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

Precursor of Color Superconductivity in Hot Quark Matter

We investigate possible precursory phenomena of color superconductivity in quark matter at finite temperature T with use of a simple Nambu-Jona-Lasinio model. It is found that the fluctuating pair field exists with a prominent strength even well above the critical temperature T_c. We show that the collective pair field has a complex energy located in the second Riemann sheet, which approaches the origin as T is lowered to T_c. We discuss the possible relevance of the precursor to the observables to be detected in heavy ion collisions.Comment: 5 pages, 3 figures, version to appear in Phys. Rev. D. Discussions are enlarged on the physical origin of the large fluctuation of the pair field and its phenomenological consequences. References are adde

Spin 3/2 Penta-quarks in anisotropic lattice QCD

A high-precision mass measurement for the pentaquark (5Q) Theta^+ in J^P=3/2^{\pm} channel is performed in anisotropic quenched lattice QCD using a large number of gauge configurations as N_{conf}=1000. We employ the standard Wilson gauge action at beta=5.75 and the O(a) improved Wilson (clover) quark action with kappa=0.1210(0.0010)0.1240 on a 12^3 \times 96 lattice with the renormalized anisotropy as a_s/a_t = 4. The Rarita-Schwinger formalism is adopted for the interpolating fields. Several types of the interpolating fields with isospin I=0 are examined such as (a) the NK^*-type, (b) the (color-)twisted NK^*-type, (c) a diquark-type. The chiral extrapolation leads to only massive states, i.e., m_{5Q} \simeq 2.1-2.2 GeV in J^P=3/2^- channel, and m_{5Q} = 2.4-2.6 GeV in J^P=3/2^+ channel. The analysis with the hybrid boundary condition(HBC) is performed to investigate whether these states are compact 5Q resonances or not. No low-lying compact 5Q resonance states are found below 2.1GeV.Comment: 15 pages, 6 figures, 4 table

Chiral and Color-superconducting Phase Transitions with Vector Interaction in a Simple Model (Addenda)

In the preceding paper(Prog.Theor.Phys.108(2002)929 or hep-ph/0207255), we have shown that the critical line of the first order chiral transition of QCD can have two endpoints. In this addendum, we elucidate the mechanism to realize the two-endpoint structure in the QCD phase diagram and argue the robustness for the appearance of such an interesting phase structure

Upper Bound on the region of Separable States near the Maximally Mixed State

A lower bound on the amount of noise that must be added to a GHZ-like entangled state to make it separable (also called the random robustness) is found using the transposition condition. The bound is applicable to arbitrary numbers of subsystems, and dimensions of Hilbert space, and is shown to be exact for qubits. The new bound is compared to previous such bounds on this quantity, and found to be stronger in all cases. It implies that increasing the number of subsystems, rather than increasing their Hilbert space dimension is a more effective way of increasing entanglement. An explicit decomposition into an ensemble of separable states, when the state is not entangled,is given for the case of qubits.Comment: 2 figures. accepted J. Opt. B: Quantum Semiclass. Opt. (2000