Hyperspherical harmonic study of identical-flavor four-quark systems

We present an exact method based on a hyperspherical harmonic expansion to study systems made of quarks and antiquarks of the same flavor. Our formalism reproduces and improves the results obtained with variational approaches. This analysis shows that identical-flavor four-quark systems with non-exotic 2(++) quantum numbers may be bound independently of the quark mass. 0(+-) and 1(+-) states become attractive only for larger quarks masses

Hyperspherical harmonic formalism for tetraquarks

We present a generalization of the hyperspherical harmonic formalism to study systems made of quarks and antiquarks of the same flavor. This generalization is based on the symmetrization of the $N-$body wave function with respect to the symmetric group using the Barnea and Novoselsky algorithm. Our analysis shows that four-quark systems with non-exotic $2^{++}$ quantum numbers may be bound independently of the quark mass. $0^{+-}$ and $1^{+-}$ states become attractive only for larger quarks masses.Comment: 4 pages, to appear in the proceedings of 9th International Workshop on Meson Production, Properties and Interaction (Meson2006), Kracow (Poland), 9 - 13 June 200

Few-body calculations of η\eta-nuclear quasibound states

We report on precise hyperspherical-basis calculations of $\eta NN$ and $\eta NNN$ quasibound states, using energy dependent $\eta N$ interaction potentials derived from coupled-channel models of the $S_{11}$ $N^{\ast}(1535)$ nucleon resonance. The $\eta N$ attraction generated in these models is too weak to generate a two-body bound state. No $\eta NN$ bound-state solution was found in our calculations in models where Re $a_{\eta N}\lesssim 1$ fm, with $a_{\eta N}$ the $\eta N$ scattering length, covering thereby the majority of $N^{\ast}(1535)$ resonance models. A near-threshold $\eta NNN$ bound-state solution, with $\eta$ separation energy of less than 1 MeV and width of about 15 MeV, was obtained in the 2005 Green-Wycech model where Re $a_{\eta N}\approx 1$ fm. The role of handling self consistently the subthreshold $\eta N$ interaction is carefully studied.Comment: a second footnote added in v2, matching published versio

Longitudinal response function of 4He with a realistic force

The longitudinal response function of 4He is calculated with the Argonne V18 potential. The comparison with experiment suggests the need of a three-body force. When adding the Urbana IX three-body potential in the calculation of the lower longitudinal multipoles, the total strength is suppressed in the quasi-elastic peak, towards the trend of the experimental data.Comment: 3 pages, 3 figures, proceedings of the 20th European Conference on Few-Body Problems in Physics (EFB20

Onset of η\eta-nuclear binding in a pionless EFT approach

$\eta NNN$ and $\eta NNNN$ bound states are explored in stochastic variational method (SVM) calculations within a pionless effective field theory (EFT) approach at leading order. The theoretical input consists of regulated $NN$ and $NNN$ contact terms, and a regulated energy dependent $\eta N$ contact term derived from coupled-channel models of the $N^{\ast}(1535)$ nucleon resonance plus a regulated $\eta NN$ contact term. A self consistency procedure is applied to deal with the energy dependence of the $\eta N$ subthreshold input, resulting in a weak dependence of the calculated $\eta$-nuclear binding energies on the EFT regulator. It is found, in terms of the $\eta N$ scattering length $a_{\eta N}$, that the onset of binding \eta\,^3He requires a minimal value of Re$\,a_{\eta N}$ close to 1 fm, yielding then a few MeV $\eta$ binding in \eta\,^4He. The onset of binding \eta\,^4He requires a lower value of Re$\,a_{\eta N}$, but exceeding 0.7 fm.Comment: v4 consists of the published Physics Letters B version [31] plus Erratum ([30], Appendix A here); main results and conclusions remain intac

Theory of inter-edge superexchange in zigzag edge magnetism

A graphene nanoribbon with zigzag edges has a gapped magnetic ground state with an antiferromagnetic inter-edge superexchange interaction. We present a theory based on asymptotic properties of the Dirac-model ribbon wavefunction which predicts $W^{-2}$ and $W^{-1}$ ribbon-width dependencies for the superexchange interaction strength and the charge gap respectively. We find that, unlike the case of conventional atomic scale superexchange, opposite spin-orientations on opposite edges of the ribbon are favored by both kinetic and interaction energies.Comment: 4 pages 8 figure