Exploring Baryon Chiral Multiplets

The full QCD chiral symmetry algebra has predictive consequences at low energies. I discuss the ground-state chiral multiplet involving the light baryons and emphasize the special role of the Roper resonance.Comment: 10 pages. Invited plenary talk at NSTAR 2002, Pittsburgh, PA, 9-12 October 200

Nucleon-Nucleon Scattering in the 1/N Expansion

The nucleon-nucleon 3S1-3D1 coupled-channel problem is solved analytically to leading order in a joint expansion in the quark masses and in 1/N. An approximate expression is derived for the 3S1 scattering length in the large-N limit, and the large-N behavior of the deuteron is discussed.Comment: 10 pages, Invited talk, The Phenomenology of Large-N_c QCD, to be published Proceedings of the Institute of Nuclear Theor

Ground state energy of the interacting Bose gas in two dimensions: an explicit construction

The isotropic scattering phase shift is calculated for non-relativistic bosons interacting at low energies via an arbitrary finite-range potential in d spacetime dimensions. Scattering on a (d-1)-dimensional torus is then considered, and the eigenvalue equation relating the energy levels on the torus to the scattering phase shift is derived. With this technology in hand, and focusing on the case of two spatial dimensions, a perturbative expansion is developed for the ground-state energy of N identical bosons which interact via an arbitrary finite-range potential in a finite area. The leading non-universal effects due to range corrections and three-body forces are included. It is then shown that the thermodynamic limit of the ground-state energy in a finite area can be taken in closed form to obtain the energy-per-particle in the low-density expansion, by explicitly summing the parts of the finite-area energy that diverge with powers of N. The leading and subleading finite-size corrections to the thermodynamic limit equation-of-state are also computed. Closed-form results --some well-known, others perhaps not-- for two-dimensional lattice sums are included in an appendix.Comment: 24 pages, 2 figure

Status of Effective Field Theory of NN Scattering

I review recent progress in developing a systematic power counting scheme for scattering processes involving more than one nucleon.Comment: 9 pages LaTeX and appb.sty, 2 figures (uses epsf); Talk given at the Workshop on 'The Structure of Mesons, Baryons and Nuclei', Cracow, May 1998, in honor of J. Speth's 60th birthday, to be published in Acta Physica Polonica

Stable Pentaquarks from Strange Chiral Multiplets

The assumption of strong diquark correlations in the QCD spectrum suggests flavor multiplets of hadrons that are degenerate in the chiral limit. Generally it would be unnatural for there to be degeneracy in the hadron spectrum that is not protected by a QCD symmetry. Here we show --for pentaquarks constructed from diquarks-- that these degeneracies can be naturally protected by the full chiral symmetry of QCD. The resulting chiral multiplet structure recovers the ideally-mixed pentaquark mass spectrum of the diquark model, and interestingly, requires that the axial couplings of the pentaquarks to states outside the degenerate multiplets vanish in the chiral limit. This result suggests that if these hadrons exist, they are stable in the chiral limit and therefore have widths that scale as the fourth power of the kaon mass over the chiral symmetry breaking scale. Natural-size widths are of order a few MeV.Comment: 13 page

Effective-range corrections to the ground-state energy of the weakly-interacting Bose gas in two dimensions

Nonuniversal effects due to leading effective-range corrections are computed for the ground-state energy of the weakly-coupled repulsive Bose gas in two spatial dimensions. Using an effective field theory of contact interactions, these corrections are computed first by considering fluctuations around the mean-field free energy of a system of interacting bosons. This result is then confirmed by an exact calculation in which the energy of a finite number of bosons interacting in a square with period boundary conditions is computed and the thermodynamic limit is explicitly taken.Comment: 5 page