We perform the first study for the static penta-quark (5Q) potential in lattice QCD with $\beta$=6.0 and $16^3 \times 32$ at the quenched level. Accurate results of the 5Q potential are extracted from the 5Q Wilson loop using the smearing method, which enhances the ground-state component. The tetra-quark potential for the $\rm QQ$-$\rm {\bar Q}{\bar Q}$ system is also studied in lattice QCD. The multi-quark potentials are found to be well described as a sum of the one-gluon-exchange Coulomb term and the multi-Y linear confinement term based on the flux-tube picture.

Anti-decuplet penta-quark baryon is studied with the quenched anisotropic lattice QCD for accurate measurement of the correlator. Both the positive and negative parity states are studied using a non-NK type interpolating field with I=0 and J=1/2. After the chiral extrapolation, the lowest positive parity state is found at m_{Theta} \simeq 2.25 GeV, which is too massive to be identified with the experimentally observed Theta^+(1540). The lowest negative parity state is found at m_{Theta}\simeq 1.75 GeV, which is rather close to the empirical value. To confirm that this state is a compact 5Q resonance, a new method with ``hybrid boundary condition (HBC)'' is proposed. The HBC analysis shows that the observed state in the negative parity channel is an NK scattering state.

The penta-quark(5Q) Theta^+(1540) is studied in anisotropic lattice QCD with renormalized anisotropy a_s/a_t=4 for a high-precision measurement. Both the positive and the negative parity 5Q baryons are studied using a non-NK type interpolating field with I=0 and J=1/2. After the chiral extrapolation, the lowest positive parity state is found at m_{Theta}\simeq 2.25 GeV, which is too heavy to be identified with Theta^+(1540). In the negative parity channel, the lowest energy state is found at m_{Theta}\simeq 1.75 GeV. Although it is rather close to the empirical value, it is considered to be an NK scattering state rather than a localized resonance state.

We evaluate the static $qqqq\bar{q}$ potential in the quenched theory at $\beta=5.8$ and $\beta=6.0$ on a lattice of size $16^3\times 32$. The mass and density-density correlator for the $\Theta^+$ is investigated in the quenched theory at $\beta=6.0$ on lattices of size $16^3\times 32$, $24^3\times 32$ and $32^3 \times 64$.

The penta-quark(5Q) baryon is studied in anisotropic quenched lattice QCD with renormalized anisotropy a_s/a_t=4 for a high-precision mass measurement. The standard Wilson action at beta=5.75 and the O(a) improved Wilson quark action with kappa=0.1210(0.0010)0.1240 are employed on a 12^3 \times 96 lattice. Contribution of excited states is suppressed by using a smeared source. We investigate both the positive- and negative-parity 5Q baryons with I=0 and spin J=1/2 using a non-NK-type interpolating field. After chiral extrapolation, the lowest positive-parity state is found to have a mass, m_{Theta}=2.25 GeV, which is much heavier than the experimentally observed Theta^+(1540). The lowest negative-parity 5Q appears at m_{Theta}=1.75 GeV, which is near the s-wave NK threshold. To distinguish spatially-localized 5Q resonances from NK scattering states, we propose a new general method imposing a ``Hybrid Boundary Condition (HBC)'', where the NK threshold is artificially raised without affecting compact five-quark states. The study using the HBC method shows that the negative-parity state observed on the lattice is not a compact 5Q but an s-wave NK-scattering state.

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 $\Lambda$(1405), which can be an exotic hadron as the $N \bar K$ 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 $\Lambda$(1405) cannot be identified as the three-quark state, which supports the possibility of the molecular-state picture of the $\Lambda$(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.

We evaluate the static $qq\bar{q}\bar{q}$ and $qqqq\bar{q}$ potentials in the quenched theory at $\beta=5.8$ and $\beta=6.0$ on a lattice of size $16^3\times 32$. We compare the static potentials to the sum of two meson potentials for the tetraquark system and to the sum of the baryonic and mesonic potentials for the pentaquark state, as well as, with the confining potential obtained in the strong coupling expansion.

The static penta-quark (5Q) potential $V_{\rm 5Q}$ is studied in SU(3) lattice QCD with $16^3\times 32$ and $\beta$=6.0 at the quenched level. From the 5Q Wilson loop, $V_{\rm 5Q}$ is calculated in a gauge-invariant manner, with the smearing method to enhance the ground-state component. $V_{\rm 5Q}$ is well described by the OGE plus multi-Y Ansatz: a sum of the OGE Coulomb term and the multi-Y-type linear term proportional to the minimal total length of the flux-tube linking the five quarks. Comparing with ${\rm Q \bar Q}$ and 3Q potentials, we find a universality of the string tension, $\sigma_{\rm Q \bar Q} \simeq \sigma_{\rm 3Q} \simeq \sigma_{\rm 5Q}$, and the OGE result for Coulomb coefficients.

We present a quenched lattice QCD calculation of spin-1/2 five-quark states with $uudd\bar{s}$ quark content for both positive and negative parities. We do not observe any bound pentaquark state in these channels for either I = 0 or I =1. The states we found are consistent with KN scattering states which are checked to exhibit the expected volume dependence of the spectral weight. The results are based on overlap-fermion propagators on two lattices, 12^3 x 28 and 16^3 x 28, with the same lattice spacing of 0.2 fm, and pion mass as low as ~ 180 MeV.

We investigate the mass spectrum of pentaquark baryons with anti-charm quark, in quenched lattice QCD with exact chiral symmetry. By chiral extrapolation to $ m_\pi = 135 $ MeV, we determine the masses of the lowest lying states of the antisextet (J^\Pi = 1/2^+) and the triplet ($J^\Pi=1/2^-$), in the isospin limit ($m_u=m_d$). The masses of the antisextet are: $2977(109)$ MeV for the iso-singlet $\Theta_c([ud][ud]\bar c)$; $3180(69)$ MeV for the iso-doublet $\{N_c^{-}([ud][ds] \bar c), N_c^0([ud][us] \bar c) \}$; and $3650(95)$ MeV for the iso-triplet $\{\Xi_{5c}^{--}([ds][ds]\bar c), \Xi_{5c}^{-}([ds][us]_{+} \bar c), \Xi_{5c}^{0}([us][us]\bar c) \} $, all above the thresholds for strong decays. For the triplet, the mass of the iso-doublet $ \{T_c^{-}([ud][ds] \bar c), T_c^{0}([ud][us] \bar c) \}$ is $2785(46)$ MeV, below the threshold for the strong decays.

We investigate the mass spectrum of pentaquark baryons in quenched lattice QCD with exact chiral symmetry. Using interpolating operators based on the diquark-diquark-antiquark picture in the Jaffe-Wilzcek model, we measure time correlation functions for 70 gauge configurations generated with Wilson gauge action at $ \beta = 6.1 $ on the $ 20^3 \times 40 $ lattice, and extract the masses of even and odd parity states respectively. With the pion decay constant ($ f_\pi a $) extracted from the pion correlation function, and the experimental input $ f_\pi = 132 $ MeV, we determine the inverse lattice spacing $ a^{-1} = 2.21(3) $ GeV. By chiral (linear) extrapolation to the pion mass $ m_\pi = 135 $ MeV, we determine the masses of lowest lying pentaquark baryons ($J^\Pi = 1/2^+$): $ m_{N}([u d] [u d] \bar d)= 1460(51) $ MeV, $ m_{\Theta}([ud][ud]\bar s)= 1539(95)$ MeV, and $ m_{\Xi}([ds][ds] \bar u) = 1826(87) $ MeV. Our results suggest that the parity of $ \Theta^{+} (1540) $ and $ \Xi^{--}_{3/2}(1860) $ is even, and $ N([ud][ud]\bar d) $ can be identified with the Roper resonance $ N(1440) P_{11} $.

We propose $S=+1$ baryon interpolating operators, which are based on an exotic description of the antidecuplet baryon like diquark-diqaurk-antiquark. Using one of the new operators, the mass spectrum of the spin-1/2 pentaquark states is calculated in quenched lattice QCD at $\beta=6/g^2=6.2$ on a $32^3\times48$ lattice. It is found that the $J^P$ assignment of the lowest $\Theta(uudd \bar s)$ state is most likely $(1/2)^-$. We have also calculated the mass of the charm analog of the $\Theta$ and find that the $\Theta_c(uudd \bar c)$ state lies much higher than the $DN$ threshold, in contrast to several model predictions.

We study spin 1/2 isoscalar and isovector candidates in both parity channels for the recently discovered \Theta^+(1540) pentaquark particle in quenched lattice QCD. Our conservative analysis takes into account all possible uncertainties, such as statistical, finite size and quenching errors when performing the chiral and continuum extrapolations. The lowest mass that we find in the I^P=0^+ channel is in complete agreement with the experimental value of the \Theta^+ mass. On the other hand, the lowest mass state in the opposite parity I^P=0^- channel is much higher. Thus based on our numerical experiment the negative parity is on the 5.5\sigma level ruled out prior to accerelator experiments.

We present our final results for the mass of the six quark flavor singlet state (J^P=0^+, S=-2) called H dibaryon, which would be the lightest possible strangelet in the context of strange quark matter. The calculations are performed in quenched QCD on (8-24)^3 x 30 lattices with the (1,2) Symanzik improved gauge action and the clover fermion action. Furthermore the fuzzing technique for the fermion fields and smearing of the gauge fields is applied in order to enhance the overlap with the ground state. Depending on the lattice size we observe an H mass slightly above or comparable with the \Lambda\Lambda threshold for strong decay. Therefore a bound H dibaryon state seemed to be ruled out by our simulation.

We present preliminary results for the mass of the 6q flavor-singlet state ($J^P=0^+$, $S=-2$) called H-dibaryon, calculated in quenched QCD on $16^3$x30 and $24^3$x30 lattices with improved gauge and fermion actions (Symanzik improvement, Clover action). For both lattice sizes we applied the fuzzing technique to enhance the overlap with the ground state. We observe a H-mass above the $\Lambda\Lambda$ threshold for strong decay. The difference in mass, $m_H - 2m_\Lambda$, increases with increasing lattice size.

The potential between static-light mesons forming a meson-meson or a meson-antimeson system is calculated in quenched and unquenched SU(3) gauge theory. We use the Sheikholeslami-Wohlert action and statistical estimators of light quark propagators with maximal variance reduction. The dependence of the potentials on the light quark spin and isospin and the effect of meson exchange is investigated. Our main motivation is exploration of bound states of two mesons and string breaking. The latter also involves the two-quark potential and the correlation between two-quark and two-meson states.

By comparing lattice data for the two heavy-light meson system (Q^2 qbar^2) with a standard many-body approach employing only interquark potentials, it is shown that the use of unmodified two-quark potentials leads to a gross overestimate of the binding energy.

Recent lattice calculations on the interaction energy of two heavy-light mesons (Q^2\bar{q}^2) are interpreted in terms of the potential of the corresponding single heavy-light meson (Q\bar{q}). This model leads to a large overestimate of the binding compared with the lattice data -- unless the basic Q\bar{q} potential is modified to become a four-quark potential.

I review recent Lattice results. In particular, the confinement mechanism and string breaking, glueballs and hybrid mesons as well as light hadron spectroscopy are discussed.

The potential between two heavy-light mesons as a function of the heavy quark separation is calculated in quenched SU(3) lattice QCD. We study the case of heavy-light mesons with a static heavy quark and light quarks of mass close to the strange quark mass. We explore the case of light quarks with the same and with different flavours, classified according to the light quark isospin. We evaluate the appropriate light quark exchange contributions and explore the spin-dependence of the interaction. Comparison is made with meson exchange.

In order to understand the binding of four static quarks, flux distributions corresponding to these binding energies are studied in quenched SU(2) and also related to a model for the energies. The potential relevant to string breaking between two heavy-light mesons is measured in quenched SU(3) using stochastic estimates of light quark propagators with the Sheikholeslami-Wohlert action.

The mass of the lowest spin-zero, strangeness-$(-2)$ flavor singlet state in the dibaryon sector has been calculated in quenched QCD on $16^3\times32$ and $24^3\times32$ lattices at $\beta=5.85$ to study whether the energy of the proposed $H$ dibaryon is near or below the $\Lambda\Lambda$ threshold. Preliminary results indicate that finite lattice volume artifacts overestimate the binding, and that on the largest lattice $m_H$ is of the order of $100\MeV$ above the $\Lambda\Lambda$ threshold.

Energies of four-quark systems with the tetrahedral geometry measured by the static quenched SU(2) lattice Monte Carlo method are analyzed by parametrizing the gluon overlap factor in the form exp(-[bs EA+{\sqrt bs}FP]) where A and P are the area and the perimeter defined mainly by the positions of the four quarks, bs is the string constant in the 2-quark potentials and E, F are constants.

An adiabatic approximation is used to derive the binding potential between two heavy-light mesons in quenched SU(2)-colour lattice QCD. Analysis of the meson-meson system shows that the potential is attractive at short- and medium-range. The numerical data is consistent with the Yukawa model of pion exchange