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Register a new userLattice monopole action in pure SU(3) QCD
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We obtain an almost perfect monopole action numerically after abelian projection in pure SU(3) lattice QCD. Performing block-spin transformations on the dual lattice, the action fixed depends only on a physical scale b. Monopole condensation occurs for large b region. The numerical results show that two-point monopole interactions are dominant for large b. We next perform the block-spin transformation analytically in a simplified case of two-point monopole interactions with a Wilson loop on the fine lattice. The perfect operator evaluating the static quark potential on the coarse b-lattice are derived. The monopole partition function can be transformed into that of the string model. The static potential and the string tension are estimated in the string model framework. The rotational invariance of the static potential is recovered, but the string tension is a little larger than the physical one.
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To check the dual superconductor picture for the quark-confinement mechanism, we evaluate monopole dominance as well as Abelian dominance of quark confinement for both quark-antiquark and three-quark systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static $Qbar Q$ system in lattice QCD with various spacing $a$ at $beta$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume lattices with $La ge$ 2fm, we find perfect Abelian dominance of the string tension for the $Qbar Q$ systems: $sigma_{Abel} simeq sigma$. Second, we accurately measure the static 3Q potential for more than 300 different patterns of 3Q systems with 1000-2000 gauge configurations using two large physical-volume lattices: ($beta$,$L^3$x$L_t$)=(5.8,$16^3$x32) and (6.0,$20^3$x32). For all the distances, the static 3Q potential is found to be well described by the Y-Ansatz: two-body Coulomb term plus three-body Y-type linear term $sigma L_{min}$, where $L_{min}$ is the minimum flux-tube length connecting the three quarks. We find perfect Abelian dominance of the string tension also for the 3Q systems: $sigma^{Abel}_{3Q}simeq sigma_{3Q} simeq sigma$. Finally, we accurately investigate monopole dominance in SU(3) lattice QCD at $beta$=5.8 on $16^3$x32 with 2,000 gauge configurations. Abelian-projected QCD in the MA gauge has not only the color-electric current $j^mu$ but also the color-magnetic monopole current $k^mu$, which topologically appears. By the Hodge decomposition, the Abelian-projected QCD system can be divided into the monopole part ($k_mu e 0$, $j_mu=0$) and the photon part ($j_mu e 0$, $k_mu=0$). We find monopole dominance of the string tension for $Qbar Q$ and 3Q systems: $sigma_{Mo}simeq 0.92sigma$. While the photon part has almost no confining force, the monopole part almost keeps the confining force.
We show how to generalize the previous result of the monopole condensation in SU(2) QCD to SU(3) QCD. We present the gauge independent Weyl symmetric Abelian decomposition of the SU(3) QCD which decomposes the gluons to the color neutral neurons and the colored chromons. The decomposition allows us to separate the gauge invariant and parity conserving monopole background gauge independently, and reduces the non-Abelian gauge symmetry to a discrete color reflection symmetry which is easier to handle. With this we obtain the infra-red finite and gauge invariant integral expression of the one-loop effective action which is Weyl symmetric in three SU(2) subgroups. Integrating it gauge invariantly imposing the color reflection invariance we obtain the SU(3) QCD effective potential which generates the stable monopole condensation and the mass gap. We discuss the physical implications of our result.
An analysis of the pion mass and pion decay constant is performed using mixed-action Lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered n_f = 2+1 MILC configurations. Calculations were performed at two lattice spacings of b~0.125 fm and b~0.09 fm, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range 0.1 <= m_l / m_s <= 0.6, while pion masses are in the range 235 < m_pi < 680 MeV. A two-flavor chiral perturbation theory analysis of the Lattice QCD calculations constrains the Gasser-Leutwyler coefficients bar{l}_3 and bar{l}_4 to be bar{l}_3 = 4.04(40)(+73-55) and bar{l}_4 = 4.30(51)(+84-60). All systematic effects in the calculations are explored, including those from the finite lattice space-time volume, the finite lattice spacing, and the finite fifth dimension in the domain-wall quark action. A consistency is demonstrated between a chiral perturbation theory analysis at fixed lattice spacing combined with a leading order continuum extrapolation, and the mixed-action chiral perturbation theory analysis which explicitly includes the leading order discretization effects. Chiral corrections to the pion decay constant are found to give f_pi / f = 1.062(26)(+42-40) where f is the decay constant in the chiral limit. The most recent scale setting by the MILC Collaboration yields a postdiction of f_pi = 128.2(3.6)(+4.4-6.0)(+1.2-3.3) MeV at the physical pion mass.
We present results for the equation of state for pure SU(3) gauge theory obtained with a renormalization-group (RG) improved action. The energy density and pressure are calculated on a $16^3times 4$ and a $32^3times 8$ lattice employing the integral method. Extrapolating the results to the continuum limit, we find the energy density and pressure to be in good agreement with those obtained with the standard plaquette action within the error of 3-4%.
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 $phi$, $phi^daggerphi$ and $phiphiphi$ (scalar-quark hadrons), as well as the bound states of $phi$ and quarks $psi$, i.e., $phi^daggerpsi$, $psipsiphi$ and $phiphipsi$ (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 $phi^daggerpsi$ and $phiphipsi$, 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.
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