Search

After presenting the motivations to explore the low-lying scalar mesons such as the $\sigma$, $a_0$ and $\kappa$ in the unquenched as well as quenched lattice QCD, we review the works done by our collaboration (SCALAR Collaboration) with a what-to-do-next list. We briefly mention the imporatance to explore the $N_c$ dependence of and possible effects of the $U_A(1)$ anomaly to the properties the low-lying scalar mesons., Comment: 4 pages, 2 figures. Invited talk at QCD08, 14th International QCD Conference, 7-12th July, 2008, Montpellier (France)

We analyse temporal and spatial meson correlators in quenched lattice QCD at T| > 0. Above T c we find different (temporal) pole masses and (spatial) screening masses, signals of plasma formation and indication of persisting mesonic excitations.

We report large scale numerical simulation data for gluon propagators together with an analysis based on the generalized Feynman rules of an extended perturbation scheme. Zwanziger's stochastic gauge fixing algorithm is employed to limit the path integration inside the Gribov region. Obtained propagators do not show a simple physical pole behavior, rather complex-conjugate pairs of singularities in the p2 plain.

We report our recent study of the κ meson by full-QCD simulation with Wilson fermions on the 83 × 16 lattice at β = 4.8. Contrary to our σ meson calculation, where the disconnected diagram results in very light mass, we obtain a rather heavy kappa particle, i.e., mκ/mK∗∼ 2. This preliminary result does not agree with recent experimental values.

We study the change of the meson and diquark propagators in a high density state of the two-color QCD with a Wilson fermion. Both Wilson gauge action and Iwasaki improved action are investigated. In order to explore the high density frontier of the phase space, we adopt an exact algorithm based on Woodbury formula which is quite robust but heavy. Lattice size is 43 × 8, a coupling is β = 0.70 and hopping parameter κ is 0.150 ∼ 0.175 for the Iwasaki improved action. In any case of our simulation, the vector meson only reveals strange rising up with large chemical potential[1].

A lattice QCD calculation of S-wave scattering length in the channel of Λp is carried out in the quenched approximation at β = 5.6, on a 43 × 8 lattice. Preliminary results show an attractive interaction with small value of scattering length.

We report our recent numerical studies on two-color QCD with Wilson fermions. First the phase structure of the system in (kappa,mu)-plane is analyzed by measuring Polyakov line, baryon number density, gluon energy density and Polyakov line susceptibility. Then meson and baryon (di-quark) propagators are investigated. We find that the vector meson mass decreases near mu_c. This phenomena can be related to the low-mass lepton-pair enhancement observed in CERES experiment. Since our lattice is small, in order to confirm the results, we calculate both periodic and anti-periodic boundary condition cases. Preliminary calculations of color averaged, symmetric and anti-symmetric forces of qq system obtained from Polyakov line correlations, and gluon propagators are reported., Comment: 3 pages, 4 figures, Lattice2002(nonzerot)

We investigate the propagator of "f$_{0}$(600) or the $\sigma$" by the full-QCD simulation with Wilson fermions. We calculate the mesonic correlator in the I=0, $J^P=0^{+}$ channel on the $8^{3} \times 16$ lattice. Plaquet action and Wilson fermion action are adopted. A coupling constant $\beta$ is set to 4.8 and three kinds of hopping parameter, $\kappa$=0.1846, 0.1874 and 0.1891 are assayed. The disconnected diagram in the propagator is evaluated through taking average over 500 or 1000 Z2 noise. Simulations with the larger hopping parameter provide us with less noisy results. Though the statistics is not yet enough, our results indicate the existence of a pole with a mass in almost the same order as that of the $\rho$.

We present very precise results from the MCRG analysis on large lattices performed in the frame of the QCD-TARO collaboration using the highly parallel computer AP1000 of Fujitsu. We find good scaling behavior of pure SU(3) theory with strong non-perturbative effects in the range 6 β

Using lattice QCD with dynamical Wilson fermions, we study I = 0 and J P = 0 + channel which is constructed by , in order to search for the σ meson. Our preliminary result shows that the connected and disconnected diagrams contribute to the σ meson propagator in the same order.

On quenched lattice simulations, we examine the relation between the hopping and fermionic anisotropy parameter on anisotropic lattices with the clover O(a) improved action. For the gauge sector we used configurations for the standard and the RG(Iwasaki) improved actions.

We report a project to provide a set of free source codes for lattice QCD. The programs may be used as fundamental blocks when one wants to construct his/her own QCD codes. They are written in Fortran 90 with use of MODULE, so that algorithms can transparently be seen. MPI is used for parallelization. We are also constructing a proto-type of QCD-GRID where one can try to run the code.

Monte Carlo renormalization group analysis on SU(3) lattice at large β is studied. On 32 4 lattice, coupling shift Δβ is 0.48 ± 0.02 and 0.53 ± 0.02 at β =6.55 and 6.80, where the lattice remains in confinement phase. Δβ is approaching its 2-loop asymptotic scaling value. However, deviation is still 20% and 13% at β =6.55 and 6.80, respectively. We also report high statistics data on 16 4 lattice at β =6.80, giving Δβ = .52 ± 0.03 in the deconfined regime.

Quenched Wilson hadron spectroscopy at β = 6.3 has been studied by using parallel computer AP1000. Spectrum of hadrons composed of various combinations of hopping parameters are measured on 32 3 × 48 and 16 3 × 48 lattices. We report results of spatial size effects based on various hadron masses. Dependence on boundary conditions along the temporal direction is also examined and discussed.

We report our results of the Monte Carlo Renormalization Group analysis in two dimensional coupling space. The qualitative features of the RG flow are described with a phenomenological RG equation. The dependence on the lattice spacing for various actions provides the conditions to determine the parameters entering the RG equation., LATTICE 99 (Improvement and Renormalization), 3 pages, LaTeX with 3 figures, espcrc2.sty, psfig.sty

The first numerical evidence of gauge-fixed vacuum copies on the lattice is presented for SU(2) and U(1) in 4 and 2 dimensions. Gauge transformations between these copies have non-trivial topological structure which is displayed. Photon propagators do not show the correct behavior if copies are not excluded.

QCDimMPI[1] is a simulation code for pure SU(3) gauge theory with an improved action consisting of 1 × 1 and 2 × 1 plaquettes. It uses Fortran77 and the Message Passing Interface Standard, MPI[2]. QCDimMPI is an extended version of QCDMPI. It is portable, allows simulations in any number of dimensions, on any number of processors, and with arbitrary dimensional partitioning. It requires a rather small working area, and yields excellent performance on single processor computers and a wide variety of parallel computers which support MPI. The program provides information on link update time and communications time. In this paper, an outline of QCDimMPI is given, and benchmark results on several parallel computers are reported.

QCD and QED with dynamical Wilson fermions are numerically studied on small lattices (4∗∗4 for QCD, 4∗∗4∼6∗∗3∗8 for QED) by using a large-step exact algorithm, i.e., evaluating the ratio of determinants each time we update one link. For QCD the plaquette energy, the Polyakov line and 〈 ψ ψ 〉 change rapidly at ( β , κ )=(4.9,0.185), (5.1,0.18) and (5.3,0.14). Values of the determinant are calculated and it is strongly correlated with the plaquette energy. After introducing a chemical potential, the phase of complex determinant is studied. In compact QED the β - κ plane is separated into two parts, the confinement and Coulomb phases. At very large κ in the Coulomb phase negative values of the determinant are observed. Gauge dependent quantities in the Landau gauge are studied for QED. Finally, the graphical representation of lattice QCD is briefly discussed.

We present results from a program of calculations for lattice gauge and matter fields theories at finite temperatures, realized by using different cut offs in the space and time directions (anisotropic lattices). Specifically, the analyses pertain to the φ 4 theory, Higgs models and QCD.

We present our new results on the renormalization group coupling obtained in 3-dimensional coupling space ( β 11 , β 12 , β twist ). The value of β twist turns out to be small and the coupling flow projected on ( β 11 , β 12 ) plane is very similar with the previous result obtained in the 2 dimensional coupling space.

We study the spectral function of mesonic correlators at finite temperature. The mesonic correlators are measured along the “time” direction with fine lattice spacing on anisotropic lattices. A new method to construct a spectral function from a correlator is proposed. The temperature dependence of the shape of the mesonic spectrum is investigated.

The transport coefficients of quark gluon plasma are calculated on a lattice 16**3X8, with the pure gauge models. Matsubara Green's functions of energy momentum tensors have very large fluctuations and about a few million MC sweeps are needed to reduce the errors reasonably small in the case of the standard action. They are much suppressed if Iwasaki's improved action is employed. Preliminary results show that the transport coefficients roughly depend on the coupling constant as a**(-3)(g) in the case of SU(2)., Talk presented at LATTICE96(finite temperature), 3 pages in latex, 4 Postscript figures

We present our calculations of the energy-momentum correlation functions on the lattice with Nt > 4 which are indispensable to obtain the transport coefficients. In order to get the meaningful values of the transport coefficients, we need fine resolution of the Matsubara frequencies, which leads inevitably to large size of the lattice in the temperature direction. We employ the anisotropic lattices as well as the conventional isotropic ones. We study U(1), SU(2) and SU(3) cases and compare the results.

We report our analysis of MCRG study where we employ an improved blocking scheme and present our first trial to determine effective coupling constants obtained on the blocked lattices.

We discuss problems related to the analysis of finite temperature general mesonic correlators and provide preliminary results on the pion wave function and dispersion law in quenched QCD at T ⋍ 0.9 Tc.

We report the first QCD calculations on a parallel vector computer, NWT, which has the peak performance of 236 GFLOPS and 35 GByte memory. After discussing its architecture, our parallel programming strategy, and QCD code performance, we present gluon propagators on a 48 3 × 64 lattice at β = 6.8, which shows the large deviation from the behavior of free massless gauge particles.

We briefly summarize our results of quenched Wilson hadron spectroscopy at β = 6.3 on a 323 × 48 lattice. The spectrum of pseudo scalar and vector mesons, (1/2)+ and (3/2)+ baryons composed of up, down, strange and charm quarks are presented. A decrease of mass splitting between (1/2)+ and (3/2)+ baryons is observed when heavy quark masses increase, as in the case of the mass difference between pseudo scalar and vector masses.

We propose an extension of Zwanziger's stochastic gauge fixing to compact lattice gauge theories. We study numerically photon and gluon propagators on the lattice using the stochastic gauge fixing implimented in the Langevin simulation. We find that the photon correlation function are not distorted by Gribov copies and behave as massless gauge propagators with renormalized gauge parameter in the Coulomb region. Preliminary analysis suggests that the gluon propagators are not simple massless ones.

Results of our autocorrelation measurement performed on Fujitsu AP1000 are reported. We analyze (i) typical autocorrelation time, (ii) optimal mixing ratio between overrelaxation and pseudo-heatbath and (iii) critical behavior of autocorrelation time around cross-over region with high statistic in wide range of $\beta$ for pure SU(3) lattice gauge theory on $8^4$, $16^4$ and $32^4$ lattices. For the mixing ratio K, small value (3-7) looks optimal in the confined region, and reduces the integrated autocorrelation time by a factor 2-4 compared to the pseudo-heatbath. On the other hand in the deconfined phase, correlation times are short, and overrelaxation does not seem to matter For a fixed value of K(=9 in this paper), the dynamical exponent of overrelaxation is consistent with 2 Autocorrelation measurement of the topological charge on $32^3 \times 64$ lattice at $\beta$ = 6.0 is also briefly mentioned., Comment: 3 pages of A4 format including 7-figures

We report the first results of a hadron spectrum measurement by the QCD_TARO Collaboration with the massively parallel computer AP1000. The main memory of AP1000 is currently 8Gbytes (final goal : 16 Gbytes), which allows us to treat rather large lattices. We measure the quenched Wilson spectrum on a 323 × 48 lattice at β = 6.3. We obtain a good agreement with an empirical curve on the Edinburgh plot.

We report results of a Monte Crlo renormalization group study with b = 2 blocking on a 34 4 lattice in progress. Δβ at β = 6.8 is consistent with previously obtained values at a large β and is smaller than the two-loop asymptotic value.

The gauge fixing (Gribov) ambiguity on the lattice is investigated in simple models. The global understanding of this phenomenon comes from singer's analysis of the bundle of connections. This bundle in continuum gauge theory is infinite dimensional and of non-trivial topology, however on the lattice it is finite dimensional and tractable. Theoretical expectations from Morse theory are supported by numerical evidence, and the structure of lattice gauge orbit space is displayed. Finally, shortcomings of standard gauge fixing prescriptions are addressed.

A project to treat dynamical Wilson fermion in an exact manner is reported. An algorithm for this purpose is briefly described and numerical results for SU(3) and U(1) on 44 are presented. Comparison with the bush-factorized algorithm is done and they agree reasonably with each other. Indications of first order phase transitions are observed near β = 5.3 and k = 0.14 with 3 flavors for SU(3) and near β = 0.9 and k = 0.17 with 1 flavor for U(1).

We report results of Monte Carlo simulations of full QCD on a small lattice (4∗∗4) by an exact algorithm at β=4.9, 5.1 and 5.3. We use dynamical Wilson fermions and observe phase transitions which can be interpreted as a confining-deconfining transition; they are accompanied with rapid change of . Performance of our program on VP400E is discussed.

A lattice calculation of meson masses at finite temperature is reported. We calculate the meson mass which corresponds to a mass pole of the spectral function by measuring Green functions along the temperature direction. A formulation for this apploach is discussed. Anisotropic lattice is introduced where temperature lattice distance is smaller than spacial one to make precise measurements of the Green functions. Preliminary numerical data on 8 ∗∗ 3 ∗ 8, 10 and 16 lattices are presented in a quenched approximation.

A project to treat dynamical Wilson fermion in an exact manner is reported. An algorithm for this purpose is briefly described and numerical results for SU(3) and U(1) on 44 are presented. Comparison with the bush-factorized algorithm is done and they agree reasonably with each other. Indications of first order phase transitions are observed near β = 5.3 and k = 0.14 with 3 flavors for SU(3) and near β = 0.9 and k = 0.17 with 1 flavor for U(1).