy range below the deuteron breakup threshold. In particular, the longstanding Ay puzzle seems to be solved thanks to the new terms considered in the 3N force. Two types of hierarchies among the subleading contact operators are also derived, based on the large-Nc counting and on a recently proposed relativistic counting. We test these hierarchies against the same experimental data and show that they are respected at a reasonable level. [ABSTRACT FROM AUTHOR]

Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. A complete set of contact terms for the axial charge up to the relevant order in the power counting is constructed. [ABSTRACT FROM AUTHOR]

Background: The A = 2 and 3 form factors are among the observables of choice for testing models of nuclear interactions and associated electromagnetic charge and current operators. Here we investigate the validity of the chiral-effective-field-theory (xEFT) approach to describe the strong-interaction dynamics in these few-nucleon systems and their response to electromagnetic probes. Purpose: The objectives of the present work are twofold. The first is to address and resolve some of the differences present in independent, /EFT derivations up to one loop, recently appearing in the literature, of the nuclear charge and current operators. The second objective is to provide a complete set of x EFT and hybrid predictions for the structure functions and tensor polarization of the deuteron, for the charge and magnetic form factors of 3He and 3H, and for the charge and magnetic radii of these few-nucleon systems. Methods: The calculations use wave functions derived from either chiral or conventional two- and three-nucleon potentials and Monte Carlo methods to evaluate the relevant matrix elements Results: In reference to the two objectives mentioned earlier, we find that (i) there are no differences between the /EFT magnetic dipole operator at one loop derived in our formalism and that obtained by Kölling et al. [Phys. Rev. C 80, 045502 (2009)] with the unitary transformation method and (ii) there is excellent agreement between theory and experiment for the static properties and elastic form factors of these A = 2 and 3 nuclei up to momentum transfers q < 2.0-2.5 fm-1. A complete analysis of the results is provided Conclusions: Nuclear /EFT provides a very satisfactory description of the isoscalar and isovector charge and magnetic structure of the A = 2 and 3 nuclei at low momentum transfers q < 3mn. In particular, contributions from two-body charge and current operators are crucial for bringing theory into close agreement with experiment. At higher q values the present XEFT predictions are similar to those obtained in the hybrid approach, as well as in older studies based on the conventional meson-exchange picture, and fail to reproduce the measured A = 2 and 3 form factors in the diffraction region. [ABSTRACT FROM AUTHOR]

The muon-capture reactions 2H(μ-, νμ)nn and 3He(μ-, νμ)3H are studied with nuclear potentials and charge-changing weak currents, derived in chiral effective field theory. The low-energy constants (LECs) cD and cE, present in the three-nucleon potential and (cD) axial-vector current, are constrained to reproduce the A = 3 binding energies and the triton Gamow-Teller matrix element. The muon-capture rates on deuteron and 3He are predicted to be 399 ± 3 sec-1 and 1494 ± 21 sec-1, respectively. The spread accounts for the cutoff sensitivity, as well as uncertainties in the LECs and electroweak radiative corrections. By comparing the calculated and precisely measured rates on 3He, a value for the induced pseudoscalar form factor is obtained in good agreement with the chiral perturbation theory prediction. [ABSTRACT FROM AUTHOR]

The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory (χEFT) up to order e Q [or next-to-next-to-next-to-next-to-leading order (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 nonstatic 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, predictions for physical observables will remain unaffected by the nonuniqueness associated with these off-the-energy-shell effects. [ABSTRACT FROM AUTHOR]

The low energy systems of three or four neutrons are treated within the adiabatic hyperspherical framework, yielding an understanding of the low energy quantum states in terms of an adiabatic potential energy curve. The dominant low energy potential curve for each system, computed here using widely accepted nucleon-nucleon interactions with and without the inclusion of a three-nucleon force, shows no sign of a low energy resonance. However, both systems exhibit a low energy enhancement of the density of states, or of the Wigner-Smith time delay, which derives from long-range universal physics analogous to the Efimov effect. That enhancement could be relevant to understanding the low energy excess of correlated four-neutron ejection events observed experimentally in a nuclear reaction by Kisamori et al. [ABSTRACT FROM AUTHOR]

The magnetic form factors of ²H, ³H, and ³He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers are calculated with the chiral two-nucleon (and three-nucleon) interactions including Δ intermediate states that have recently been constructed in configuration space. The A = 3 wave functions are obtained from hyperspherical-harmonics solutions of the Schrödinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by one- and two-pion exchange (OPE and TPE, respectively) mechanisms and contact interactions. The contributions associated with Δ intermediate states are only retained at the OPE level and are neglected in TPE loop (tree-level) corrections to two-body (three-body) current operators. Expressions for these currents are derived and regularized in configuration space for consistency with the interactions. The low-energy constants that enter the contact currents are determined by reproducing the magnetic moments of these few-nucleon systems. The predicted form factors and deuteron electrodisintegration cross section are in excellent agreement with experiment for momentum transfers up to 2-3 fm-1. However, the experimental values for the deuteron photodisintegration cross section are consistently underestimated by theory, unless use is made of the Siegert form of the electric dipole transition operator. A complete analysis of the results is provided, including the clarification of the origin of the aforementioned discrepancy. [ABSTRACT FROM AUTHOR]

The Gamow-Teller (GT) matrix element contributing to tritium β decay is calculated with trinucleon wave functions obtained from hyperspherical-harmonics solutions of the Schrödinger equation with the chiral two- and three-nucleon interactions including Δ intermediate states that have recently been constructed in configuration space. Predictions up to next-to-next-to-next-to-leading order (N3LO) in the chiral expansion of the axial current (with Δ's) overestimate the empirical value by 1-4%. By exploiting the relation between the low-energy constant (LEC) in the contact three-nucleon interaction and two-body axial current, we provide new determinations of the LECs cD and cE that characterize this interaction by fitting the trinucleon binding energy and tritium GT matrix element. Some of the implications that the resulting models of three-nucleon interactions have on the spectra of light nuclei and the equation of state of neutron matter are briefly discussed. We also provide a partial analysis, which ignores Δ's, of the contributions due to loop corrections in the axial current at next-to-next-to-next-to-next-to-leading order (N4LO). Finally, explicit expressions for the axial current up to N4LO have been derived in configuration space, which other researchers in the field may find useful. [ABSTRACT FROM AUTHOR]

In recent years local chiral interactions have been derived and implemented in quantum Monte Carlo methods in order to test to what extent the chiral effective field theory framework impacts our knowledge of few- and many-body systems. In this Letter, we present Green's function Monte Carlo calculations of light nuclei based on the family of local two-body interactions presented by our group in a previous paper in conjunction with chiral three-body interactions fitted to bound- and scattering-state observables in the three-nucleon sector. These interactions include Δ intermediate states in their two-pion-exchange components. We obtain predictions for the energy levels and level ordering of nuclei in the mass range A = 4 - 12, accurate to ≤ 2% of the binding energy, in very satisfactory agreement with experimental data. [ABSTRACT FROM AUTHOR]

We present fully local versions of the minimally nonlocal nucleon-nucleon potentials constructed in a previous paper [Piarulli et al., Phys. Rev. C 91, 024003 (2015)], and use them in hypersperical harmonics and quantum Monte Carlo calculations of ground and excited states of ³H, ³He, 4He, 6He, and 6Li nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with ? isobars in the intermediate states up to order Q³ (Q denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order Q4. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0-125 MeV or 0-200 MeV, and to the deuteron binding energy and nn singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, RL and RS, respectively, ranging from (RL,RS)=(1.2,0.8) fm down to (0.8,0.6) fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential. [ABSTRACT FROM AUTHOR]

We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium β decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory (χEFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrödinger equation with two- and three-nucleon potentials corresponding to either χEFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations. [ABSTRACT FROM AUTHOR]

The astrophysical S factor for the radiative capture d(p,γ)³He in the energy range of interest for big bang nucleosynthesis (BBN) is calculated using an ab initio approach. The nuclear Hamiltonian retains both two- and three-nucleon interactions--the Argonne v18 and the Urbana IX, respectively. Both one- and many-body contributions to the nuclear current operator are included. The former retain for the first time, besides the 1/m leading order contribution (m is the nucleon mass), also the next-to-leading order term, proportional to 1/m³. The many-body currents are constructed in order to satisfy the current conservation relation with the adopted Hamiltonian model. The hyperspherical harmonics technique is applied to solve the A=3 bound and scattering states. Particular attention is paid in this second case in order to obtain, in the energy range of BBN, an uncertainty on the astrophysical S factor of the order or below ∼1%. Then, in this energy range, the S factor is found to be ∼10% larger than the currently adopted values. Part of this increase (1%-3%) is due to the 1/m³ one-body operator, while the remaining is due to the new more accurate scattering wave functions. We have studied the implication of this new determination for the d(p,γ)³He S factor on the deuterium primordial abundance. We find that the predicted theoretical value for ²H/H is in excellent agreement with its experimental determination, using the most recent determination of the baryon density of the Planck experiment, and with a standard number of relativistic degrees of freedom Neff=3.046 during primordial nucleosynthesis. This calls for a more accurate measurement of the astrophysical S factor in order to confirm the present predictions. [ABSTRACT FROM AUTHOR]

We present a theoretical study of the processes d(d,p)^{3}H and d(d,n)^{3}He at energies of interest for energy production and for big-bang nucleosynthesis. We accurately solve the four body scattering problem using the ab initio hyperspherical harmonics method, starting from nuclear Hamiltonians which include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report results for the astrophysical S factor, the quintet suppression factor, and various single and double polarized observables. A first estimate of the theoretical uncertainty for all these quantities is provided by varying the cutoff parameter used to regularize the chiral interactions at high momentum.

While the phenomenon of gluon nuclear shadowing at small x has been getting confirmation in QCD analyses of various LHC measurements involving heavy nuclei, it has not been possible so far to establish experimentally the number of target nucleons responsible for nuclear shadowing in a given process. To address this issue, we study coherent J/ψ electroproduction on ^{4}He and ^{3}He in the kinematics of a future electron-ion collider and show that this process has the power to disentangle the contributions of the interaction with a specific number of nucleons k, in particular, with two nucleons at the momentum transfer t≠0. We predict a dramatic shift of the t dependence of the differential cross section toward smaller values of |t| due to a nontrivial correlation between x and k. This calculation, which makes use for the first time of realistic wave functions, provides a stringent test of models of nuclear shadowing and a novel probe of the 3D imaging of gluons in light nuclei. In addition, thanks to this analysis, unique information on the real part of the corresponding scattering amplitude could be accessed.

This corrects the article DOI: 10.1103/PhysRevLett.108.052502.

The charge and magnetic form factors, F&#95;{C} and F&#95;{M}, respectively, of ^{3}He are extracted in the kinematic range 25  fm^{-2}≤Q^{2}≤61  fm^{-2} from elastic electron scattering by detecting ^{3}He recoil nuclei and scattered electrons in coincidence with the two High Resolution Spectrometers of the Hall A Facility at Jefferson Lab. The measurements find evidence for the existence of a second diffraction minimum for the magnetic form factor at Q^{2}=49.3  fm^{-2} and for the charge form factor at Q^{2}=62.0  fm^{-2}. Both minima are predicted to exist in the Q^{2} range accessible by this Jefferson Lab experiment. The data are in qualitative agreement with theoretical calculations based on realistic interactions and accurate methods to solve the three-body nuclear problem.