Numerical studies of confinement in the Landau gauge by the larger lattice simulation
Figure 1 and Figure 2(right) are replaced and the slope parameter $α_D$ is corrected to -0.4.
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arXiv subjects
Sadataka Furui
Publications and source records attributed to Sadataka Furui.
Color Confinement in Lattice Landau Gauge
The problem of color confinement in lattice Landau gauge QCD is briefly reviewed in the light of Kugo-Ojima criterion and Gribov-Zwanziger theory. The infrared properties of the Landau gauge QCD is studied by the measurement of the gluon propagator, ghost propagator, Kugo-Ojima parameter and the running coupling via $β=6.4,32^4,48^4$ lattice simulation. The data are analyzed in the principle of minimum sensitivity(PMS) in the $\widetilde{MOM}$ scheme. We observe the running coupling $α_s(q)$ has a maximum about 1 and decreases near q=0. The Kugo-Ojima parameter, which is expected to be 1 was about 0.8.
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Numerical studies of confinement in the lattice Landau gauge
Critical conjectures on confinement in the Landau gauge is numerically tested in focus to Gribov copy effects. One of the subjects is of the Kugo-Ojima confinement criterion and the other is of various viewpoints in the Gribov-Zwanziger theory. We use the smearing gauge as a reference gauge free of Gribov copy, and performed three types of simulations, log U, U-linear and log U in the smearing gauge. It is found that Gribov copy effect on the Kugo-Ojima parameter is small. log U and U-linear simulations yield only global scale factor difference in gluon propagator and in ghost propagator, and about 10% difference in Kugo-Ojima parameter. The horizon function defined by Zwanziger is evaluated in three types of gauge field and compared. All data show the negative horizon function as expected.
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Colour Confinement in the Lattice Landau Gauge QCD Simulation
The colour confinement criterion proposed by Kugo and Ojima is tested in the lattice Landau gauge QCD simulation. The renormalization effects are studied by measuring the gluon propagator, ghost propagator, three gluon vertex and the ghost-antighost-gluon vertex.
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Numerical study of the Kugo-Ojima criterion and the Gribov problem in the Landau gauge
The Kugo-Ojima color confinement criterion, which is based on the BRST symmetry of the continuum QCD is numerically tested by the lattice Landau gauge simulation. We first discuss the Gribov copy problem and the BRST symmetry on the lattice. The lattice Landau gauge can be formulated with options of the gauge field definition, U(link)-linear type or log U type. The Kugo-Ojima parameter u^a_b which is expected to be -1^a_b in the continuum theory is found to be -0.7*1^a_b in the strong coupling region, and the magnitude is a little less in the weak coupling region in log U type simulation. Those values are weakened even further in U-linear type. The horizon function defined by Zwanziger is evaluated in both types of gauge field and compared. The horizon function in the log U version is larger than the other, but in the weak coupling region, the expectation value of the horizon function is suggested to be zero or negative.
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Numerical tests of the Kugo-Ojima color confinement criterion
The Kugo-Ojima color confinement criterion, which is based on the BRST symmetry of QCD is numerically tested by the lattice Landau gauge simulation. We first discuss the BRST symmetry on the lattice and the Gribov copy problem. The horizon function defined by Zwanziger based on the U-linear definition of the gauge field and that based on log U are compared. The parameter u which is expected to be $-1δ^a_b$ in the continuum theory was found to be $-0.7δ^a_b$ in the strong coupling region. There are about 20% difference between the two horizon functions, but in the weak coupling region, the expectation value of the horizon function is suggested to be zero or negative.
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On the colour confinement and the minimal surface
In the analysis of the energy of the four-quark system obtained in the SU(2) lattice Monte Carlo, the f-model in which the transition potential is expressed in the form $f=f_c exp(-k_A b_s A-k_P\sqrt{b_s}P)$, where A is the area and P is the perimeter of the Wilson loop, was successful in the simple configurations of the four quarks. In the case of tetrahedral geometry, an estimation of the minimal surface whose contours run the positions of the four quarks is necessary. We show that the regular surface approximation whose area can be calculated analytically, is a good approximation for evaluating the minimal surface. The numerical value of the coefficient $k_A b_s$ is close to $2 fm^{-2}$ which is the density of the $Z_2$ vortex in the SU(2) lattice Monte Carlo.
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A test of the Kugo-Ojima confinement criterion by lattice Landau gauge QCD simulations
The first test of the Kugo-Ojima colour confinement criterion by the lattice Landau gauge QCD simulation is performed. The parameter u which is expected to be -1δ^a_b in the continuum theory was found to be -0.7δ^a_b in the strong coupling region. The data is analyzed in connection with the theory of Zwanziger. In the weak coupling region, the expectation value of the horizon function is negative or consistent to 0.
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An analysis of 4-quark energies in SU(2) lattice Monte Carlo
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.
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The Landau gauge lattice QCD simulation and the gluon propagator
The gluon propagator in the Landau gauge lattice QCD simulation of quenched 8^3 x 16 lattice is measured. The data suggests the confinement mechanism of the Gribov-Zwanziger theory.
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The new definition of lattice gauge fields and the Landau gauge
The Landau gauge fixing algorithm in the new definition of gauge fields is presented. In this algorithm a new solver of the Poisson equations based on the Green's function method is used. Its numerical performance of the gauge fixing algorithm is presented. Performance of the smeared gauge fixing in SU(3) is also investigated.
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A new algorithm of Langevin simulation and its application to the SU(2) and SU(3) lattice gauge
The 2nd order Runge-Kutta scheme Langevin simulation of unquenched QCD in pseudofermion method derived from our general theory shows a behaviour as a function of the Langevin step t better than the Fukugita,Oyanagi,Ukawa's scheme.
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