SU(3) lattice QCD study for octet and decuplet baryon spectra

The spectra of octet and decuplet baryons are studied using SU(3) lattice QCD at the quenched level. As an implementation to reduce the statistical fluctuation, we employ the anisotropic lattice with $O(a)$ improved quark action. In relation to $\Lambda(1405)$, we measure also the mass of the SU(3) flavor-singlet negative-parity baryon, which is described as a three quark state in the quenched lattice QCD, and its lowest mass is measured about 1.6 GeV. Since the experimentally observed negative-parity baryon $\Lambda(1405)$ is much lighter than 1.6 GeV, $\Lambda(1405)$ may include a large component of a $N \bar K$ bound state rather than the three quark state. The mass splitting between the octet and the decuplet baryons are also discussed in terms of the current quark mass.Comment: 8 pages, 3 figures, proceeding of "International Symposium on Hadron and Nuclei" at Yonsei Univ., Seoul, Korea 20-22 Feb. 200

Geometric and combinatorial realizations of crystal graphs

For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For affine type A, we extend the Young wall construction to arbitrary level, describing a combinatorial realization of the crystals in terms of new objects which we call Young pyramids.Comment: 34 pages, 17 figures; v2: minor typos corrected; v3: corrections to section 8; v4: minor typos correcte

Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: We construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial models for each highest weight crystal. Applying this construction to the crystal of the fundamental representation recovers a family of combinatorial realizations recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as a generalization to higher level. We also discuss a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some references; v3: many small correction

Inverted Hybrid Inflation as a solution to gravitino problems in Gravity Mediation

It was recently found that the decay of inflaton and the SUSY breaking field produces many gravitinos in the gravity mediation scenario. These discoveries led to an exclusion of many inflation models such as chaotic, (smooth) hybrid, topological and new inflation models. Under these circumstances we searched for a successful inflation model and found that the ``inverted'' hybrid inflation models can solve the gravitino overproduction problem by their distinctive shape of the potential. Furthermore, we found that this inflation model simultaneously can explain the observed baryon asymmetry through the non-thermal leptogenesis and is consistent with the WMAP results, that is, $n_s=0.951^{+0.015}_{-0.019}$ and the negligible tensor to scalar ratio.Comment: 23 pages, 2 figures in

Current-feedback-stabilized laser system for quantum simulation experiments using Yb clock transition at 578 nm

We developed a laser system for the spectroscopy of the clock transition in ytterbium (Yb) atoms at 578 nm based on an interference-filter stabilized external-cavity diode laser (IFDL) emitting at 1156 nm. Owing to the improved frequency-to-current response of the laser-diode chip and the less sensitivity of the IFDL to mechanical perturbations, we succeeded in stabilizing the frequency to a high-finesse ultra-low-expansion glass cavity with a simple current feedback system. Using this laser system, we performed high-resolution clock spectroscopy of Yb and found that the linewidth of the stabilized laser was less than 320 Hz.Comment: 5 pages, 7 figure

Negative-Parity Baryons in Quenched Anisotropic Lattice QCD

We study negative-parity baryon spectra in quenched anisotropic lattice QCD. The negative-parity baryons are measured as the parity partner of the ground-state baryons. In addition to the flavor octet and decuplet baryons, we pay much attention to the flavor-singlet negative-parity baryon as a three-quark state and compare it with the Lambda(1405) baryon. Numerical results of the flavor octet and decuplet negative-parity baryon masses are close to experimental values of lowest-lying negative-parity baryons, while the flavor-singlet baryon is much heavier than Lambda(1405). This indicates that the Lambda(1405) would be a multi-quark state such as the N-Kbar molecule rather than the flavor-singlet 3 quark state.Comment: 4 pages, 4 figs. Talk given at 16th International Conference on Particles and Nuclei (PANIC 02), Osaka, Japan, 30 Sep - 4 Oct 200