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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

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

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.

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.

We report on a determination of the Earth-Moon distance performed by students of an Italian high school, based on measurements of the time delay of the "echo" in the radio communications between Nasa mission control in Houston and the Apollo astronauts on the lunar surface. By using an open-source audio-editing software, the distance can be determined with three digits accuracy, allowing to detect the effect due to the eccentricity of the orbit of the Moon., Comment: 7 pages, 2 figures

It is shown that the number of independent operators in the nucleon-nucleon parity-violating contact Lagrangian at the leading order in the low-momentum expansion, can be reduced to five, by using Fierz rearrangements of the nucleon fields., Comment: 4 pages, one reference added, matches the journal version

The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh-Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A=3 and 4 nuclear systems. When the wave function of the system is expanded over a sufficiently large set of HH basis functions, containing or not correlation factors, quite accurate results can be obtained for the observables of interest. In this paper, the main aspects of the method are discussed together with its application to the A=3 and 4 nuclear bound and zero-energy scattering states. Results for a variety of nucleon-nucleon (NN) and three-nucleon (3N) local or non-local interactions are reported. In particular, NN and 3N interactions derived in the framework of the chiral effective field theory and NN potentials from which the high momentum components have been removed, as recently presented in the literature, are considered for the first time within the context of the HH method. The purpose of this paper is two-fold. First, to present a complete description of the HH method for bound and scattering states, including also detailed formulas for the computation of the matrix elements of the NN and 3N interactions. Second, to report accurate results for bound and zero-energy scattering states obtained with the most commonly used interaction models. These results can be useful for comparison with those obtained by other techniques and are a significant test for different future approaches to such problems., 51 pages

We present an exploratory study consisting in the formulation of a relativistic quantum mechanics to describe the few-nucleon system at low energy, starting from the quantum field theoretical chiral Lagrangian involving pions and nucleons. To this aim we construct a Bakamjian-Thomas mass operator and perform a truncation of the Fock space which respects at each stage the relativistic covariance. Such truncation is justified, at sufficiently low energy, in the framework of a systematic chiral expansion. As an illustration we discuss the low-energy phaseshifts of the nucleon-nucleon and pion-nucleon scattering.

The structure of A=3 low-energy scattering states is described using the hyperspherical harmonics method with realistic Hamiltonian models, consisting of two- and three-nucleon interactions. Both coordinate and momentum space two-nucleon potential models are considered., Comment: 3 pages, 1 table, Proceedings of the 20th European Conference on Few-Body Problems in Physics (EFB20), Pisa, September 2007

We present an exploratory study consisting in the formulation of a relativistic quantum mechanics to describe the few-nucleon system at low energy, starting from the quantum field theoretical chiral Lagrangian involving pions and nucleons. To this aim we construct a Bakamjian-Thomas mass operator and perform a truncation of the Fock space which respects at each stage the relativistic covariance. Such truncation is justified, at sufficiently low energy, in the framework of a systematic chiral expansion. As an illustration we discuss the bound state observables and low-energy phaseshifts of the nucleon-nucleon and pion-nucleon scattering at the leading order of our scheme., Comment: 17 pages, 10 figures. Revised formulation, matches the journal version

The application of the hyperspherical harmonic approach to the case of non-local two-body 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 other ground state properties of A=3 and 4 nuclei are calculated using the CD Bonn 2000 and N3LO two-body potentials. The results are shown to be in excellent agreement with corresponding ones obtained by other accurate techniques., Comment: 12 pages, 6 tables, RevTex4

Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy pi-pi scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m_s/(m_u+m_d) > 14 at 95 % confidence level. We outline how additional information may be incorporated to further constrain the pattern of ChSB in the N_f=3 chiral limit., 58 pages, 8 figures

We propose a novel way to formulate Chiral Perturbation Theory in a nuclear background, characterized by a static, non-uniform distribution of the baryon number that describes the finite nucleus. In the limiting case of a uniform distribution, the theory reduces to the well-known zero-temperature in-medium ChPT. The proposed approach is used to calculate the self-energy of the charged pion in the background of the heavy nucleus at O(p^5) in the chiral expansion, and to derive the leading terms of the pion-nucleus optical potential., 42 pages, Latex, 4 Postscript figures

The recently published E865 data on charged K_e4 decays and Pi-Pi phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters alpha and beta, of the low-energy constants l3-bar and l4-bar as well as of the main two-flavour order parameters: and F_pi in the limit m_u = m_d = 0 taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on Pi-Pi phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2 a_0^0 - 5 a_0^2 and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1-sigma level is found and commented upon., Comment: Published version, to appear in Eur. Phys. J. C

We argue that light quark loops produce a paramagnetic suppression of infrared-sensitive order parameters such as , as the number N_f of light fermions increases. The possibly strong dependence of on N_f is related to the observed Zweig rule violation in the scalar channel. Presuming the existence of a chiral phase transition for not too large N_f, we discuss the phenomenological possibilities of separately determining the two-flavour and three-flavour condensates and the quark mass ratio r=2m_s/(m_u+m_d). The issue is closely related to the interpretation of new forthcoming precise pi-pi data at low energy., Comment: 15 pages, Latex, using JHEP.cls (included), 1 PS figure

A combination of finite energy sum rule techniques and Chiral Perturbation Theory (ChPT) is used in order to exploit recent ALEPH data on the non-strange tau vector (V) and axial-vector (A) spectral functions with respect to an experimental determination of the ChPT quantity L_{10}. A constrained fit of R_{��,V-A}^(k,l) inverse moments (l=0) adjusts simultaneously L_{10} and the nonperturbative power terms of the Operator Product Expansion. We give explicit formulae for the first k=0,1 and l=-1,-2 strange and non-strange inverse moment chiral sum rules to one-loop order generalized ChPT. Our final result reads L^r_{10}(M_��)=-(5.13 +/- 0.19)x10^{-3}, where the error includes experimental and theoretical uncertainties., LaTex, 20 pages, 5 figures (EPS)

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 A_y observable., Comment: 9 pages, 9 figures, to be published in the Proceedings of the 19th International IUPAP Conference on Few-Body Problems in Physics, Bonn, 2009

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 {Delta} resonance saturation, leads to a reasonable pattern of convergence of the chiral expansion.