Exploring the light-quark interaction

Two basic motivations for an upgraded JLab facility are the needs: to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking (DCSB); and to understand nucleon structure and spectroscopy in terms of QCD's elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson-Schwinger equation perspective on this effort with numerous illustrations, amongst them: an interpretation of string-breaking; a symmetry-preserving truncation for mesons; the nucleon's strangeness σ-term; and the neutron's charge distribution.     

Origin of three-body resonances

We expose the relation between the properties of the three-body continuum states and their two-body subsystems. These properties refer to their bound and virtual states and resonances, all defined as poles of the S-matrix. For one infinitely heavy core and two non-interacting light particles, the complex energies of the three-body poles are the sum of the two two-body complex pole-energies. These generic relations are modified by center-of-mass effects which alone can produce a Borromean system. We show how the three-body states evolve in ⁶He, ⁶Li, and ⁶Be when the nucleon-nucleon interaction is continuously switched on. The schematic model is able to reproduce the main properties in their spectra. Realistic calculations for these nuclei are shown in detail for comparison. The implications of a core with non-zero spin are investigated and illustrated for ¹⁷Ne ( ¹⁵O + p + p). Dimensionless units allow predictions for systems of different scales.     

Electron-molecule and atom-molecule scattering within the few-body approximation

A quantum theory of few-body scattering based on the Faddeev-Yakubovsky equations is applied to the calculation of cross sections of electron and atom scattering by diatomic molecules in specified excited rovibrational states. The results of the calculations are compared with the available experimental data and other calculations.     

Elastic cross sections of 1s-muonic atoms at low energies in non-adiabatic approach

The low-energy elastic cross-section in collisions of a muonic atom with the hydrogen isotope is investigated, employing a new wave function (trial) and using the coordinate-space Faddeev–Hahn model. The wave function includes non-adiabatic terms. Our results of s–wave cross-sections are given, at the tμ(1s) + d scattering. Calculated cross-sections are in good accord with the results published by Chiccoli et al., while having no good agreement with other recent reports.     

Three-body model for neutron-halo nuclei

The neutron-halo nuclei, ¹¹Li, ¹⁴Be, and ¹⁷B, are studied in the three-body model. The Yukawa interaction is used to describe the interaction of the two-body subsystem. For given parameters of the two-body interaction, the properties of these neutron-halo nuclei are calculated with the Faddeev equations and the results are compared with those in the variational method. It is shown that the method of the Faddeev equations is more accurate. Then the dependencies of the two- and three-body energies on the parameters are studied. We find numerically that two- and three-body correlations differ greatly from each other with the variation of the intrinsic force range.     

Exploring the light-quark interaction

Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and spectroscopy in terms of QCD＇s elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson- Schwinger equation perspective on this effort with numerous illustrations, amongst them： an interpretation of string~breaking; a symmetry-preserving truncation for mesons; the nucleon＇s strangeness σ-term; and the neutron＇s charge distribution.     

Global solutions of the evolutionary Faddeev model with small initial data

We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space ℝ¹⁺ⁿ to the unit sphere $ \mathbb{S} $ \mathbb{S} ², which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.     

Revisit of the Faddeev Model in Dimension Two

The Faddeev model is a fundamental model in relativistic quantum ?eld theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and semi-linear non-linearities, which is particularly challenging in two space dimensions. A key feature of the system is that there exist undi?erentiated wave components in the non-linearities, which somehow causes extra di?culties. Nevertheless, the Cauchy problem in two space dimenions was tackled by Lei-Lin-Zhou (2011) with small, regular, and compactly supported initial data, using Klainerman’s vector ?eld method enhanced by a novel angular-radial anisotropic technique. In the present paper, the authors revisit the Faddeev model and remove the compactness assumptions on the initial data by Lei-Lin-Zhou (2011). The proof relies on an improved L2 norm estimate of the wave components in Theorem 3.1 and a decomposition technique for non-linearities of divergence form.