Possible Hadronic Molecule Λ(1405) and Thermal Glueballs in SU(3) Lattice QCD

We aim to construct quark hadron physics based on QCD. First, using lattice QCD, we study mass spectra of positive-parity and negative-parity baryons in the octet, the decuplet and the singlet representations of the SU(3) flavor. In particular, we consider the lightest negative-parity baryon, the Λ(1405), which can be an exotic hadron as theNK̄ molecular state or the flavor-singlet three-quark state. We investigate the negative-parity flavor-singlet three-quark state in lattice QCD using the quenched approximation, where the dynamical quark-anitiquark pair creation is absent and no mixing occurs between the three-quark and the five-quark states. Our lattice QCD analysis suggests that the flavor-singlet three-quark state is so heavy that the Λ(1405) cannot be identified as the three-quark state, which supports the possibility of the molecular-state picture of the Λ(1405). Second, we study thermal properties of the scalar glueball in an anisotropic lattice QCD, and find about 300 MeV mass reduction near the QCD critical temperature from the pole-mass analysis. Finally, we study the three-quark potential, which is responsible to the baryon properties. The detailed lattice QCD analysis for the 3Q potential indicates the Y-type flux-tube formation linking the three quarks. 1. Lattice QCD study for Λ(1405) Among a lot of hadrons, the Λ(1405) is a very special interesting hadron. In spite of the strange baryon, the Λ(1405) is the lightest negative-parity baryon. In fact, the Λ(1405) is much lighter than the low-lying non-strange negative-parity baryons, the N(1520) with J = 3 2 − and the N(1535) with J = 1 2 − . Moreover, there are two interesting physical interpretations on the Λ(1405). • In the quark-model framework, the Λ(1405) is described as the flavor-singlet threequark system. (cf. The H-dibaryon is also a flavor-singlet candidate.) • As another interpretation, the Λ(1405) is an interesting candidate of the hadronic molecule such as the NK̄ bound state with a large binding energy about 30MeV. (cf. For deutrons, the binding energy is about 2.2MeV.) In the valence picture, the NK̄ hadronic molecule is described as qqq-qq̄, and hence we call this state as the “5-quark (5Q) state” for the simple notation. Of course, in the real