Search

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 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.

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.

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.

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.

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.

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 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.

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 harmonic approach to the case of the N −d scattering problem is described. The nuclear Hamiltonian includes local and non-local two- and three-nucleon interactions. Also, Coulomb repulsion is included in the p − d case. Accurate calculation for p − d and n − d cross section and polarization observables at two center-of-mass energies are performed and the theoretical results are compared with the available experimental data. A satisfactory agreement between theory and experiment is found, except for the vector polarization observables. A quantitative estimate of the agreement or disagreement between theory and experiment is obtained performing a chi^2 analysis.

The Kohn variational principle and the hyperspherical harmonics technique are applied to study the n-H-3 elastic scattering at low energies. In this contribution the first results obtained using a non-local realistic interaction derived from the chiral perturbation theory are reported. They are found to be in good agreement with those obtained solving the Faddeev-Yakubovsky equations. The calculated total and differential cross sections are compared with the available experimental data. The effect of including a three-nucleon interaction is also discussed.

The neutron spin rotation induced by parity-violating (PV) components in the nucleon-nucleon potential is studied in n-polarized - d scattering at zero energy. Results are obtained corresponding to the Argonne v(18) two-nucleon and Urbana-IX three-nucleon strong-interaction potentials in combination with either the Desplanques-Donoghue-Holstein or pionless effective field theory models for the weak-interaction potential. We find that this observable is dominated by the contribution of the long-range part of the PV potential associated with pion exchange. Thus its measurement could provide a further constraint, complementary to that coming from measurements of the photon asymmetry in n-polarized - p radiative capture, on the strength of this component of the hadronic weak interaction.

In order to isolate the contribution of the nucleon strange electric form factor to the parity-violating asymmetry measured in He-4(e,e('))He-4 experiments, it is crucial to have a reliable estimate of the magnitude of isospin-symmetry-breaking (ISB) corrections in both the nucleon and He-4. We examine this issue in the present Letter. Isospin admixtures in the nucleon are determined in chiral perturbation theory, while those in He-4 are derived from nuclear interactions, including explicit ISB terms. A careful analysis of the model dependence in the resulting predictions for the nucleon and nuclear ISB contributions to the asymmetry is carried out. We conclude that, at the low momentum transfers of interest in recent measurements reported by the HAPPEX Collaboration at Jefferson Lab, these contributions are of comparable magnitude to those associated with strangeness components in the nucleon electric form factor.

We describe the calculation of the pi-nucleus optical potential to NLO in Chiral Perturbation Theory (ChPT) within a new formulation of the effective theory in the presence of a nuclear background, characterized by a static, non-uniform distribution of the baryon number, describing the finite nucleus. This formulation reduces to the conventional In-medium ChPT in the case of a uniform distribution. In this way we are able to identify unambiguously the nuclear finite size effects and disentangle the S-, P- and D-wave contributions to the optical potential without invoking the local density approximation.

We propose a method for implementing the large-N-c, large-N-f limit of QCD at the effective Lagrangian level. Depending on the value of the ratio N-f/N-c, different patterns of chiral symmetry breaking can arise, leading in particular to different behaviors of the eta ' mass in the combined large-N limit.

We express the two-massless-flavor Gell-Mann-Oakes-Renner ratio in terms of low-energy pi pi observables including the O(p(6)) double chiral logarithms of generalized chiral perturbation theory. Their contribution is sizeable and tends to compensate the one from the single chiral logarithms. However it is not large enough to spoil the convergence of the chiral expansion. As a signal of reduced theoretical uncertainty, we find that the scale dependence from the one-loop single logarithms is almost completely canceled by the one from the two-loop double logarithms.

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 ., Comment: contribution to QCD99, 4 pages, Latex, using espcrc2.sty (included), 2 PS figure

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.

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.

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

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.

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 the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavours, 23 terms for three and 5 for two flavours. In the two flavour case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well., Comment: 12 pages, misprint in table 2 corrected

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

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 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

Four of the six parameters defining the two-loop \pi\pi scattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard \chi PT expressions, we obtain the threshold parameters, low-energy phases and the O(p^4) constants $l_1^r, l_2^r$. The result $l_2^r ( M_{\rho} ) = ( 1.6 \pm 0.4 \pm 0.9 ) \times 10^{-3} ( {\bar l_2} = 4.17 \pm 0.19 \pm 0.43$) reproduces the correct D-waves but it is incompatible with existing Standard \chi PT analyses of $K_{l4}$ form factors beyond one loop., Comment: 14 pages, Latex209, 2 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