Theoretical Overview of the Pentaquark Baryons

A review is given of the theoretical ideas concerning the mysterious pentaquark baryons proposed during the first year after its discovery. We focus on the difficulties involved with the constituent quark models and the discrepancy between the QCD predictions and most of the phenomenological models.Comment: Review based on the talk given at the YITP Workshop on ``Multi-quark Hadrons; Four, Five and More?'', held on Feb. 17-19, 2004. To be published in Progress of Theoretical Physics as an invited pape

Nuclear G-Matrix Elements from Nonlocal Potentials

We study effects of nonlocality in the nuclear force on the G-matrix elements for finite nuclei. Nuclear G-matrix elements for \O16 are calculated in the harmonic oscillator basis from a nonlocal potential which models quark exchange effects between two nucleons. We employ a simple form of potential that gives the same phase shifts as a realistic local nucleon potential. The G-matrix elements calculated from the nonlocal potential show moderate increase in repulsion from those derived from the local potential.Comment: 11 page, LaTeX, 2 PS figures, uses epsf.st

Spin Content of Lambda in QCD Sum Rules

We calculate the isoscalar axial-vector coupling constants of the Lambda hyperon using the method of QCD sum rules. A determination of these coupling constants reveals the individual contributions of the u, d and the s quarks to the spin content of Lambda. Our results for the light-quark contributions are in agreement with those from experiment assuming flavor SU(3). We also find that the flavor-SU(3)-breaking effects are small and the contributions from the u and the d quarks to the Lambda polarization are negatively polarized as in the flavor-SU(3) limit.Comment: 6 pages, 2 figure

Operator product expansion and the short distance behavior of 3-flavor baryon potentials

The short distance behavior of baryon-baryon potentials defined through Nambu-Bethe-Salpeter wave functions is investigated using the operator product expansion. In a previous analysis of the nucleon-nucleon case, corresponding to the SU(3) channels $27_s$ and $\overline{10}_a$, we argued that the potentials have a repulsive core. A new feature occurs for the case of baryons made up of three flavors: manifestly asymptotically attractive potentials appear in the singlet and octet channels. Attraction in the singlet channel was first indicated by quark model considerations, and recently been found in numerical lattice simulations. The latter have however not yet revealed asymptotic attraction in the octet channels; we give a speculative explanation for this apparent discrepancy.Comment: 11 pages, 2 figure

K→2πK \to 2 \pi Decay in the Nambu-Jona-Lasinio Model

We study the $K \to 2 \pi$ decays using the $U_L(3) \times U_R(3)$ version of the Nambu-Jona-Lasinio model with the effective $\Delta S = 1$ nonleptonic weak interaction. The $\Delta I = {3/2}$ amplitude is in reasonable agreement with experimental data. On the other hand, the calculated $\Delta I = {1/2}$ amplitudes strongly depend on the mass of the low-lying scalar-isoscalar $\sigma$ meson, and therefore give a strong constraint on the parameters of the model.Comment: 10 pages, 3 Postscript figures, Talk given at YITP Workshp: From Hadronic Matter to Quark Matter: Evolving View of Hadronic Matter, Kyoto, Japan, Oct. 30-Nov. 1, 1994, to be published in Prog. Theor. Phys. Supp

η\eta-Meson Decays and Strong UA(1)U_A(1) Breaking in the Three-Flavor Nambu-Jona-Lasinio Model

We study the $\eta \to \gamma \gamma$ and $\eta \to \pi^0 \gamma \gamma$ decays using an extended three-flavor Nambu-Jona-Lasinio model that includes the 't~Hooft instanton induced interaction. We find that the $\eta$-meson mass, the $\eta \to \gamma \gamma$ decay width and the $\eta \to \pi^0 \gamma \gamma$ decay width are in good agreement with the experimental values when the $U_{A}(1)$ breaking is strong and the flavor $SU(3)$ singlet-octet mixing angle $\theta$ is about zero. The effects of the $U_A(1)$ breaking on the baryon number one and two systems are also studied.Comment: 12 pages, LaTeX, 2 eps figures, Talk given at the Joint Japan-Australia Workshop on Quarks, Hadrons and Nuclei, Adelaide, Australia, Nov. 15-24, 199

Negative Parity Baryons in the QCD Sum Rule

Masses and couplings of the negative parity excited baryons are studied in the QCD sum rule. Separation of the negative-parity spectrum is proposed and is applied to the flavor octet and singlet baryons. We find that the quark condensate is responsible for the mass splitting of the ground and the negative-parity excited states. This is expected from the chiral symmetry and supports the idea that the negative-parity baryon forms a parity doublet with the ground state. The meson-baryon coupling constants are also computed for the excited states in the QCD sum rule. It is found that the \pi NN^* coupling vanishes in the chiral limit.Comment: 13pp, LaTeX, 1 EPS figure, uses epsf.sty, Talk given by M.O. at CEBAF/INT workshop "N* physics", Seattle, September (1996), to appear in the proceeding