Background: Weak interactions between quarks induce a parity-violating (PV) component in the nucleon-nucleon 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 charge-exchange reaction. Methods: The χEFT PV potential includes one-pion-exchange, two-pion-exchange, and contact terms as well as 1/M (M being the nucleon 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 h1_pi 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.

Using modern nucleon-nucleon interactions in the description of A = 3, 4 nuclei, it is not possible to reproduce both the three- and the four-nucleon binding energies simultaneously. This is one manifestation of the necessity of including a three- nucleon force in the nuclear Hamiltonian. In this paper we perform a comparative study of some widely used three- nucleon force models. We analyze their capability to describe the aforementioned binding energies as well as the n-d doublet scattering length. The correct description of these quantities can be considered a stringent requirement for a nuclear Hamiltonian containing two- and three- nucleon interaction terms. As we show, this requirement is not fulfilled by several of the models available in the literature. To satisfy it, we propose modifications in the parametrization of the three- nucleon forces and we study their effects on a few selected N-d low-energy scattering observables.

The effect of the inclusion of different models of three nucleon (3N) forces in p − 3He elastic scattering at low energies is studied. Two models 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 using the Kohn variational principle and the hyperspherical harmonic technique and the results are compared with available experimental data. We have found that with the inclusion of both 3N force models the agreement with the experimental data is improved, in particular for the proton vector analyzing power A y .

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.

Recently, we have derived a two nucleon potential and consistent nuclear electromagnetic currents in chiral effective field theory with pions and nucleons as explicit degrees of freedom The calculation of the currents has been carried out to include (NLO)-L-3 corrections, consisting of two-pion exchange and contact contributions The latter involve unknown low-energy constants (LECs), some of which have been fixed by fitting the up S- and P-wave phase shifts up to 100 MeV lab energies The remaining LECs entering the current operator are determined so as to reproduce the experimental deuteron and trinucleon magnetic moments, as well as the rip cross section This electromagnetic current operator is utilized to study the mid and n(3)He radiative captures at thermal neutron energies Here we discuss our results stressing on the important role played by the LECs in reproducing the experimental data

We summarize our recent work dealing with the construction of the nucleon-nucleon potential and associated electromagnetic currents up to one loop in chiral effective field theory (χEFT). The magnetic dipole operators derived from these currents are then used in hybrid calculations of static properties and low-energy radiative capture processes in few-body nuclei. A preliminary set of results are presented for the magnetic moments of the deuteron and trinucleons and thermal neutron captures on p, d, and 3He.

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 (χEFT) approach to describe the strong-interaction dynamics in these few-nucleon systems and their response to electromagnetic probes. Purpose: The objectives of the presentwork are twofold. The first is to address and resolve some of the differences present in independent, χEFT 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 χEFT 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 χEFT magnetic dipole operator at one loop derived in our formalism and that obtained by K¨olling 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 χEFT 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 3mπ . 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 χEFT 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.

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.

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.

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 H-3, He-3, He-4, He-6, and Li-6 nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with Delta 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.

We construct a coordinate-space chiral potential, including Δ-isobar intermediate states in its two-pion-exchange component up to order Q^3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q^2 and Q^4, respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0–300 MeV. For the total 5291 pp and np data in this range, we obtain a χ2/datum of roughly 1.3 for a set of 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.

The muon-capture reactions 2H(μ-,νμ)nn and 3He(μ-,νμ)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.

We review our recent work on the derivation of the nuclear electromagnetic charge and current operators in chiral perturbation theory, based on time-ordered perturbation theory. We then discuss the strategies for fixing the relevant low energy constants, and compare the resulting predictions for the electric and magnetic form factors of the deuteron and trinucleons with experimental data, using as input accurate nuclear wave functions derived with realistic potentials.

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.

We describe our method for deriving the nuclear electromagnetic charge and current operators in chiral perturbation theory, based on time-ordered perturbation theory. We then discuss possible strategies for fixing the relevant low-energy constants, from the magnetic moments of the deuteron and of the trinucleons, and from the radiative np capture cross sections, and identify a scheme which, partly relying on D resonance saturation, leads to a reasonable pattern of convergence of the chiral expansion.

The longitudinal asymmetry induced by parity-violating (PV) components in the nucleon-nucleon potential is studied in the charge-exchange reaction He-3(n-polarized, p)H-3 at vanishing incident neutron energies. An expression for the PV observable is derived in terms of T-matrix elements for transitions from the L-2S+1(J) = S-1(0) and S-3(1) states in the incoming n-He-3 channel to states with J = 0 and 1 in the outgoing p-H-3 channel. The T-matrix elements involving PV transitions are obtained in first-order perturbation theory in the hadronic weak-interaction potential, while those connecting states of the same parity are derived from solutions of the strong-interaction Hamiltonian with the hyperspherical-harmonics method. The coupled-channel nature of the scattering problem is fully accounted for. Results are obtained corresponding to realistic or chiral two-and three-nucleon strong-interaction potentials in combination with either the DDH or pionless EFT model for the weak-interaction potential. The asymmetries, predicted with PV pion and vector-meson coupling constants corresponding (essentially) to the DDH "best values" set, range from -9.44 to -2.48 in units of 10(-8), depending on the input strong-interaction Hamiltonian. This large model dependence is a consequence of cancellations between long-range (pion) and short-range (vector-meson) contributions and is of course sensitive to the assumed values for the PV coupling constants.

We investigate whether the subleading three nucleon contact interaction, depending on 10 low-energy constants (LECs), may provide enough flexibility to solve existing discrepancies between theory and experiment in A=3 scattering observables. To this aim we choose a realistic two-nucleon interaction (AV18) supplemented with the leading and subleading three-nucleon contact interaction, and fit the LECs to very precise data on polarization observables in elastic p−d scattering at 3 MeV proton energy.

The Kohn variational principle and the hyperspherical harmonic technique are applied to study p − 3He elastic scattering at low energies. Preliminary results obtained using several interaction models are reported. The calculations are compared to a recent phase shift analysis performed at the Triangle University Nuclear Laboratory and to the available experimental data. Using a three-nucleon interaction derived from chiral perturbation theory at N2LO, we have found a noticeable reduction of the discrepancy observed for the Ay observable.

In the first part of the contribution, we discuss the results of a recent benchmark calculation of n − 3H and p − 3He phase-shifts below the trinucleon disintegration thresholds. Three different methods— Alt, Grassberger and Sandhas, Hyperspherical Harmonics, and Faddeev–Yakubovsky—have been used and their results are compared. For both n − 3H and p − 3He we observe a rather good agreement between the three different theoretical methods. In the second part of the contribution, we study the longitudinal asymmetry An3He z in the 3He(n, p)3H reaction in order to obtain information about the parity-violating components of the nucleon–nucleon interaction.

Relativistic covariance restricts the number of two-nucleon contact operators. We show that these constraints can be implemented starting from a complete set of relativistically invariant contact operators up to order Q in the parity-violating sector and order Q2 in the parity-conserving one.

We construct the most general, relativistically invariant, contact Lagrangian at order Q(2) in the power counting, with Q denoting the low momentum scale. A complete, but nonminimal, set of (contact) interaction terms is identified, which upon nonrelativistic reduction generate two leading independent operator combinations of order Q(0) and seven subleading ones of order Q(2)-a result derived previously in the heavy-baryon formulation of effective field theories (EFTs). We show that Poincare covariance of the theory requires that additional terms with fixed coefficients be included, to describe the two-nucleon potential in reference frames other than the center-of-mass frame. These terms will contribute in systems with mass numberA > 2, and their impact on EFT calculations of binding energies and scattering observables in these systems should be studied.

Parity violation in few-nucleon systems is studied using a nucleon-nucleon parityviolating (PV) potential derived within an effective field theory framework at next-to-next-toleading order. The potential includes one- and two-pion exchanges, contact interactions and relativistic corrections and depends on six low-energy constants: the pion-nucleon coupling constant h1π and five parameters multiplying the independent contact interaction terms (with one four-gradient). This potential is used to study the p(polarized)-p longitudinal asymmetry, the neutron spin rotation in n(polarized)-d scattering, and the longitudinal asymmetry in the 3He(n-polarized, p)3H reaction.

We obtain a minimal form of the two-derivative three-nucleon contact Lagrangian, by imposing all constraints deriving from discrete symmetries, Fierz identities, and Poincare' covariance. The resulting interaction, depending on 10 unknown low-energy constants, leads to a three-nucleon potential which we give in a local form in configuration space. We also consider the leading (no-derivative) four-nucleon interaction and show that there exists only one independent operator.

The longitudinal asymmetry A_z(n-3He) in the 3He(n, p)3H reaction is an observable directly related to parity-violating (PV) components in the nucleon-nucleon (NN) interaction. Here we study A_z(n-3He) using a PV NN potential derived from an effective field theory framework at next-to-next-to-leading order, including one- and two-pion exchanges, contact interactions and relativistic corrections. This potential depends on six low-energy constants. Some of these parameters are constrained to reproduce the existing accurate measurements of the p-p longitudinal asymmetry. Using these constraints we compute A_z(n-3He) and study the sensitivity of such an observable to the unconstrained parameters.

We report on a study of the nd and n3He radiative captures at thermal neutron energies, using wave functions obtained from either chiral or conventional two- and three-nucleon realistic potentials with the hyperspherical-harmonics method, and electromagnetic currents derived in chiral effective field theory up to one loop. The predicted nd and n3He cross sections are in good agreement with data, but exhibit a significant dependence on the input Hamiltonian. A comparison is also made between these and new results for the nd and n3He cross sections obtained in the conventional framework for both potentials and currents.

A satisfactory description of bound and scattering states of the three-nucleon (3N) system is still lacking, contrary to what happens in the two-nucleon case. In the framework of chiral effective theory, it is possible that a realistic 3N interaction will require the inclusion of subleading contact terms, which are unconstrained by chiral symmetry. We construct the minimal 3N contact Lagrangian imposing all constraints from the discrete symmetries, Fierz identities and Poincaré covariance, and show that it consists of 10 independent operators. By integrating out the pions from the effective theory we derive the pion-induced contributions to the corresponding low-energy constants (LECs), and find no clear signal of convergence of the pionful theory between N2LO and N3LO.

We present a preliminary study of the effect of a three-nucleon force (3NF) in p-H(3) and n-He(3) scattering at low energies. The used 3NF is derived from effective field theory at next-to-next-to-leading order. The four-nucleon scattering observables are calculated using the Kohn variational principle and the hyperspherical harmonics technique and the results are compared with available experimental data. We have found that the effect of introducing this type of 3NF is tiny, and sometimes worsens the agreement with the experimental data.

We derive the minimal form of the two-derivative three-nucleon contact interaction by imposing all constraints from discrete symmetries and Fierz identities. In order to comply with the requirements of Poincare' covariance, a basis of operators depending on relative momenta is used. The resulting interaction depends on 10 unknown low-energy constants and leads to a three-nucleon potential which we give in local form in coordinate space.

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 Schroedinger 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.

We report on our progress in the inclusion of the subleading 3N contact operators for the elastic p−d scattering below the deuteron break-up. We find that, with a nuclear interaction consisting of the AV18 2N potential, supplemented by the leading and subleading 3N contact operators, existing discrepancies between theory and experiment, like the well-known Ay puzzle, are substantially reduced.

The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory (χEFT) up to order eQ [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.