Subleading contributions to the three-nucleon contact interaction

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.Comment: 11 pages. Three more operators found after correcting some mistaken Fierz relation

Double chiral logarithms of Generalized Chiral Perturbation Theory for low-energy pi-pi scattering

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

Effect of three nucleon forces in p-3He scattering

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, Japa

Comparative study of three-nucleon force models in A=3,4A=3,4 systems

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 figure

Effect of three-nucleon interaction in p-3He elastic scattering

We present a detailed study of the effect of different three-nucleon interaction models in p-3He elastic scattering at low energies. In particular, 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 harmonics technique and the results are compared with available experimental data. We have found that the inclusion of either one of the other force model improves the agreement with the experimental data, in particular for the proton vector analyzing power.Comment: 4 pages, 3 figure

Bakamjian-Thomas mass operator for the few-nucleon system from chiral dynamics

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 versio

Chiral order and fluctuations in multi-flavour QCD

Multi-flavour (N_f>=3) Chiral Perturbation Theory (ChPT) may exhibit instabilities due to vacuum fluctuations of sea q-bar q pairs. Keeping the fluctuations small would require a very precise fine-tuning of the low-energy constants L_4 and L_6 to L_4[crit](M_rho) = - 0.51 * 10^(-3), and L_6[crit](M_rho) = - 0.26 * 10^(-3). A small deviation from these critical values -- like the one suggested by the phenomenology of OZI-rule violation in the scalar channel -- is amplified by huge numerical factors inducing large effects of vacuum fluctuations. This would lead in particular to a strong N_f-dependence of chiral symmetry breaking and a suppression of multi-flavour chiral order parameters. A simple resummation is shown to cure the instability of N_f>=3 ChPT, but it modifies the standard expressions of some O(p^2) and O(p^4) low-energy parameters in terms of observables. On the other hand, for r=m_s/m > 15, the two-flavour condensate is not suppressed, due to the contribution induced by massive vacuum s-bar s pairs. Thanks to the latter, the standard two-flavour ChPT is protected from multi-flavour instabilities and could provide a well-defined expansion scheme in powers of non-strange quark masses.Comment: Published versio

The two-nucleon electromagnetic charge operator in chiral effective field theory (χ\chiEFT) up to one loop

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 figure

Electromagnetic Structure and Reactions of Few-Nucleon Systems in χ\chiEFT

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 Physic

Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory

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.Comment: 5 pages, 3 figure