Search

Low-lying $\Lambda$ baryons with spin 1/2 are analyzed in two-flavor lattice QCD. In order to extract two low-lying states for each parity, we construct $2 \times 2$ cross correlators from flavor SU(3) ``octet'' and ``singlet'' baryon operators, and diagonalize them. Two-flavor CP-PACS gauge configurations are employed, which are generated with the renormalization-group improved gauge action and the ${\mathcal O}(a)$-improved quark action. Simulation are performed at three different $\beta$'s, $\beta = 1.80$, 1.95 and 2.10, whose corresponding lattice spacings are $a = 0.2150$, 0.1555 and 0.1076 fm. For each cutoff, we adopt four different hopping parameters, ($\kappa_{\rm val}, \kappa_{\rm sea}$). The corresponding pion masses range from about 500 MeV to 1.1 GeV. The results are extrapolated to the physical quark-mass point. Our results indicate that there are two negative-parity $\Lambda$ states nearly degenerate at around 1.6 GeV, whereas no state as low as $\Lambda (1405)$ is observed. By extracting the flavor components of each state, we find that the lowest (1st-excited) negative-parity state is dominated by flavor-singlet (flavor-octet) component., Comment: Proceedings of a talk given at "New Frontiers in QCD 2010 (NFQCD10)", Kyoto, Japan, 18 January to 19 March, 2010

We evaluate the pseudoscalar-meson octet-baryon coupling constants and the corresponding axial charges in eight channels ($\pi N\N$, $\pi\Sigma\Sigma$, $\pi\Lambda\Sigma$, $K\Lambda N$, $K \Sigma N $, $\pi\Xi\Xi$, $K\Lambda\Xi$ and $K\Sigma\Xi$) in lattice QCD with two flavors of dynamical quarks. The parameter $\alpha\equiv F/(F+D)$ representing the SU(3)-flavor symmetry is computed at each u,d-quark hopping parameter and at the flavor-SU(3) symmetric point where the three quark flavors are degenerate at the physical $s$-quark mass. In particular, we obtain $\alpha=0.395(6)$ at the SU(3) symmetric limit. The quark-mass dependences of the coupling constants are obtained by changing the $u$- and the $d$-quark masses and we find that the SU(3)-flavor symmetry is broken by only a few percent at each quark-mass we employ., Comment: 4 pages, Talk given at HYP-X, September 14-18, 2009, Tokai, Japan

We evaluate interhadron interactions in two-color lattice QCD from Bethe-Salpeter amplitudes on the Euclidean lattice. The simulations are performed in quenched SU(2) QCD with the plaquette gauge action at $\beta = 2.45$ and the Wilson quark action. We concentrate on S-wave scattering states of two scalar diquarks. Evaluating different flavor combinations with various quark masses, we try to find out the ingredients in hadronic interactions. Between two scalar diquarks ($u C\gamma_5 d$, the lightest baryon in SU(2) system), we observe repulsion in short-range region, even though present quark masses are not very light. We define and evaluate the "quark-exchange part" in the interaction, which is induced by adding quark-exchange diagrams, or equivalently, by introducing Pauli blocking among some of quarks. The repulsive force in short-distance region arises only from the "quark-exchange part", and disappears when quark-exchange diagrams are omitted. We find that the strength of repulsion grows in light quark-mass regime and its quark-mass dependence is similar to or slightly stronger than that of the color-magnetic interaction by one-gluon-exchange (OGE) processes. It is qualitatively consistent with the constituent-quark model picture that a color-magnetic interaction among quarks is the origin of repulsion. We also find a universal long-range attractive force, which enters in any flavor channels of two scalar diquarks and whose interaction range and strength are quark-mass independent. The weak quark-mass dependence of interaction ranges in each component implies that meson-exchange contributions are small and subdominant, and the other contributions, {\it ex.} flavor exchange processes, color-Coulomb or color-magnetic interactions, are considered to be predominant, in the quark-mass range we evaluated., Comment: 14 pages, 20 figures

Low-lying $\Lambda$ baryons with spin 1/2 are analyzed in two-flavor unquenched lattice QCD. We construct $2 \times 2$ cross correlators from flavor SU(3) ``octet'' and ``singlet'' baryon operators, and diagonalize them so that we can extract two low-lying states for each parity. The two-flavor CP-PACS gauge configurations are employed, which are generated in the renormalization-group improved gauge action and the ${\mathcal O}(a)$-improved quark action. Simulation are performed at three different $\beta$'s, $\beta = 1.80$, 1.95 and 2.10, whose corresponding lattice spacings are $a = 0.2150$, 0.1555 and 0.1076 fm. For each cutoff, we adopt four different hopping parameters, ($\kappa_{\rm val}, \kappa_{\rm sea}$). The corresponding pion masses range about from 500 MeV to 1.1 GeV. Results indicate that there are two negative-parity $\Lambda$ states nearly degenerate at around 1.6 GeV, while no state as low as $\Lambda (1405)$ is observed. By decomposing the flavor components of each state, we find that the lowest (1st-excited) negative-parity state is dominated by flavor-singlet (flavor-octet) component., Comment: 7pages, 2figures, presented at the "XXVII International Symposium on Lattice Field Theory", July 26-31, 2009, Peking University, Beijing, China

We show the first lattice QCD results on the axial charges $g_A^{N^*N^*}$ of $N^*(1535)$ and $N^*(1650)$. The measurements are performed with two flavors of dynamical quarks employing the renormalization-group improved gauge action at $\beta$=1.95 and the mean-field improved clover quark action with the hopping parameters, $\kappa$=0.1375, 0.1390 and 0.1400. We construct 2$\times$2 correlation matrices and diagonalize them so that the signals of $N^*(1535)$ and $N^*(1650)$ are properly separated. Wraparound contributions in the correlator, which can be another source of signal contaminations, are eliminated by imposing the Dirichlet boundary condition in the temporal direction. The axial charge of $N^*(1535)$ is found to take small values as $g_A^{N^*N^*}\sim {\mathcal O}(0.1)$, whereas that of $N^*(1650)$ is approximately 0.5, which is almost independent of quark masses and consistent with the predictions by the naive nonrelativistic quark model., Comment: 4 pages, 2 figures, presented at the 14th High-Energy Physics International Conference on Quantum ChromoDynamics (QCD08) Montpellier, France, 7-12 July, 2008

Low-lying $\Lambda$ baryons with spin 1/2 are analyzed in full (unquenched) lattice QCD. We construct $2 \times 2$ cross correlators from flavor SU(3) "octet" and "singlet" baryon operators, and diagonalize them so as to extract information of two low-lying states for each parity. The two-flavor CP-PACS gauge configurations are used, which are generated in the renormalization-group improved gauge action and the ${\mathcal O}(a)$-improved quark action. Three different $\beta$'s, $\beta = 1.80$, 1.95 and 2.10, are employed, whose corresponding lattice spacings are $a = 0.2150$, 0.1555 and 0.1076 fm. For each cutoff, we use four hopping parameters, ($\kappa_{\rm val}, \kappa_{\rm sea}$), which correspond to the pion masses ranging about from 500 MeV to 1.1 GeV. Results indicate that there are two negative-parity $\Lambda$ states nearly degenerate at around 1.6 GeV, while no state as low as $\Lambda (1405)$ is observed. By decomposing the flavor components of each state, we find that the lowest (1st-excited) negative-parity state is dominated by flavor-singlet (flavor-octet) component. We also discuss meson-baryon components of each state, which has drawn considerable attention in the context of multi-quark pictures of $\Lambda (1405)$., Comment: 11 pages, 11 figures, 3 tables; version to appear in Phys. Rev. D

We perform the first study for the bound states of colored scalar particles $\phi$ ("scalar quarks") in terms of mass generation with quenched SU(3)$_c$ lattice QCD. We investigate the bound states of $\phi$, $\phi^\dagger\phi$ and $\phi\phi\phi$ ("scalar-quark hadrons"), as well as the bound states of $\phi$ and quarks $\psi$, i.e., $\phi^\dagger\psi$, $\psi\psi\phi$ and $\phi\phi\psi$ ("chimera hadrons"). All these new-type hadrons including $\phi$ have a large mass of several GeV due to large quantum corrections by gluons, even for zero bare scalar-quark mass $m_\phi=0$ at $a^{-1}\sim 1{\rm GeV}$. We find a similar $m_\psi$-dependence between $\phi^\dagger\psi$ and $\phi\phi\psi$, which indicates their similar structure due to the large mass of $\phi$. From this study, we conjecture that all colored particles generally acquire a large effective mass due to dressed gluons.

We consider prescriptions that are free from the direct charge-screening effects by quark loops and enable us to clarify the confining nature of a vacuum. We test two candidates for an order parameter, a Polyakov loop ($P$) evaluated in zero-triality backgrounds and fermionic determinants (${\mathcal D}_{1,2}$) with non-zero triality. Especially, ${\mathcal D}_{1,2}$ has very small fluctuations in comparison with a Polyakov loop in zero-triality sector, and seems to well reflect the characteristic of a vacuum. Such prescriptions could be still usable for the clarification of the confinement property of a vacuum., Comment: 6 pages, 7 figures

We study the properties of low-lying Dirac modes in quenched compact QED at $\beta =1.01$, employing $12^3\times N_t$ ($N_t =4,6,8,10,12$) lattices and the overlap formalism for the fermion action. We pay attention to the spatial distributions of low-lying Dirac modes below and above the ``phase transition temperature'' $T_c$. Near-zero modes are found to have universal anti-correlations with monopole currents, and are found to lose their temporal structures above $T_c$ exhibiting stronger spatial localization properties. We also study the nearest-neighbor level spacing distribution of Dirac eigenvalues and find a Wigner-Poisson transition., Comment: 10 pages, 10 figures, 1 table

We show the first lattice QCD results on the axial charge $g_A^{N^*N^*}$ of $N^*(1535)$ and $N^*(1650)$. The measurements are performed with two flavors of dynamical quarks employing the renormalization-group improved gauge action at $\beta$=1.95 and the mean-field improved clover quark action with the hopping parameters, $\kappa$=0.1375, 0.1390 and 0.1400. In order to properly separate signals of $N^*(1535)$ and $N^*(1650)$, we construct 2$\times$2 correlation matrices and diagonalize them. Wraparound contributions in the correlator, which can be another source of signal contaminations, are eliminated by imposing the Dirichlet boundary condition in the temporal direction. We find that the axial charge of $N^*(1535)$ takes small values as $g_A^{N^*N^*}\sim {\mathcal O}(0.1)$, whereas that of $N^*(1650)$ is about 0.5, which is found independent of quark masses and consistent with the predictions by the naive nonrelativistic quark model., Comment: 5pages, 3 figures, 1 table; Confusing notations were corrected. (v2); Results on N(1650) were added. (v3)

We study the properties of low-lying Dirac modes in quenched compact QED at $\beta$=0.99, 1.01 and 1.03, employing $12^3\times 12$ lattices and the overlap formalism for the fermion action. We pay special attention to the spatial distributions of the low-lying Dirac modes. Near-zero modes are found to have universal anti-correlations with monopole currents below/above the critical $\beta$. We also study the nearest-neighbor level spacing distribution of Dirac eigenvalues and find a signal of a Wigner-Poisson transition. We make a possible speculation on the chiral phase transition in 4D compact QED., Comment: 10 pages, 6 figures, 1 tables

A possiblity of measuring the cosmic neutrino temperature $\sim 1.9 K$ and other important quantities such as the chemical potential $\mu$ and the decoupling temperature $T_d$ is discussed, using the recently proposed process of photon irradiated neutrino pair emission from metastable atoms. The Pauli blocking effect of relic neutrinos reduces the rate by a large factor $\approx (1 + m_1/T_d)/4$ at the threshold of the lightest neutrino pair (of mass $2m_1$). Correction of linear order in $\mu$ near the mass thresholds can be used to improve the constraint on the lepton asymmetry., Comment: 12 pages and 6 figures

We study the meson-meson and meson-baryon interactions in lattice QCD. The simulation is performed on 20^3 * 24 lattice at \beta=5.7 using Wilson gauge action and Wilson fermion at the quenched level. By adopting one static quark for each hadron as "heavy-light meson" and "heavy-light-light baryon", we define the distance $r$ of two hadrons and extract the inter-hadron potential from the energy difference of the two-particle state and its asymptotic state. We find that both of the meson-meson and meson-baryon potentials are nontrivially weak for the whole range of 0.2 fm <= r <= 0.8 fm. The effect of including/excluding the quark-exchange diagrams is found to be marginal., Comment: Talk given at Particles and Nuclei International Conference (PANIC05), Santa Fe, NM, USA, 24-28 Oct. 2005. 3 pages, 2 figures

We study multi-quark (3Q,4Q,5Q) systems in lattice QCD. We perform the detailed studies of multi-quark potentials in lattice QCD to clarify the inter-quark interaction in multi-quark systems. We find that all the multi-quark potentials are well described by the OGE Coulomb plus multi-Y-type linear potential, i.e., the multi-Y Ansatz. For multi-quark systems, we observe lattice QCD evidences of ``flip-flop'', i.e., flux-tube recombination. These lattice QCD studies give an important bridge between elementary particle physics and nuclear physics., Comment: A talk given at Particles and Nuclei International Conference(PANIC05), Santa Fe, NM, Oct. 24-28, 2005. 3 pages, 6 figures

We study spin $\frac12$ hadronic states in quenched lattice QCD to search for a possible $S=+1$ pentaquark resonance. Our work is the first systematic lattice QCD study which properly carries out the following analyses: {\it (1) the careful extraction of the first two low energy states with very high statistics and the variational method} and {\it (2) the study of volume dependences of eigenenergies and spectral weights to distinguish resonance states from scattering states}. Simulations are carried out on $8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices at $\beta$=5.7 with the standard plaquette gauge action and the Wilson quark action. Our result indicates the existence of a resonance state lying slightly above the NK threshold in $(I,J^P)=(0,\frac12^-)$ channel in quenched QCD., Comment: Talk presented at the 23rd International Symposium on Lattice Field Theory "Lattice2005", Dublin, July 25-30, 2005; uses PoS.cls

Using SU(3) lattice QCD, we perform the detailed studies of the three-quark and the multi-quark potentials. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we perform the accurate calculation for the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ by diagonalizing the QCD Hamiltonian in the presence of three quarks, and find a large gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a physical reason of the success of the quark model. $\Delta E_{\rm 3Q}$ is found to be reproduced by the ``inverse Mercedes Ansatz'', which indicates a complicated bulk excitation for the gluonic-excitation mode. We study also the tetra-quark and the penta-quark potentials in lattice QCD, and find that they are well described by the OGE Coulomb plus multi-Y type linear potential, which supports the flux-tube picture even for the multi-quarks., Comment: Invited talk at Int. Conf. on "High Energy and Mathematical Physics" Cadi Ayyad Univ. Marrakech, Morocco, April 4-7, 2005 (Moroccan Publisher) 13 pages

We study spin $\frac12$ hadronic states in quenched lattice QCD to search for a possible $S=+1$ pentaquark resonance. Simulations are carried out on $8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices at $\beta$=5.7 at the quenched level with the standard plaquette gauge action and the Wilson quark action. We adopt a Dirichlet boundary condition in the time direction for the quark to circumvent the possible contaminations due to the (anti)periodic boundary condition for the quark field, which are peculiar to the pentaquark. By diagonalizing the $2\times 2$ correlation matrices constructed from two independent operators with the quantum numbers $(I,J)=(0,\frac12)$, we successfully obtain the energies of the lowest state and the 2nd-lowest state in this channel. The analysis of the volume dependence of the energies and spectral weight factors indicates that a resonance state is likely to exist slightly above the NK threshold in $(I,J^P)=(0,\frac12^-)$ channel., Comment: 21 pages, 14 figures, 1 table; v2: "N_eff" in Sec.4 was changed to "N_fit" to avoid the confusion in the notation; v3: The discussions in Sec.6 were made clearer. Sec7,8,9B were slightly modified. Some references were added; v4: accepted version

We study the narrow decay width of low-lying penta-quark baryons in the QCD string theoryin terms of gluonic excitations. In the QCD string theory, the penta-quark baryon decays via a gluonic-excited state of a baryon and meson system, where a pair of Y-shaped junction and anti-junction is created. Since lattice QCD shows that the lowest gluonic-excitation energy takes a large value of about 1 GeV, the decay of the penta-quark baryon near the threshold is considered as a quantum tunneling process via a highly-excited state (a gluonic-excited state) in the QCD string theory. This mechanism strongly suppresses the decay and leads to an extremely narrow decay width of the penta-quark system., Comment: Talk given at International Conference on the Structure of Baryons (Baryons 04) October 25 - 29, 2004, Ecole Polytechnique, Palaiseau, France

We study the three-quark and multi-quark potentials in SU(3) lattice QCD. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we perform the accurate calculation for the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ by diagonalizing the QCD Hamiltonian in the presence of three quarks, and find a large gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a physical reason of the success of the quark model. $\Delta E_{\rm 3Q}$ is found to be reproduced by the ``inverse Mercedes Ansatz'', which indicates a complicated bulk excitation for the gluonic-excitation mode. We study also the tetra-quark and the penta-quark potentials in lattice QCD, and find that they are well described by the OGE Coulomb plus multi-Y type linear potential, which supports the flux-tube picture even for the multi-quarks. Finally, the narrow decay width of penta-quark baryons is discussed in terms of the QCD string theory., Comment: Invited talk at Int. Conference on Quark Confinement and the Hadron Spectrum 6, Sardinia, Italy, 21-25 Sep 2004

Using the QCD string theory, we investigate the physical reason of the narrow width of penta-quark baryons in terms of the large gluonic-excitation energy. In the QCD string theory, the penta-quark baryon decays via a gluonic-excited state of a baryon and meson system, where a pair of Y-shaped junction and anti-junction is created. On the other hand, we find in lattice QCD that the lowest gluonic-excitation energy takes a large value of about 1 GeV. Therefore, in the QCD string theory, the decay of the penta-quark baryon near the threshold is considered as a quantum tunneling process via a highly-excited state (a gluonic-excited state), which leads to an extremely narrow decay width of the penta-quark system., Comment: Talk at Int. Workshop on Pentaquark04, SPring-8, Japan, 20-23 Jul 2004

We perform the detailed study of the tetraquark (4Q) potential $V_{\rm 4Q}$ for various QQ-$\rm \bar{Q}\bar{Q}$ systems in SU(3) lattice QCD with $\beta=6.0$ and $16^3 \times 32$ at the quenched level. For about 200 different patterns of 4Q systems, $V_{\rm 4Q}$ is extracted from the 4Q Wilson loop in 300 gauge configurations, with the smearing method to enhance the ground-state component. We calculate $V_{\rm 4Q}$ for planar, twisted, asymmetric, and large-size 4Q configurations, respectively. Here, the calculation for large-size 4Q configurations is done by identifying $16^2 \times 32$ as the spatial size and 16 as the temporal one, and the long-distance confinement force is particularly analyzed in terms of the flux-tube picture. When QQ and $\rm \bar{Q}\bar{Q}$ are well separated, $V_{\rm 4Q}$ is found to be expressed as the sum of the one-gluon-exchange Coulomb term and multi-Y type linear term based on the flux-tube picture. When the nearest quark and antiquark pair is spatially close, the system is described as a "two-meson" state. We observe a flux-tube recombination called as "flip-flop" between the connected 4Q state and the "two-meson" state around the level-crossing point. This leads to infrared screening of the long-range color forces between (anti)quarks belonging to different mesons, and results in the absence of the color van der Waals force between two mesons., Comment: 17 pages, 23 figures

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., Comment: Talk given at the International Workshop on PENTAQUARK04, SPring-8, Japan, 20-23 July 2004

In SU(3) lattice QCD, we perform the detailed study for the ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, i.e., the energies of the ground state and the 1st excited state of the gluon field in the presence of the static three quarks. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we calculate the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, and find a large gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a physical reason of the success of the quark model even without gluonic excitations. We present also the first study for the penta-quark potential $V_{\rm 5Q}$ in lattice QCD, and find that $V_{\rm 5Q}$ is well described by the sum of the OGE Coulomb plus multi-Y type linear potential., Comment: Invited talk at International Workshop on QCD Down Under, Adelaide, Australia, 10-19 Mar 2004

Using SU(3) lattice QCD, we perform the first systematic study for the ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$, {\it i.e.}, the energies of the ground state and the 1st excited state of the gluon field in the presence of the static three quarks. From the accurate and thorough calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear potential, {\it i.e.}, Y-Ansatz, within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For more than 100 patterns of 3Q systems, we calculate the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ in quenched lattice QCD, and find the gluonic excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ to be about 1 GeV. This large gluonic-excitation energy is conjectured to ensure the success of the quark model for the low-lying hadrons even without gluonic excitations., Comment: Talk given at International Conference on Color Confinement and Hadrons in Quantum Chromodynamics - Confinement 2003, RIKEN, Japan, 21-24 Jul 2003

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., Comment: 4 pages, 5 figures

For more than 300 different patterns of the 3Q systems, the ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is investigated using SU(3) lattice QCD with $12^3\times 24$ at $\beta=5.7$ and $16^3\times 32$ at $\beta=5.8, 6.0$ at the quenched level. As a result of the detailed analyses, we find that the ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ is well described with so-called Y-ansatz as $V_{\rm 3Q}=-A_{\rm 3Q}\sum_{i

We present the first study of the gluonic excitation in the three-quark (3Q) system in SU(3) lattice QCD with $\beta$=5.8 and $16^3 \times 32 $ at the quenched level. For the spatially-fixed 3Q system, we measure the gluonic excited-state potential, which corresponds to the flux-tube vibrational energy in the flux-tube picture. The lowest gluonic-excitation energy in the 3Q system is found to be about 1GeV in the hadronic scale. This large gluonic-excitation energy is expected to bring about the success of the simple quark model without gluonic modes., Comment: 8 pages, 3 figures