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International audience; The Efimov window, or universal window, is a particular energy region in which few-body systems are loosely bound. Many characteristics of those systems are universal; their properties are largely independent of the particular interaction that produces the binding. This suggests the use of simple potential models characterized by few parameters to describe dynamical properties. Essentially, the potential parameters are set in order to reproduce a small number of data, and then the potential strength can be varied to explore the window. Among others, the Gaussian potential has been used to characterize the universal window. From calculations of the ground state and of the first excited state of three identical bosons using a Gaussian potential along the window, we determine what is called the gaussian-level function. This function is independent of the particular Gaussian potential used in this procedure. Moreover, it contains finite-range corrections which are of particular importance when theoretical predictions are compared to experimental data.

Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry induces a universal behavior for different systems, independent of the details of the underlying interaction, rooted in the smallness of the ratio $\ell/a_B \ll 1$, where the length $a_B$ is associated to the binding energy of the two-body system $E_2=\hbar^2/m a_B^2$ and $\ell$ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the on-set of system-specific non-universal effects. In this work we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which $a_B\rightarrow\infty$, and show that nuclear systems belong to this class of universality., 27 pages, 8 figures

Classes of two-nucleon ($2N$) contact interactions are developed in configuration space at leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N3LO) by fitting the experimental singlet $np$ scattering length and deuteron binding energy at LO, and $np$ and $pp$ scattering data in the laboratory-energy range 0--15 MeV at NLO and 0--25 MeV at N3LO. These interactions are regularized by including two Gaussian cutoffs, one for $T\,$=$\,0$ and the other for $T\,$=$\,1$ channels. The cutoffs are taken to vary in the ranges $R_0\,$=$(1.5$--2.3) fm and $R_1\,$=$(1.5$--3.0) fm. The 780 (1,100) data points up to 15 (25) MeV energy, primarily differential cross sections, are fitted by the NLO (N3LO) models with a $\chi^2$/datum about 1.7 or less (well below 1.5), when harder cutoff values are adopted. As a first application, we report results for the binding energies of nuclei with mass numbers $A\,$=$\,3$--6 and 16 obtained with selected LO and NLO $2N$ models both by themselves as well as in combination with a LO three-nucleon ($3N$) contact interaction. The latter is characterized by a single low-energy constant that is fixed to reproduce the experimental $^3$H binding energy. The inclusion of the $3N$ interaction largely removes the sensitivity to cutoff variations in the few-nucleon systems and leads to predictions for the $^3$He and $^4$He binding energies that cluster around 7.8 MeV and 30 MeV, respectively. However, in $^{16}$O this cutoff sensitivity remains rather strong. Finally, predictions at LO only are also reported for medium-mass nuclei with $A\,$=$\,40$, 48, and 90., Comment: 23 pages, 6 figures

We identify a redundancy between two- and three-nucleon contact interactions at the fourth and fifth orders of the chiral expansion, respectively. In particular, we show that tensor-type and spin-orbit three-nucleon contact interactions effectively account for that part of the two-nucleon interaction which depends on the total center-of-mass momentum and is unconstrained by relativity. This might give the chiral effective field theory enough flexibility to successfully address $A=3$ scattering observables already at N3LO.

The $n+^{3}\mathrm{H},$ $p+^{3}\mathrm{He},$ $p+^{3}\mathrm{H},$ and $n+^{3}\mathrm{He}$ elastic and charge exchange reactions at low energies are studied by means of the hyperspherical harmonic method. The considered nuclear Hamiltonians include modern two- and three-nucleon interactions, and in particular results are reported in case of chiral two-nucleon potentials, with and without the inclusion of chiral three-nucleon (3N) interactions. A detailed study of the convergence and numerical stability of the method is presented. We have found that the effect the 3N force is in general tiny except for $p+^{3}\mathrm{H}$ scattering below the opening of the $n+^{3}\mathrm{He}$ channel. In such a case, the effect of 3N forces is appreciable and a clear dependence on the cutoff used to regularize the high-momentum tail of the interactions is observed. Such a dependence is related to the presence of the poorly known sharp ${0}^{+}$ resonance, considered to be the first excited state of $^{4}\mathrm{He}$.

We present a study of the effect of three-nucleon forces (3NFs) in (formula presented), (formula presented) and (formula presented) 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 particular 3NF is in general tiny except for (formula presented) scattering below the opening of the (formula presented) channel. In such a case, the effect of 3NF is evident and a clear dependence on the cutoff used to regularize the high-momentum tail of the interactions is observed. Such a dependence is related to the presence of a poorly known sharp (formula presented) resonance, considered to be the first excited state of (formula presented).

Parity-violating and time-reversal conserving (PVTC) and parity-violating and time-reversal-violating (PVTV) forces in nuclei form only a tiny component of the total interaction between nucleons. The study of these tiny forces can nevertheless be of extreme interest because they allow to obtain information on fundamental symmetries using nuclear systems. The PVTC interaction derives from the weak interaction between the quarks inside nucleons and nuclei and the study of PVTC effects opens a window on the quark-quark weak interaction. The PVTV interaction is sensitive to more exotic interactions at the fundamental level, in particular to strong CP violation in the Standard Model Lagrangian, or even to exotic phenomena predicted in various beyond-the-Standard-Model scenarios. The presence of these interactions can be revealed either by studying various asymmetries in polarized scattering of nuclear systems, or by measuring the presence of non-vanishing permanent electric dipole moments of nucleons, nuclei and diamagnetic atoms and molecules. In this contribution, we review the derivation of the nuclear PVTC and PVTV interactions within various frameworks. We focus in particular on the application of chiral effective field theory, which allows for a more strict connection with the fundamental interactions at the quark level. We investigate PVTC and PVTV effects induced by these potential on several few-nucleon observables, such as the longitudinal asymmetry in proton-proton scattering and radiative neutron-proton capture, and the electric dipole momentsof the deuteron and the trinucleon system., Comment: 68 pages, contribution to Frontiers in Physics

We construct accurate models of 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 long-standing $A_y$ 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-$N_c$ 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., Comment: 35 pages, 9 figures

The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with a number of nucleons A ≤ 4. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both bound and scattering states can be addressed, using either local or non-local interactions. Thanks to this versatility, the method can be used to test the two- and three-nucleon components of the nuclear interaction. In the present review we introduce the formalism of the HH method, both for bound and scattering states. In particular, we describe the implementation of the method to study the A = 3 and 4 scattering problems. Second, we present a selected choice of results of the last decade, most representative of the latest achievements. Finally, we conclude with a discussion of what we believe will be the most significant developments within the HH method for the next 5–10 years., SCOPUS: re.j, info:eu-repo/semantics/published

The magnetic form factors of $^2$H, $^3$H, and $^3$He, 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 $\Delta$ intermediate states that have recently been constructed in configuration space. The $A\,$=$\,$3 wave functions are obtained from hyperspherical-harmonics solutions of the Schr\"odinger 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 $\Delta$ 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 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., Comment: 24 pages, 13 figures

International audience; The understanding of nuclear systems as composed of interacting nucleons has been considerably sharpened by the effective field theory (EFT) framework. The latter provides a link between the nuclear interaction and the underlying quantum chromodynamics, as the relevant degrees of freedom result, at least ideally, from a decimation process starting from fundamental quarks and gluons. Owing to chiral symmetry and the Goldstone bosons’ characters of the interchanged pions among nucleons, the properties of heavier nuclei can in principle be traced back to a restricted set of low-energy constants (LECs) to be determined in lighter systems in the framework of a systematic low-energy expansion. At smaller energy scales, in pionless EFT, the interactions simplify becoming of contact type. The low-energy expansion is organized differently, relying on the emergence of universal properties, characteristic of systems with large two-body scattering lengths. We will examine the two above schemes and discuss their relation, with the aim of devising viable power counting schemes for applications in nuclear physics.

We study the effect of the three-nucleon force (3NF) in $$p+{}^3{\mathrm{H}}$$ and $$n+{}^3{\mathrm{He}}$$ scattering at low energies. The used 3NF was 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 also extract information on the excited states of $${}^4\mathrm {He}$$ from the calculated S-matrix.

These are the notes of a lecture given at the Pisa summer school on Basic nuclear interactions and their link to nuclear processes in the cosmos and on earth. Taking a historical perspective we will describe the gauge principle, which lies at the basis of all known fundamental interactions.

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 $\beta$-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., Comment: 5 pages, 3 figures

Si propone un esperimento volto a quantificare l'effetto Doppler per onde sonore in due modi diversi. L'apparato sperimentale consiste in un generatore di frequenze, due altoparlanti, uno dei quali è appeso all'estremità di un pendolo, un microfono posto sul piano di oscillazione del pendolo, e un apposito software di acquisizione dati. Inizialmente si registra il suono emesso dal solo altoparlante in moto oscillatorio. L'andamento della frequenza del suono registrato in funzione del tempo consiste in una variazione periodica tra una frequenza massima e una frequenza minima. Il fit dei dati acquisiti fornisce lo spostamento Doppler massimo. Successivamente viene registrato il suono emesso dai due altoparlanti, collegati al generatore di frequenza, uno dei quali è in moto oscillatorio e l'altro in quiete in corrispondenza della posizione di equilibrio del pendolo. La registrazione mostra chiaramente due serie di battimenti per ogni periodo, la cui frequenza fornisce un'ulteriore misura dello spostamento Doppler massimo.

We present a preliminary study of the effect of a three-nucleon force (3NF) in $$p{\text{-}}^3\mathrm{H}$$ and $$n{\text{-}}^3\mathrm{He}$$ 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.

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., 5 pages, 3 figures

A major goal of nuclear theory is to explain the spectra and stability of nuclei in terms of effective many-body interactions amongst the nucleus' constituents-the nucleons, i.e., protons and neutrons. Such an approach, referred to below as the basic model of nuclear theory, is formulated in terms of point-like nucleons, which emerge as effective degrees of freedom, at sufficiently low energy, as a result of a decimation process, starting from the fundamental quarks and gluons, described by Quantum Chromodynamics (QCD). A systematic way to account for the constraints imposed by the symmetries of QCD, in particular chiral symmetry, is provided by chiral effective field theory, in the framework of a low-energy expansion. Here we show, in quantum Monte Carlo calculations accurate to $\leq\!2\%$ of the binding energy, that two- and three-body chiral interactions fitted {\sl only} to bound- and scattering-state observables in, respectively, the two- and three-nucleon sectors, lead to predictions for the energy levels and level ordering of nuclei in the mass range $A\,$=$\,$4-12 in very satisfactory agreement with experimental data. Our findings provide strong support for the fundamental assumptions of the basic model, and pave the way to its systematic application to the electroweak structure and response of these systems as well as to more complex nuclei., Comment: 21 pages, 3 figures

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.

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 A y puzzle, are substantially reduced.

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 $^{3}\mathrm{H}$, $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{6}\mathrm{He}$, and $^{6}\mathrm{Li}$ nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with $\mathrm{\ensuremath{\Delta}}$ isobars in the intermediate states up to order ${Q}^{3}$ ($Q$ denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order ${Q}^{4}$. 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, ${R}_{\mathrm{L}}$ and ${R}_{\mathrm{S}}$, respectively, ranging from $({R}_{\mathrm{L}},{R}_{\mathrm{S}})=(1.2,0.8)$ 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.

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 $${A_z^{n^3{\rm He}}}$$ in the 3He(n, p)3H reaction in order to obtain information about the parity-violating components of the nucleon–nucleon interaction.

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 N$^3$LO 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 $np$ 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 $np$ cross section. This electromagnetic current operator is utilized to study the $nd$ 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., Comment: Invited talk at the 5th International Conference on Quarks and Nuclear Physics, to appear in Chinese Physics C

It is not possible to reproduce both the three- and four-nucleon binding energies using the available two-nucleon potentials. This is one manifestation of the need to include a three-nucleon force in the corresponding Hamiltonian. In this paper we will analyze the capability of a three-nucleon force model to describe not only the aforementioned binding energies but also some N − d low energy scattering observables.

The application of the hyperspherical harmonics method to the case of non-local potentials is described. Given the properties of the hyperspherical harmonic functions, there are no difficulties in considering the approach in both coordinate and momentum space. The binding energies and some scattering observables of A = 4 systems are calculated using modern two-body potentials. For the α -particle, the results are shown to be in excellent agreement with corresponding ones obtained by other techniques. A study of the n – 3 H scattering lengths is also reported.

We construct a coordinate-space chiral potential, including $\Delta$-isobar intermediate states in its two-pion-exchange component. The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders ($Q^2$ and $Q^4$, respectively, $Q$ denoting generically the low momentum scale) 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 $\chi^2$/datum of roughly 1.3 for a set of three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ 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., Comment: 32 pages, 19 figures, accepted for publication as a Regular Article in Physical Review C

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 ($\ensuremath{\chi}$EFT) 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, $\ensuremath{\chi}$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 $\ensuremath{\chi}$EFT and hybrid predictions for the structure functions and tensor polarization of the deuteron, for the charge and magnetic form factors of ${}^{3}$He and ${}^{3}$H, 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 $\ensuremath{\chi}$EFT 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 $q\ensuremath{\lesssim}2.0$--2.5 fm${}^{\ensuremath{-}1}$. A complete analysis of the results is provided.Conclusions: Nuclear $\ensuremath{\chi}$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 $q\ensuremath{\lesssim}3{m}_{\ensuremath{\pi}}$. 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 $\ensuremath{\chi}$EFT 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.

We reconsider the derivation of the nucleon-nucleon parity-violating (PV) potential within a chiral effective field theory framework. We construct the potential up to next-to-next-to-leading order by including one-pion-exchange, two-pion-exchange, contact, and 1/M (M being the nucleon mass) terms, and use dimensional regularization to renormalize the pion-loop corrections. A detailed analysis of the number of independent low-energy constants (LEC's) entering the potential is carried out. We find that it depends on six LEC's: the pion-nucleon PV coupling constant $h^1_\pi$ and five parameters multiplying contact interactions. We investigate PV effects induced by this potential on several few-nucleon observables, including the $\vec{p}$-$p$ longitudinal asymmetry, the neutron spin rotation in $\vec{n}$-$p$ and $\vec{n}$-$d$ scattering, and the longitudinal asymmetry in the $^3$He$(\vec{n},p)^3$H charge-exchange reaction. An estimate for the range of values of the various LEC's is provided by using available experimental data., Comment: 31 pages, 7 figures, submitted to Physical Review C

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.

The possibility of detecting the S-wave of the decays tau -> 3 pi + nu(tau) in the threshold region is explored, with emphasis on the sensitivity to the size of the quark antiquark condensate .

The decays tau -> 3 pi + nu(tau) are analyzed at one loop order in the framework of Generalized Chiral Perturbation Theory, in order to test the sensitivity to the size of spontaneous chiral symmetry breaking parameters, contained in the S-wave. The latter, due to a kinematical suppression, at threshold, of the P-wave, is relatively large enough to be detectable at high energy machines, through azimuthal left-right asymmetries. This quantity (for the pi- pi- pi+ mode), integrated from threshold to Q^2 = 0.35 GeV^2, varies from (17 +- 3) % in the standard case of large condensate up to (40 +- 5) % in the extreme case of tiny condensate. The feasibility of such measurement at high luminosity colliders (e.g. CLEO) is discussed. This method provides a completely independent cross-check of forthcoming experimental determination of the quark condensate, based on low energy pi-pi scattering., Comment: 29 pages, Latex, using JHEP.cls (included), 7 PS figures

The objectives of the present work are twofold. The first is to address and resolve some of the differences present in independent, chiral-effective-field-theory (\chiEFT) derivations up to one loop, recently appeared in the literature, of the nuclear charge and current operators. The second objective is to provide a complete set of \chiEFT 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. The calculations use wave functions derived from high-order chiral two- and three-nucleon potentials and Monte Carlo methods to evaluate the relevant matrix elements. Predictions based on conventional potentials in combination with \chiEFT charge and current operators are also presented. There is excellent agreement between theory and experiment for all these observables for momentum transfers up to q< 2.0-2.5 (1/fm); for a subset of them, this agreement extends to momentum transfers as high as q~5-6 (1/fm). A complete analysis of the results is provided., 34 pages, Revtex

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 Poincar\'e 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., Comment: 6 pages, presented at the Sixth International Conference on Quarks and Nuclear Physics, April 16-20, 2012. Ecole Polytechnique, Palaiseau, Paris, France

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., Comment: 8 pages, 4 figures, talk presented at the 20th International IUPAP Conference on Few-Body Problems in Physics, 20 - 25 August, 2012, Fukuoka, Japan

The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory ($\chi$EFT) up to order $e\, Q$ (or N4LO), where $Q$ denotes the low-momentum scale and $e$ is the electric charge. The specific form of the N3LO and N4LO corrections from, respectively, one-pion-exchange and two-pion-exchange depends on the off-the-energy-shell prescriptions adopted for the non-static terms in the corresponding potentials. We show that different prescriptions lead to unitarily equivalent potentials and accompanying charge operators. Thus, provided a consistent set is adopted, predictions for physical observables will remain unaffected by the non-uniqueness associated with these off-the-energy-shell effects., Comment: 16 pages, 10 figures

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 13 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., 11 pages. Three more operators found after correcting some mistaken Fierz relations

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.

The longitudinal asymmetry induced by parity-violating (PV) components in the nucleon-nucleon potential is studied in the charge-exchange reaction 3He(~n, p)3H at vanishing incident neutron energies. An expression for the PV observable is derived in terms of T-matrix elements for transitions from the 2S+1LJ = 1S0 and 3S1 states in the incoming n-3He channel to states with J = 0 and 1 in the outgoing p-3H 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 formore » the PV coupling constants.« less

We construct the most general, relativistically invariant, contact Lagrangian at order Q^2 in the power counting, Q denoting the low momentum scale. A complete, but non-minimal, set of (contact) interaction terms is identified, which upon non-relativistic reduction generate 2 leading independent operator combinations of order Q^0 and 7 sub-leading ones of order Q^2 - a result derived previously in the heavy-baryon formulation of effective field theories (EFT's). We show that Poincare covariance of the theory requires that additional terms with fixed coefficients be included, in order to describe the two-nucleon potential in reference frames other than the center-of-mass frame. These terms will contribute in systems with mass number A>2, and their impact on EFT calculations of binding energies and scattering observables in these systems should be studied., 17 pages, 1 eps figure

Using modern nucleon-nucleon interactions in the description of the $A=3,4$ nuclei, it is not possible to reproduce both the three- and 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 will perform a comparative study of some, widely used, three-nucleon force models. We will analyze their capability to describe the aforementioned binding energies as well as the $n-d$ doublet scattering length. A correct description of these quantities can be considered a stringent requirement for a nuclear Hamiltonian containing two- and three-nucleon interaction terms. As we will 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 few selected $N-d$ low energy scattering observables., Comment: 30 pages, 10 figures

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 ($\chi$EFT). 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 $^3$He., Comment: Invited talk to the 19th International IUPAP Conference on Few-Body Problems in Physics

A two-nucleon potential and consistent electromagnetic currents are derived in chiral effective field theory $(\ensuremath{\chi}\mathrm{EFT})$ at, respectively, ${Q}^{2}$ (or ${\mathrm{N}}^{2}\mathrm{LO}$) and $eQ$ (or ${\mathrm{N}}^{3}\mathrm{LO}$), where $Q$ generically denotes the low-momentum scale and $e$ is the electric charge. Dimensional regularization is used to renormalize the pion-loop corrections. A simple expression is derived for the magnetic dipole $(M1)$ operator associated with pion loops, consisting of two terms, one of which is determined, uniquely, by the isospin-dependent part of the two-pion-exchange potential. This decomposition is also carried out for the $M1$ operator arising from contact currents, in which the unique term is determined by the contact potential. Finally, the low-energy constants entering the ${\mathrm{N}}^{2}\mathrm{LO}$ potential are fixed by fits to the $\mathit{np}$ $S$- and $P$-wave phase shifts up to 100 MeV laboratory energies.