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Hideo Nakajima

Publications and source records attributed to Hideo Nakajima.

At least 19 recordsLinked to original sources
arXiv2009

Horizon function in Landau gauge QCD revisited -- Free boundary case from viewpoint of network QCD --

In Gribov-Zwanziger scenario of color confinement, Zwanziger proposed two types of horizon function in lattice Landau gauge, the first one and the second one of which foundation was discussed in detail. The second type horizon function is focussed on in the present study. Its derivation and the horizon condition are briefly reviewed along the line of Zwanziger, and it is also reviewed that this horizon condition and Kugo-Ojima color confinement criterion coincide in the continuum limit. In case of free boundary condition in contrast to periodic boundary condition, it was shown that the horizon condition holds for each gauge fixed configuration in Landau gauge. It is clarified that this fact can be derived from some identity relation which holds on an arbitrary network of links in Landau gauge. Thus the origin of the pointwise validity of horizon condition is highlighted.

hep-th↗
arXiv2007

Roles of the quark field in the infrared lattice Coulomb gauge and Landau gauge QCD

The effective coupling of QCD is measured by using the gauge configurations produced by the MILC collaboration in which the Kogut Susskind (KS) fermion is incorporated and by using that produced by the QCDOC collaboration in which the domain wall fermion (DWF) is incorporated. We fix the gauge to the Landau gauge and to the Coulomb gauge. The infrared effective coupling in the Coulomb gauge agrees with the recent extraction at JLab, but that in the Landau gauge shows infrared suppression. The suppression is expected to be due to the color anti-symmetric ghost propagator which in the unquenched configurations has stronger infrared singularity than the color diagonal ghost propagator. The Coulomb form factor in the infrared depends on the kind of the fermion incorporated in the system and the temperature. The quark has the effect of quenching randomness and the fluctuation of the color anti-symmetric ghost propagator is reduced in the unquenched configuration, and the Kugo-Ojima parameter c is closer to 1 in the unquenched configuration than in the quenched configuration.

hep-lat↗
arXiv2007

Infrared features of unquenched finite temperature lattice Landau gauge QCD

The color diagonal and color antisymmetric ghost propagators slightly above $T_c$ of $N_f=2$ MILC $24^3\times 12$ lattices are measured and compared with zero temperature unquenched $N_f=2+1$ MILC$_c$ $20^3\times 64$ and MILC$_f$ $28^3\times 96$ lattices and zero temperature quenched $56^4$ $β=6.4$ and 6.45 lattices. The expectation value of the color antisymmetric ghost propagator $ϕ^c(q)$ is zero but its Binder cumulant, which is consistent with that of $N_c^2-1$ dimensional Gaussian distribution below $T_c$, decreases above $T_c$. Although the color diagonal ghost propagator is temperature independent, the $l^1$ norm of the color antisymmetric ghost propagator is temperature dependent. The expectation value of the ghost condensate observed at zero temperature unquenched configuration is consistent with 0 in $T>T_c$. We also measure transverse, magnetic and electric gluon propagator and extract gluon screening masses. The running coupling measured from the product of the gluon dressing function and the ghost dressing function are almost temperature independent but the effect of $A^2$ condensate observed at zero temperature is consistent with 0 in $T>T_c$. The transverse gluon dressing function at low temperature has a peak in the infrared but it becomes flatter at high temperature. Its absolute value in the high momentum is larger for high temperature and similar to the magnetic gluon dressing function. The electric gluon propagator at high momentum is temperature independent. These data imply that the magnetic gluon propagator and the color antisymmetric ghost propagator are affected by the presence of dynamical quarks and there are strong non-perturbative effects through the temperature dependent color anti-symmetric ghost propagator.

hep-lat↗
arXiv2007

Infrared features of KS fermion and Wilson fermion in Lattice Landau Gauge QCD

The running coupling and the Kugo-Ojima parameter of unquenched lattice Landau gauge are simulated and compared with the continuum theory. Presence of infrared fixed point of $α_0\sim 2-2.5$ irrespective of the fermion actions (Wilson fermions and Kogut-Susskind(KS) fermions) in the continuum and in the chiral limit is suggested. Although there exists dependence on the polarization due to asymmetry of the lattice (time axis is longer than spacial axes), the Kugo-Ojima parameter $c$ is consistent with 1. Presence of $1+c_1/q^2$ correction factor in the running coupling depends on the lattice size and the sea quark mass. In the large lattice size and small sea quark mass, $c_1\sim 2.8$GeV is confirmed. The MILC configuration of $a=0.09$fm suggests also presence of dimension 4 condensates with sign opposite to the dimension 2 condensates. The gluon propagator, the ghost propagator and the running coupling are compared with recent pQCD results including anomalous dimension of fields up to the 4-loop level.

hep-lat↗
arXiv2006

Correlation of the ghost and the quark in the lattice Landau gauge QCD

Effects of the quark field on the ghost propagator of the lattice Landau gauge are investigated by using the quenched gauge configuration of SU(2) first copy and the parallel tempering (PT) gauge fixed samples, quenched SU(3) $56^4$ configuration and unquenched SU(3) configurations produced by the MILC collaboration. We measure color symmetric and color antisymmetric ghost propagator and the Binder cumulant of $l^1$ norm and $l^2$ norm of color antisymmetric ghost propagator and investigate deviation from that of Gaussian distribution. The dynamical quarks make color antisymmetric ghost propagator closer to Gaussian distribution and Kugo-Ojima color confinement parameter $c$ closer to 1.

hep-lat↗
arXiv2006

Effects of the quark field on the ghost propagator of Lattice Landau Gauge QCD

Infrared features of the ghost propagator of color diagonal and color antisymmetric ghost propagator of quenched SU(2) and quenched SU(3) are compared with those of unquenched Kogut-Susskind fermion SU(3) lattice Landau gauge. We compare 1) the fluctuation of the ghost propagator, 2) the ghost condensate parameter $v$ of the local composite operator (LCO) approach and 3) the Binder cumulant of color anti-symmetric ghost propagator between quenched and unquenched configurations.

hep-lat↗
arXiv2006

Unqueched Kogut-Susskind quark propagator in Lattice Landau Gauge QCD

Quark propagators of the unquenched Kogut-Susskind(KS) fermion obtained from the gauge configurations of the MILC collaboration are measured after Landau gauge fixing and using the Staple+Naik action. Presence of the $\bar q q$ condensates and $A^2$ condensates in the dynamical mass $M(q)$ and the quark wave function renormalization $Z_ψ(q^2)$ are investigated. We obtain the correlation of the renormalization factor of the running coupling taken at $μ\sim 6$GeV and that of the quark wave function renormalization $Z_ψ(q^2)$ of the Staple+Naik action. The mass function $\displaystyle M(q)$ is finite at $q=0$ and its chiral limit is $\sim 0.38$GeV. We compared the results corrected by the scale of the vertex renormalization and the tadpole renormalization with the corresponding values obtained by the Asqtad action without renormalization and observed good agreement.Implication of infrared finite $Z_2(q)=1/Z_ψ(q^2)$ to the Kugo-Ojima confinement criterion is discussed.

hep-lat↗
arXiv2005

Color Confinement in lattice Landau gauge with unquenched Wilson and KS fermions

The Kugo-Ojima confinement criterion is verified in the unquenched Landau gauge QCD simulation. The valence quark propagator of the Kogut-Susskind fermion with use of the fermion action including the Naik term and the staple contribution is calculated on MILC Asqtad unquenched gauge configurations, and it shows infrared suppression of the quark propagator.

hep-lat↗
arXiv2005

The running coupling in lattice Landau gauge with unquenched Wilson fermion and KS fermion

The running coupling of the Wilson fermon(JLQCD/CP-PACS) and that of Kogut-Susskind(KS) fermion(MILC) are measured in the lattice Landau gauge QCD in $\widetilde{MOM}$ scheme. The quark propagator of the KS fermion is also measured and we find that it is infrared suppressed. The renormalization factor of the running coupling and the tadpole renormalization define the scale of the quark wave function. Effects of the $A_μ^2$ condensates of a few GeV$^2$ are observed in the running coupling and also in the quark propagator.

hep-lat↗
arXiv2005

Confinement in the lattice Landau Gauge QCD simulation

The running coupling and the Kugo-Ojima parameter of the confinement criterion are measured for the quenched SU(3) β=6.4, 6.45, 56^4 lattice and the unquenched β=5.2, 20^3 x 48 lattice of JLQCD, β=2.1, κ=0.1357, 0.1382, 24^3 x 48 lattice of CP-PACS and β_{imp}=6.76,a m_{u,d}=0.007, 6.83,a m_{u,d}=0.040, 20^3 x 64 lattice of MILC collaboration. The quenched SU(3) 56^4 lattice data suggest presence of infrared fixed point of α_s=2.5(5) and the approach of the ensemble of the 1st copy to the Gribov boundary. The running coupling of q>2GeV can be fitted by the perturbative QCD(pQCD) + c/q^2 correction. We find the Kugo-Ojima parameter u(0)=-0.83(3). The rotational symmetry of the gluon propagator of the unquenched SU(3) is partially recovered, but its magnitude depends on whether the Wilson fermion or the Kogut-Susskind(KS) fermion are coupled to the gauge field. The gluon propagator coupled to KS fermion is more suppressed than that coupled to Wilson fermion. The running coupling inherits the same trend. The unquenched running coupling of the of q>3GeV can be fitted by the pQCD without c/q^2 term. The Kugo-Ojima parameter of unquenched configurations with light fermion masses is consistent with u(0)=-1.0.

hep-lat↗
arXiv2004

What the Gribov copy tells on the confinment and the theory of dynamical chiral symmetry breaking

We performed lattice Landau gauge QCD simulation on β=6.0, 16^4, 24^4, 32^4 and β=6.4, 32^4, 48^4 and 56^4 by adopting the gauge fixing that minimizes the norm of the gauge field, and measured the running coupling by using the gluon propagator and the ghost propagator. In view of ambiguity in the vertex renormalization factor \tilde Z_1 in the lattice, we adjust the normalization of the running coupling by the perturbative QCD results near the highest momentum point. It has a maximum α_s(q)~ 2.1(3) at around q=0.5 GeV and decreases as q approaches 0, and the Kugo-Ojima parameter reached -0.83(2). The infrared exponent of the ghost propagator at 0.4GeV region is α_G=0.20 but there is an exceptional Gribov copy with α_G=0.27. The features of the exceptional Gribov copy are investigated by measuring four one-dimensional Fourier transform(1-d FT) of the gluon propagator transverse to each lattice axis. We observe, in general, correlation between absolute value of the Kugo-Ojima parameter and the degree of reflection positivity violation in the 1-d FT of the gluon propagator. The 1-d FT of the exceptional Gribov copy has an axis whose gluon propagator manifestly violates reflection positivity, and the average of the Cartan subalgebra components of the Kugo-Ojima parameter along this axis is consistent to -1. The running coupling of the enemble average shows a suppression at 0 momentum, but when the ghost propagator of the exceptional Gribov copy is adopted, the suppression disappears and the data implies presence of the infrared fixed point α_s(0)~ 2.5(5) and κ=0.5 suggested by the Dyson-Schwinger approach in the multiplicative renormalizable scheme. Comparison with the SU(2) QCD and N_f=2 unquenched SU(3) QCD are also made.

hep-lat↗
arXiv2004

Numerical Study of Lattice Landau Gauge QCD and the Gribov Copy Problem

The infrared properties of lattice Landau gauge QCD of SU(3) are studied by measuring gluon propagator, ghost propagator, QCD running coupling and Kugo-Ojima parameter of $β=6.0, 16^4,24^4,32^4$ and $β=6.4, 32^4, 48^4, 56^4$ lattices. By the larger lattice measurements, we observe that the runnning coupling measured by the product of the gluon dressing function and the ghost dressing function squared rescaled to the perturbative QCD results near the highest lattice momentum has the maximum of about 2.2 at around $q=0.5$ GeV/c, and behaves either approaching constant or even decreasing as $q$ approaches zero. The magnitude of the Kugo-Ojima parameter is getting larger but staying around -0.83 in contrast to the expected value -1 in the continuum theory. We observe, however, there is an exceptional sample which has larger magnitude of the Kugo-Ojima parameter and stronger infrared singularity of the ghost propagator. The reflection positivity of the 1-d Fourier transform of the gluon propagator of the exceptional sample is manifestly violated. Gribov noise problem was studied by performing the fundamental modular gauge (FMG) fixing with use of the parallel tempering method of $β=2.2, 16^4$ SU(2) configurations. Findings are that the gluon propagator almost does not suffer noises, but the Kugo-Ojima parameter and the ghost propagator in the FMG becomes $\sim 5$% less in the infrared region than those suffering noises. It is expected that these qualitative aspects seen in SU(2) will reflect in the infrared properties of SU(3) QCD as well.

hep-lat↗
arXiv2004

Infrared Features of the Landau Gauge QCD

The infrared features of Landau gauge QCD are studied by the lattice simulation of $β=6.0, 16^4, 24^4, 32^4$ and $β=6.4, 32^4, 48^4$. We adopt two definitions of the gauge field; 1) $U-$linear 2) $\log U$ and measured the gluon propagator and ghost propagator. Infrared singularity of the gluon propagator is less than that of tree level result but the gluon propagator at 0 momentum remains finite. The infrared singularity of ghost propagator is stronger than the tree level. The QCD running coupling measured by using the gluon propagator and the ghost propagator has a maximum $α_s(p)\simeq 1$ at around $p=0.5GeV$ and decreases as $p$ approaches 0. The data are analyzed in use of formula of the principle of minimal sensitivity(PMS), the effective charge method and the contour-improved perturbation method, which suggest necessity of the resummation of perturbation series in the infrared region together with existence of the infrared fixed point. Kugo-Ojima parameter saturates at about -0.8 in contrast to the theoretically expected value -1.

hep-lat↗
arXiv2003

Infrared Features of the Lattice Landau Gauge QCD

The infrared properties of lattice Landau gauge QCD of SU(3) are studied by measuring gluon propagator, ghost propagator, QCD running coupling and Kugo-Ojima parameter of $β=6.0, 16^4,24^4,32^4$ and $β=6.4, 32^4,48^4$ lattices. We study Gribov copy problem by parallel tempering (PT) gauge fixing of $β=2.2, 16^4$ SU(2) configurations. Rather unexpected features of the unique gauge(fundamental modular gauge, FMG) are observed in relation of physical values vs the optimizing function.

hep-lat↗
arXiv2003

Infrared Features of Lattice Landau Gauge QCD and the Gribov Copy Problem

Infrared features of gluon propagator, ghost propagator, QCD running coupling and the Kugo-Ojima parameter in lattice Landau gauge QCD are presented. The framework of PMS analysis suggests that there appear infrared, intermediate and ultraviolet regions specified by $Λ_{\bar{MS}}$, $β_0$ and $β_1$. The propagators and the running coupling of $q>1GeV$ are fitted by the $\widetilde{MOM}$ scheme using the factorization scale as the scale parameter. The running coupling data of $q<14GeV$ are fitted by the contour improved perturbation method. The Gribov copy problem is studied in SU(2), $β= 2.2$ samples by comparing the data gauge fixed by the parallel tempering method and the data gauge fixed by the straightforward gauge fixing. The Gribov noise effect turned out to be about 2%.

hep-lat↗
arXiv2003

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.

hep-lat↗
arXiv2002

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.

hep-lat↗