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Using SU(3) lattice QCD, we study for the first time the effective potential of the Polyakov loop $\langle P \rangle$ at finite temperature, i.e., the thermodynamic potential, in the field-theoretical way. In the framework of the reweighting method in lattice QCD, we express the effective potential $V_{\rm eff}(\langle P \rangle)$ using the expectation value without a source term. In particular, we consider the most difficult and interesting case of vacuum coexistence at the critical temperature $T_c$. We adopt SU(3) quenched lattice QCD on $48^3 \times 6$ at $\beta$= 5.89379, which corresponds exactly to the critical temperature $T_c$ of the deconfinement phase transition, and use 200,000 Monte Carlo configurations. After categorizing the gauge configurations into one $Z_3$-symmetric and three $Z_3$-broken vacua each, we perform a vacuum-associated reweighting method, using the gauge configurations around each vacuum separately. Finally, we obtain the Polyakov-loop effective potential, which is well depicted around the $Z_3$-symmetric and $Z_3$-broken vacua., Comment: 11 pages, 4 figures, prepared for XIIth Int. Conf. on New Frontiers in Physics (ICNFP2023)

Motivated by one-dimensional color-electric flux-tube formation in four-dimensional (4D) QCD, we investigate a possibility of effective dimensional reduction in the 4D Yang-Mills (YM) theory. We propose a new gauge fixing of "dimensional reduction (DR) gauge" defined so as to minimize $R_{\mathrm{DR}}~\equiv~\int d^{4}s ~ \mathrm{Tr} \left[ A_{x}^{2}(s) + A_{y}^{2}(s) \right]$, which has a residual gauge symmetry for the gauge function $\Omega (t,z)$ like 2D QCD on the $t$-$z$ plane. We investigate effective dimensional reduction in the DR gauge using SU(3) quenched lattice QCD at $\beta = 6.0$. The amplitude of $A_{x}(s)$ and $A_{y}(s)$ are found to be strongly suppressed in the DR gauge. We consider "$tz$-projection" of $A_{x,y}(s) \to 0$ for the gauge configuration generated in the DR gauge, in a similar sense to Abelian projection in the maximally Abelian gauge. By the $tz$-projection in the DR gauge, the interquark potential is not changed, and $A_{t}(s)$ and $A_{z}(s)$ play a dominant role in quark confinement. In the DR gauge, we calculate a spatial correlation $\langle \mathrm{Tr} A_{\perp}(s) A_{\perp}(s+ra_{\perp}) \rangle ~ (\perp = x,y)$ and estimate the spatial mass of $A_{\perp}(s) ~ (\perp = x,y)$ as $M \simeq 1.7 ~ \mathrm{GeV}$. It is conjectured that this large mass makes $A_{\perp}(s)$ inactive and realizes the dominance of $A_{t}(s)$ and $A_{z}(s)$ in infrared region in the DR gauge. We also calculate the spatial correlation of two temporal link-variables and find that the correlation decreases as $\exp (-mr)$ with $m \simeq 0.6 ~ \mathrm{GeV}$. Using a crude approximation, the 4D YM theory is reduced into an ensemble of 2D YM systems with the coupling of $g_{\rm 2D} = g m$., Comment: 15 pages, 11 figures

The deconfinement transition in non-Abelian gauge theory is understood as spontaneous breaking of $\mathbb{Z}_N$ symmetry at high temperatures. Accordingly, quark-gluon plasma generally includes some partial cells called center domains, each with a homogeneous Polyakov-loop expectation value. In this work, constructing an effective action describing the deconfinement vacuum of Yang-Mills theory with $N$ colors, we discuss the properties of center domains. First, we evaluate the spatial correlation of local Polyakov-loop fluctuation and demonstrate that some fluctuation becomes a Nambu-Goldstone-like mode in the large-$N$ limit. We also discuss surface tension between two $\mathbb{Z}_N$ center domains. Second, we estimate the global vacuum-to-vacuum transition in a single center domain. We find that some threshold volume exists, where a domain larger than this volume is stable, and vice versa. Identifying the threshold as the lower bound of a stable center domain volume, we quantitatively argue the typical volume scale of center domains., Comment: 7 pages, 4 figures; Proceedings of the 40th International Symposium on Lattice Field Theory (LATTICE2023)

We investigate a baryon and its dilatation modes in holographic QCD based on the Sakai-Sugimoto model, which is expressed as a 1+4 dimensional U($N_f$) gauge theory in the flavor space. For spatially rotational symmetric systems, we apply a generalized version of the Witten Ansatz, and reduce 1+4 dimensional holographic QCD into a 1+2 dimensional Abelian Higgs theory in a curved space. In the reduced theory, the holographic baryon is described as a two-dimensional topological object of an Abrikosov vortex. We numerically calculate the baryon solution of holographic QCD using a fine and large lattice with spacing of 0.04 fm and size of 10 fm. Using the relation between the baryon size and the zero-point location of the Higgs field in the description with the Witten Ansatz, we investigate a various-size baryon through this vortex description. As time-dependent size-oscillation modes (dilatation modes) of a baryon, we numerically obtain the lowest excitation energy of 577 MeV and deduce the dilatational excitation of a nucleon to be the Roper resonance N$^*$(1440)., Comment: 22 pages, 14 figures

Using the Polyakov-loop effective action, we investigate the structure of spontaneously broken $\mathbb{Z}_N$ symmetry in the deconfinement vacuum in the SU($N$) Yang-Mills theory with finite $N$. First, we examine the Polyakov-loop fluctuation around a $\mathbb{Z}_N$-broken vacuum and calculate the spatial correlation of its phase variable. We show that the phase variable of the Polyakov loop becomes a Nambu-Goldstone mode in the large-$N$ limit. Second, we estimate the global vacuum-to-vacuum transition rate in a finite-volume domain of the quark-gluon plasma. Based on our estimation, we state that some threshold volume exists, a domain larger than which is stable, and vice versa. Identifying the threshold as the lower bound of a stable center domain volume, we find the typical volume scale of center domains., Comment: 14 pages, 9 figures

Using SU(3) lattice QCD, we investigate role of spatial gluons for hadron masses in the Coulomb gauge, considering the relation between QCD and the quark model. From the Coulomb-gauge configurations at the quenched level on a $16^3 \times 32$ lattice at $\beta$ = 6.0, we consider the $\vec{A} = 0$ projection, where all the spatial gluon fields are set to zero. In this projection, the inter-quark potential is unchanged. We investigate light hadron masses and find that nucleon and delta baryon masses are almost degenerate. This result suggests that the N-$\Delta$ mass difference arises from the color-magnetic interactions, which is consistent with the quark model picture. Next, as a generalization of this projection, we expand spatial gluon fields in terms of Faddeev-Popov eigenmodes and leave only some partial components. We find that the ${\rm N}-\Delta$ and $0^{++}-2^{++}$ glueball mass splittings are almost reproduced only with 1 \% low-lying components. This suggests that low-lying color-magnetic interaction leads to the hadron mass splitting., Comment: 8 pages, 5 figures, contribution to the proceedings of the 15th Quark Confinement and the Hadron Spectrum conference (ConfXV), 1st-6th August 2022, Stavanger, Norway

Aiming at the relation between QCD and the quark model, we consider projections of gauge configurations generated in quenched lattice QCD simulations in the Coulomb gauge on a 16$^{\rm 3}$ $\rm \times$ 32, $\rm \beta$ = 6.0 lattice. First, we focus on a fact that the static quark-antiquark potential is independent of spatial gauge fields. We explicitly confirm this by performing $\vec{A}$ = 0 projection, where spatial gauge fields are all set to zero. We also apply the $\vec{A}$ = 0 projection to light hadron masses and find that nucleon and delta baryon masses are almost degenerate, suggesting vanishing of the color-magnetic interactions. After considering the physical meaning of the $\vec{A}$ = 0 projection, we next propose a generalized projection, where spatial gauge fields are expanded in terms of Faddeev-Popov eigenmodes and only some eigenmodes are left. We apply the proposed projection to light hadron and glueball masses and find that the N-$\rm \Delta$ and 0$^{\rm ++}$-2$^{\rm ++}$ mass splittings become evident when projected with more than 33 (0.10 \%) low-lying eigenmodes, suggesting emergence of the color-magnetic interactions. We also find that the original hadron masses are approximately reproduced with just 328 (1.00 \%) low-lying eigenmodes. These findings indicate an important role of low-lying eigenmodes on hadron masses and would be useful in clarifying the relation between QCD and the quark model., Comment: 22 pages, 9 figures, and 2 tables, to appear in EPJA

Using the lattice gauge field theory, we study the relation among the local chiral condensate, monopoles, and color magnetic fields in quantum chromodynamics (QCD). First, we investigate idealized Abelian gauge systems of 1) a static monopole-antimonopole pair and 2) a magnetic flux without monopoles, on a four-dimensional Euclidean lattice. In these systems, we calculate the local chiral condensate on quasi-massless fermions coupled to the Abelian gauge field, and find that the chiral condensate is localized in the vicinity of the magnetic field. Second, using SU(3) lattice QCD Monte Carlo calculations, we investigate Abelian projected QCD in the maximally Abelian gauge, and find clear correlation of distribution similarity among the local chiral condensate, monopoles, and color magnetic fields in the Abelianized gauge configuration. As a statistical indicator, we measure the correlation coefficient $r$, and find a strong positive correlation of $r \simeq 0.8$ between the local chiral condensate and an Euclidean color-magnetic quantity ${\cal F}$ in Abelian projected QCD. The correlation is also investigated for the deconfined phase in thermal QCD. As an interesting conjecture, like magnetic catalysis, the chiral condensate is locally enhanced by the strong color-magnetic field around the monopoles in QCD., Comment: 15 pages, 7 figures

We study spontaneous chiral-symmetry breaking in SU(3) QCD in terms of the dual superconductor picture for quark confinement in the maximally Abelian (MA) gauge, using lattice QCD Monte Carlo simulations with four different lattices of $16^4$, $24^4$, $24^3\times 6$ at $\beta=6.0$ (i.e., the spacing $a \simeq$ 0.1 fm), and $32^4$ at $\beta=6.2$ (i.e., $a \simeq$ 0.075 fm), at the quenched level. First, in the confinement phase, we find Abelian dominance and monopole dominance in the MA gauge for the chiral condensate in the chiral limit,using the two different methods of i) the Banks-Casher relation with the Dirac eigenvalue density and ii) finite quark-mass calculations with the quark propagator and its chiral extrapolation. In the high-temperature deconfined phase, the chiral restoration is observed also for the Abelian and the monopole sectors. Second, we investigate local correlation between the chiral condensate and monopoles, which topologically appear in the MA gauge. We find that the chiral condensate locally takes a quite large value near monopoles. As an interesting possibility, the strong magnetic field around monopoles is responsible to chiral symmetry breaking in QCD, similarly to the magnetic catalysis., Comment: 8 pages, 4 figures

We study topological objects in holographic QCD based on the Sakai-Sugimoto model, which is constructed with $N_c$ D4 branes and $N_f$ D8/$\bar{\rm D8}$ branes in the superstring theory, and is infrared equivalent to 1+3 dimensional massless QCD. Using the gauge/gravity duality, holographic QCD is described as 1+4 dimensional U($N_f$) gauge theory in flavor space with a background gravity, and its instanton solutions correspond to baryons. First, using the Witten Ansatz, we reduce holographic QCD into a 1+2 dimensional Abelian Higgs theory in a curved space and consider its topological aspect. We numerically obtain the Abrikosov vortex solution and investigate single baryon properties. Second, we study a single meron and two merons in holographic QCD. The single meron carrying a half-integer baryon number is found to have a infinite energy also in holographic QCD. We propose a new-type baryon excitation of the two-merons oscillation in the extra-direction of holographic QCD., Comment: 16 pages, 6 figures

We present the first study of the Abelian-projected gluonic-excitation energies for the static quark-antiquark (Q$\bar{\rm Q}$) system in SU(3) lattice QCD at the quenched level, using a $32^4$ lattice at $\beta = 6.0$. We investigate ground-state and three excited-state Q$\bar{\rm Q}$ potentials, using smeared link variables on the lattice. We find universal Abelian dominance for the quark confinement force of the excited-state Q$\bar{\rm Q}$ potentials as well as the ground-state potential. Remarkably, in spite of the excitation phenomenon in QCD, we find Abelian dominance for the first gluonic-excitation energy of about 1 GeV at long distances in the maximally Abelian gauge. On the other hand, no Abelian dominance is observed for higher gluonic-excitation energies even at long distances. This suggests that there is some threshold between 1 and 2 GeV for the applicable excitation-energy region of Abelian dominance. Also, we find that Abelian projection significantly reduces the short-distance $1/r$-like behavior in gluonic-excitation energies., Comment: 7 pages, 3 figures

The non-abelian Higgs (NAH) theory is studied in a strong magnetic field. For simplicity, we study the SU(2) NAH theory with the Higgs triplet in a constant strong magnetic field $\vec B$, where the lowest-Landau-level (LLL) approximation can be used. Without magnetic fields, charged vector fields $A_\mu^\pm$ have a large mass $M$ due to Higgs condensation, while the photon field $A_\mu$ remains to be massless. In a strong constant magnetic field near and below the critical value $eB_c \equiv M^2$, the charged vector fields $A_\mu^\pm$ behave as 1+1-dimensional quasi-massless fields, and give a strong correlation along the magnetic-field direction between off-diagonal charges coupled with $A_\mu^\pm$. This may lead a new type of confinement caused by charged vector fields $A_\mu^\pm$., Comment: 8 pages, 2 figures

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 $Q\bar Q$ 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 $Q\bar Q$ 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 ($k_\mu \ne 0$, $j_\mu=0$) and the photon part ($j_\mu \ne 0$, $k_\mu=0$). We find monopole dominance of the string tension for $Q\bar Q$ and 3Q systems: $\sigma_{Mo}\simeq 0.92\sigma$. While the photon part has almost no confining force, the monopole part almost keeps the confining force., Comment: 8 pages, 8 figures

We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various "confinement indicators", such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue $\lambda_n$ such as $\lambda_n^{N_t-1}$, which behaves as a reduction factor for small $\lambda_n$. Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly small contribution to the confinement quantities,while they are essential for chiral symmetry breaking. These relations indicate no direct, one-to-one correspondence between confinement and chiral symmetry breaking in QCD. In other words, there is some independence of quark confinement from chiral symmetry breaking, which can generally lead to different transition temperatures/densities for deconfinement and chiral restoration. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, respectively, and find the similar results. The independence of quark confinement from chiral symmetry breaking seems to be natural, because confinement is realized independently of quark masses and heavy quarks are also confined even without the chiral symmetry., Comment: 20 pages, 10 figures. arXiv admin note: text overlap with arXiv:1611.08742

We propose a "matter-antimatter coexistence method" for finite-density lattice QCD, aiming at a possible solution of the sign problem. In this method, we consider matter and anti-matter systems on two parallel ${\bf R}^4$-sheets in five-dimensional Euclidean space-time. For the matter system $M$ with a chemical potential $\mu \in {\bf C}$ on a ${\bf R}^4$-sheet, we also prepare the anti-matter system $\bar M$ with $-\mu^*$ on the other ${\bf R}^4$-sheet shifted in the fifth direction. In the lattice QCD formalism, we introduce a correlation term between the gauge variables $U_\nu \equiv e^{iagA_\nu}$ in $M$ and $\tilde U_\nu \equiv e^{iag \tilde A_\nu}$ in $\bar M$, such as $S_\lambda \equiv \sum_{x,\nu} 2\lambda \{N_c-{\rm Re~tr} [U_\nu(x) \tilde U_\nu^\dagger(x)]\} \simeq \sum_x \frac{1}{2}\lambda a^2 \{A_\nu^a(x)-\tilde A_\nu^a(x)\}^2$ with a real parameter $\lambda$. In the limit of $\lambda \rightarrow \infty$, a strong constraint $\tilde U_\nu(x)=U_\nu(x)$ is realized, and the total fermionic determinant is real and non-negative. In the limit of $\lambda \rightarrow 0$, this system goes to two separated ordinary QCD systems with the chemical potential of $\mu$ and $-\mu^*$. On a finite-volume lattice, if one takes an enough large value of $\lambda$, $\tilde U_\nu(x) \simeq U_\nu(x)$ is realized and there occurs a phase cancellation approximately between two fermionic determinants in $M$ and $\bar M$, which is expected to suppress the sign problem and to make the lattice calculation possible. For the obtained gauge configurations of the coexistence system, matter-side quantities are evaluated through their measurement only for the matter part $M$. By the calculations with gradually decreasing $\lambda$ and their extrapolation to $\lambda=0$, physical quantities in finite density QCD are expected to be estimated., Comment: 6 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1705.07516

Toward the lattice QCD calculation at finite density, we propose "matter-antimatter coexistence method", where matter and anti-matter systems are prepared on two parallel ${\bf R}^4$-sheets in five-dimensional Euclidean space-time. We put a matter system $M$ with a chemical potential $\mu \in {\bf C}$ on a ${\bf R}^4$-sheet, and also put an anti-matter system $\bar M$ with $-\mu^*$ on the other ${\bf R}^4$-sheet shifted in the fifth direction. Between the gauge variables $U_\nu \equiv e^{iagA_\nu}$ in $M$ and $\tilde U_\nu \equiv e^{iag \tilde A_\nu}$ in $\bar M$, we introduce a correlation term with a real parameter $\lambda$. In one limit of $\lambda \rightarrow \infty$, a strong constraint $\tilde U_\nu(x)=U_\nu(x)$ is realized, and therefore the total fermionic determinant becomes real and non-negative, due to the cancellation of the phase factors in $M$ and $\bar M$, although this system resembles QCD with an isospin chemical potential. In another limit of $\lambda \rightarrow 0$, this system goes to two separated ordinary QCD systems with the chemical potential of $\mu$ and $-\mu^*$. For a given finite-volume lattice, if one takes an enough large value of $\lambda$, $\tilde U_\nu(x) \simeq U_\nu(x)$ is realized and phase cancellation approximately occurs between two fermionic determinants in $M$ and $\bar M$, which suppresses the sign problem and is expected to make the lattice calculation possible. For the obtained gauge configurations of the coexistence system, matter-side quantities are evaluated through their measurement only for the matter part $M$. The physical quantities in finite density QCD are expected to be estimated by the calculations with gradually decreasing $\lambda$ and the extrapolation to $\lambda=0$. We also consider more sophisticated improvement of this method using an irrelevant-type correlation., Comment: 4 pages

We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD, which seems to be natural because confinement is realized independently of the quark mass.

The H-dibaryon (uuddss) is studied in holographic QCD for the first time. In holographic QCD, four-dimensional QCD, i.e., SU($N_c$) gauge theory with chiral quarks, can be formulated with $S^1$-compactified D4/D8/$\overline{\rm D8}$-brane system. In holographic QCD with large $N_c$, all the baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons, and the H-dibaryon can be described as an SO(3)-type topological soliton with $B=2$. We derive the low-energy effective theory to describe the H-dibaryon in holographic QCD. The H-dibaryon mass is found to be twice of the $B=1$ hedgehog-baryon mass, $M_{\rm H} \simeq 2.00 M_{B=1}^{\rm HH}$, and is estimated about 1.7GeV, which is smaller than mass of two nucleons (flavor-octet baryons), in the chiral limit., Comment: 6 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1610.00475

We study interplay between confinement/deconfinement and chiral properties. We derive some analytical relations of the Dirac modes with the confinement quantities, such as the Polyakov loop, its susceptibility and the string tension. For the confinement quantities, the low-lying Dirac eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. This indicates no direct, one-to-one correspondence between confinement/deconfinement and chiral properties in QCD. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, respectively., Comment: 5 pages, 3 figures

We study baryons in holographic QCD corresponding to 1+1 dimensional single-flavor ($N_f$=1) QCD for the first time. We formulate 1+1 QCD using an $S^1$-compactified D2/D8/$\overline{\rm D8}$ branes in the superstring theory, and describe the baryon as a topological configuration in 1+1 $N_f$=1 QCD, corresponding to $\Pi_1({\rm U(1)})={\bf Z}$. Unlike 1+3 QCD with $N_f \ge 2$, however, we find that the low-dimensional baryonic soliton is generally unstable against a scale transformation/variation and swells infinitely in 1+1 $N_f$=1 QCD at the leading of large $N_c$. We thus point out a serious difficulty on the soliton picture of baryons in large $N_c$ in the single-flavor world in both 1+1 and 1+3 QCD. We also compare the low-dimensional holographic baryon with the Abrikosov vortex, i.e., a stable topological configuration in Type-II superconductors., Comment: 5 pages, 3 figures

We study the H-dibaryon (uuddss) in holographic QCD for the first time. Holographic QCD is derived from a QCD-equivalent D-brane system ($S^1$-compactified D4/D8/$\overline{\rm D8}$) in the superstring theory via the gauge/gravity correspondence. In holographic QCD, all baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons. In this framework, the H-dibaryon can be described as an SO(3)-type hedgehog state. We present the formalism of the H-dibaryon in holographic QCD, and perform the calculation to investigate its properties in the chiral limit., Comment: 5 pages, 2 figures

We study the static three-quark (3Q) potential for more than 300 different patterns of 3Q systems with high statistics, i.e., 1000-2000 gauge configurations, in SU(3) lattice QCD at the quenched level. For all the distances, the 3Q potential is found to be well described by the Y-ansatz, i.e., one-gluon-exchange (OGE) Coulomb plus Y-type linear potential. Also, we investigate Abelian projection of quark confinement in the context of the dual superconductor picture proposed by Yoichiro~Nambu~{\it et al.} in SU(3) lattice QCD. Remarkably, quark confinement forces in both Q$\bar{\rm Q}$ and 3Q systems can be described only with Abelian variables in the maximally Abelian gauge, i.e., $\sigma_{\rm Q \bar Q} \simeq \sigma_{\rm Q \bar Q}^{\rm Abel} \simeq \sigma_{\rm 3Q} \simeq \sigma_{\rm 3Q}^{\rm Abel}$, which we call ``perfect Abelian dominance'' of quark confinement., Comment: 7 pages, 4 figures

Dirac spectrum representations of the Polyakov loop fluctuations are derived on the temporally odd-number lattice, where the temporal length is odd with the periodic boundary condition. We investigate the Polyakov loop fluctuations based on these analytical relations. It is semianalytically and numerically found that the low-lying Dirac eigenmodes have little contribution to the Polyakov loop fluctuations, which are sensitive probe for the quark deconfinement. Our results suggest no direct one-to-one corresponding between quark confinement and chiral symmetry breaking in QCD., Comment: 7 pages and 1 figure. Proceeding of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International Conference Center, Kobe, Japan. Also regarded as the Proceeding of the 4th International Conference on new Frontiers in Physics (ICNFP 2015), 23-30 August 2015, Conference Center of the Orthodox Academy of Crete, Crete, Greece

We investigate correlations of the Polyakov loop fluctuations with eigenmodes of the lattice Dirac operator. Their analytic relations are derived on the temporally odd-number size lattice with the normal non-twisted periodic boundary condition for the link-variables. We find that the low-lying Dirac modes yield negligible contributions to the Polyakov loop fluctuations. This property is confirmed to be valid in confined and deconfined phase by numerical simulations in SU(3) quenched QCD. These results indicate that there is no direct, one-to-one correspondence between confinement and chiral symmetry breaking in QCD in the context of different properties of the Polyakov loop fluctuation ratios., Comment: 9 pages, 5 figures

We study the baryonic three-quark (3Q) potential and its Abelian projection in terms of the dual-superconductor picture in SU(3) quenched lattice QCD. The non-Abelian SU(3) gauge theory is projected onto Abelian U(1)$^2$ gauge theory in the maximal Abelian gauge. We investigate the 3Q potential and its Abelian part for more than 300 different patterns of static 3Q systems in total at $\beta=5.8$ on $16^332$ and at $\beta=6.0$ on $20^332$ with 1000-2000 gauge configurations. For all the distances, both the 3Q potential and Abelian part are found to be well described by the Y ansatz, i.e., two-body Coulomb term plus three-body Y-type linear term $\sigma_{3\mathrm{Q}} L_{\mathrm{min}}$, where $L_{\mathrm{min}}$ is the minimum flux-tube length connecting the three quarks. We find equivalence between the three-body string tension $\sigma_{3\mathrm{Q}}$ and its Abelian part $\sigma_{3\mathrm{Q}}^{\rm Abel}$ with an accuracy within a few percent deviation, i.e., $\sigma_{3\mathrm{Q}} \simeq \sigma_{3\mathrm{Q}}^{\rm Abel}$, which means Abelian dominance of the quark-confining force in 3Q systems., Comment: 7pages, 7figures, 3tables; published version

In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with $32^4$ at $\beta$=6.4 (i.e., $a \simeq$ 0.058 fm). We investigate the static quark-antiquark potential $V(r)$, its Abelian part $V_{\rm Abel}(r)$ and its off-diagonal part $V_{\rm off}(r)$, respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., $\sigma_{\rm Abel} \simeq \sigma$ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of $V(r) \simeq V_{\rm Abel}(r) + V_{\rm off}(r)$., Comment: Invited talk at International Conference on "Quark Confinement and the Hadron Spectrum XI" (confinement XI), St. Petersburg, Russia, 7-13 Sep. 2014

The Polyakov loop and the Dirac modes are connected via a simple analytical relation on the temporally odd-number lattice, where the temporal lattice size is odd with the normal (nontwisted) periodic boundary condition. Using this relation, we investigate the relation between quark confinement and chiral symmetry breaking in QCD. In this paper, we discuss the properties of this analytical relation and numerically investigate each Dirac-mode contribution to the Polyakov loop in both confinement and deconfinement phases at the quenched level. This relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop, and we numerically confirmed this fact. From our analysis, it is suggested that there is no direct one-to-one corresponding between quark confinement and chiral symmetry breaking in QCD. Also, in the confinement phase, we numerically find that there is a new "positive/negative symmetry" in the Dirac-mode matrix elements of link-variable operator which appear in the relation and the Polyakov loop becomes zero because of this symmetry. In the deconfinement phase, this symmetry is broken and the Polyakov loop is non-zero., Comment: 12 pages (AIP proceedings style), 5 figures, proceeding of Quark Confinement and the Hadron Spectrum XI, 8-12 September 2014, Saint-Petersburg State University, Russia

We study the Abelian projection of quark confinement in SU(3) quenched lattice QCD, in terms of the dual superconductor picture. In the maximal Abelian gauge, we perform the Cartan decomposition of the non-Abelian gauge field on a $32^4$ lattice with spacing $a \simeq0.058, 0.10$ fm (i.e., $\beta =6.4, 6.0$), and investigate the interquark potential $V(r)$, the Abelian part $V_{\mathrm{Abel}}(r)$, and the off-diagonal part $V_{\mathrm{off}}(r)$. For the potential analysis, we use both on-axis data and several types of off-axis data, with larger numbers of gauge configurations. Remarkably, we find almost perfect Abelian dominance of the string tension (quark-confining force) on the large-volume lattice. Also, we find a simple but nontrivial relation of $V(r) \simeq V_{\mathrm{Abel}}(r) + V_{\mathrm{off}}(r)$., Comment: 6 pages, 4 figures; published version

In the lattice QCD formalism, we investigate the relation between confinement and chiral symmetry breaking. A gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes is derived on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition for link-variables. This analytical relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop, and it is numerically confirmed at the quenched level in both confinement and deconfinement phases. This fact indicates no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD. Using the relation, we also investigate the contribution from each Dirac mode to the Polyakov loop. In the confinement phase, we find a new "positive/negative symmetry" of the Dirac-mode matrix element of the link-variable operator, and this symmetry leads to the zero value of the Polyakov loop. In the deconfinement phase, there is no such symmetry and the Polyakov loop is nonzero. Also, we develop a new method for spin-diagonalizing the Dirac operator on the temporally odd-number lattice modifying the Kogut-Susskind formalism., Comment: 15pages, 9 figures

We derive an analytical gauge-invariant formula between the Polyakov loop $L_P$ and the Dirac eigenvalues $\lambda_n$ in QCD, i.e., $L_P \propto \sum_n \lambda_n^{N_t -1} \langle n|\hat U_4|n \rangle$, in ordinary periodic square lattice QCD with odd-number temporal size $N_t$. Here, $|n\rangle$ denotes the Dirac eigenstate, and $\hat U_4$ temporal link-variable operator. This formula is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes $|n\rangle$. Because of the factor $\lambda_n^{N_t -1}$ in the Dirac spectral sum, this formula indicates negligibly small contribution of low-lying Dirac modes to the Polyakov loop in both confinement and deconfinement phases, while these modes are essential for chiral symmetry breaking. Next, we find a similar formula between the Wilson loop and Dirac modes on arbitrary square lattices, without restriction of odd-number size. This formula suggests a small contribution of low-lying Dirac modes to the string tension $\sigma$, or the confining force. These findings support no crucial role of low-lying Dirac modes for confinement, i.e., no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD, which seems to be natural because heavy quarks are also confined even without light quarks or the chiral symmetry., Comment: 16 pages, 4 figures

As a topic of "quantum color dynamics", we study various mass generation of colored particles and gluonic dressing effect in a non-perturbative manner, using the Schwinger-Dyson (SD) formalism in (scalar) QCD. First, we review dynamical quark-mass generation in QCD in the SD approach as a typical fermion-mass generation via spontaneous chiral-symmetry breaking. Second, using the SD formalism for scalar QCD, we investigate the scalar diquark, a bound-state-like object of two quarks, and its mass generation, which is clearly non-chiral-origin. Here, the scalar diquark is treated as an extended colored scalar field, like a meson in effective hadron models, and its effective size $R$ is introduced as a form factor. As a diagrammatical difference, the SD equation for the scalar diquark has an additional 4-point interaction term, in comparison with the single quark case. The diquark size $R$ is taken to be smaller than a hadron, $R\sim 1$ fm, and larger than a constituent quark, $R\sim 0.3$ fm. We find that the compact diquark with $R\simeq 0.3$ fm has a large effective mass of about 900 MeV, and therefore such a compact diquark is not acceptable in effective models for hadrons. We also consider the artificial removal of 3- and 4-point interaction, respectively, to see the role of each term, and find that the 4-point interaction plays the dominant role of the diquark self-energy. From the above two different cases, quarks and diquarks, we guess that the mass generation of colored particles is a general result of non-perturbative gluonic dressing effect., Comment: 17 pages, 15 figures

We calculate the tensor and axial charges of the quark in the Schwinger-Dyson formalism of Landau gauge QCD. It is found that the dressed tensor and isovector axial charges of the quark are suppressed against the bare quark contribution, and the result agrees qualitatively with the experimental data. We show that this is due to the superposition of the spin flip of the quark arising from the successive emission of gluons which dress the vertex. For the isoscalar quark axial charge, we have analyzed the Schwinger-Dyson equation by including the leading unquenching quark-loop effect. It is found that the suppression is more significant, due to the axial anomaly effect., Comment: 5 pages, 4 figures, Contribution of proceedings of XV International Conference on Hadron Spectroscopy-Hadron 2013 (Hadron 2013)

We investigate the contribution from each Dirac modes to the Polyakov loop based on a gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition. The dumping factor in the relation plays crucial role for the negligible contribution of low-lying Dirac modes to the Polyakov loop. The zero-value of the Polyakov loop in the confinement phase is due to the ``positive/negative symmetry'' of the Dirac-mode contribution to the Polyakov loop. In the deconfinement phase, there is no such symmetry., Comment: 5 pages, 4 figures, Proc. of Hadron 2013. arXiv admin note: text overlap with arXiv:1311.4640

We study the relation between quark confinement and spontaneous chiral-symmetry breaking directly in QCD. In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $\lambda_n$, i.e., $\langle L_P \rangle \propto \sum_n \lambda_n^{N_t -1} \langle n|\hat U_4|n \rangle$, on a temporally odd-number lattice, where the temporal lattice size $N_t$ is odd. Here, $|n \rangle$ denotes the Dirac eigenmode, i.e., $\not D|n \rangle=i\lambda_n|n \rangle$, and $\hat U_4$ the temporal link-variable operator. We here use an ordinary square lattice with the normal periodic boundary condition for link-variables $U_\mu(s)$ in the temporal direction. Because of the factor $\lambda_n^{N_t -1}$ in the analytical relation, the contribution of low-lying Dirac modes to the Polyakov loop is negligibly small in both confined and deconfined phases, while the low-lying Dirac modes are essential for chiral symmetry breaking. Also, in lattice QCD simulations, we numerically confirm the analytical relation, non-zero finiteness of $\langle n|\hat U_4|n \rangle$ for each Dirac mode, and negligibly small contribution of low-lying Dirac modes to the Polyakov loop. Thus, we conclude that low-lying Dirac modes are not essential for confinement, which indicates no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD., Comment: 5 pages, Proc. of Hadron 2013. arXiv admin note: substantial text overlap with arXiv:1311.3838, arXiv:1401.2414

The diquark has been considered to be important effective degrees of freedom in hadron physics, especially for multi-quark physics and the structure of heavy hadronic states. Using the Schwinger-Dyson formalism, we investigate the non-perturbative effect of gluons for scalar diquarks with renormalization-group improved coupling in the Landau gauge. Here, we treat the scalar diquark as an effective degree of freedom with a peculiar size, while the diquark is originally a bound-state-like object of two quarks. Since the diquark has a non-zero color charge, it strongly interacts with gluons. We evaluate the gluonic non-perturbative effect to the diquark, considering the size effect of the diquark. We investigate the mass function of the diquark in both cases with a constant bare diquark mass and twice of the running quark self-energy. It is found that the diquark, especially the small diquark, obtains a large effective mass by the gluonic dressing effect. The scalar diquark mass seems to be dynamically generated by the non-perturbative effect, although it does not have the chiral symmetry., Comment: 5 pages, 5 figures, Contribution of proceedings of XV International Conference on Hadron Spectroscopy-Hadron 2013 (Hadron 2013)

We calculate the scalar, axial, and pseudoscalar charges of the quark in the Schwinger-Dyson formalism of Landau gauge QCD. It is found that the dressed quark scalar density of the valence quark is significantly enhanced against the bare quark contribution, and the result explains qualitatively the phenomenologically known value of the pion-nucleon sigma term and also that given by lattice QCD. Moreover, we show that the Richardson's interquark potential suppresses the quark scalar density in the Higashjima-Miransky approximation. This fact suggests that the quark scalar density is an observable that is sensitive to quark confinement. For the quark axial charge, we find that it is suppressed due to the gluon dynamics. The result of the quenched analysis agrees qualitatively with the experimental data of the isovector axial coupling constant $g_A$. We show that the suppression of the quenched axial charge is due to a mechanism similar to that of the quark tensor charge. In the Schwinger-Dyson equation with the leading unquenching quark-loop contribution the quark axial charge is more suppressed, due to the anomaly effect. The quark pseudoscalar density is found to be large, and is divergent as the bare quark becomes massless. This result is in agreement with the phenomenological current algebraic analysis, and explains well the dominance of the pion-pole contribution., Comment: 28 pages, 22 figures

In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $\lambda_n$ in QCD, i.e., $\langle L_P \rangle \propto \sum_n \lambda_n^{N_t -1} \langle n|\hat U_4|n \rangle$, by considering ${\rm Tr} (\hat{U}_4\hat{\not{D}}^{N_t-1})$ on a temporally odd-number lattice, where the temporal lattice size $N_t$ is odd. This formula is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes $|n\rangle$. We here use an ordinary square lattice with the normal (nontwisted) periodic boundary condition for link-variables $U_\mu(s)$ in the temporal direction. From this relation, one can estimate each contribution of the Dirac eigenmode to the Polyakov loop. Because of the factor $\lambda_n^{N_t -1}$ in the Dirac spectral sum, this analytical relation generally indicates quite small contribution of low-lying Dirac modes to the Polyakov loop in both confined and deconfined phases, while the low-lying Dirac modes are essential for chiral symmetry breaking. Also in lattice QCD calculations in confined and deconfined phases, we numerically confirm the analytical relation, non-zero finiteness of $\langle n|\hat U_4|n \rangle$ for each Dirac mode, and negligibly small contribution of low-lying Dirac modes to the Polyakov loop, i.e., the Polyakov loop is almost unchanged even by removing low-lying Dirac-mode contribution from the QCD vacuum generated by lattice QCD simulations. Thus, we conclude that low-lying Dirac modes are not essential modes for confinement, which indicates no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD., Comment: 12 pages, 8 figures, invited talk at QCD-TNT-III

To clarify the relation between confinement and chiral symmetry breaking in QCD, we consider a temporally odd-number lattice, with the temporal lattice size $N_t$ being odd. We here use an ordinary square lattice with the normal (nontwisted) periodic boundary condition for link-variables in the temporal direction. By considering ${\rm Tr} (\hat{U}_4\hat{\not D}^{N_t-1})$, we analytically derive a gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $\lambda_n$ in QCD, i.e., $\langle L_P \rangle \propto \sum_n \lambda_n^{N_t -1} \langle n|\hat U_4|n \rangle$, which is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes $|n\rangle$. Owing to the factor $\lambda_n^{N_t -1}$ in the Dirac spectral sum, this relation generally indicates fairly small contribution of low-lying Dirac modes to the Polyakov loop, while the low-lying Dirac modes are essential for chiral symmetry breaking. Also in lattice QCD calculations in both confined and deconfined phases, we numerically confirm the analytical relation, non-zero finiteness of $\langle n|\hat U_4|n \rangle$ for each Dirac mode, and negligibly small contribution from low-lying Dirac modes to the Polyakov loop, i.e., the Polyakov loop is almost unchanged even by removing low-lying Dirac-mode contribution from the QCD vacuum generated by lattice QCD simulations. We thus conclude that low-lying Dirac modes are not essential modes for confinement, which indicates no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD., Comment: 8 pages, 5 figures, Proc. of 2nd Int. Conf. on New Frontiers in Physics (ICNFP 2013). arXiv admin note: substantial text overlap with arXiv:1311.3838

In the lattice QCD formalism, we derive a gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition. This analytical relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop. Using lattice QCD simulations, we numerically confirm the analytical relation and the negligible contribution of low-lying Dirac modes to the Polyakov loop at the quenched level, i.e., the Polyakov loop is almost unchanged by removing low-lying Dirac-mode contribution from the QCD vacuum generated by lattice QCD in both confinement and deconfinement phases. Thus, we conclude that there is no one-to-one correspondence between confinement and chiral symmetry breaking in QCD. As a new method, modifying the Kogut-Susskind formalism, we develop a method for spin-diagonalizing the Dirac operator on the temporally odd-number lattice., Comment: 7 pages, proceeding of Lattice 2013

We derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $\lambda_n$ in QCD, i.e., $\langle L_P \rangle \propto \sum_n \lambda_n^{N_t -1} \langle n|\hat U_4|n \rangle$, on a temporally odd-number lattice, where the temporal lattice size $N_t$ is odd. Here, we use an ordinary square lattice with the normal (nontwisted) periodic boundary condition for link-variables in the temporal direction. This relation is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes $|n\rangle$. Because of the factor $\lambda_n^{N_t -1}$ in the Dirac spectral sum, this analytical relation indicates negligibly small contribution of low-lying Dirac modes to the Polyakov loop in both confined and deconfined phases, while the low-lying Dirac modes are essential for chiral symmetry breaking. Also, we numerically confirm the analytical relation, non-zero finiteness of $\langle n|\hat U_4|n \rangle$, and tiny contribution of low-lying Dirac modes to the Polyakov loop in lattice QCD simulations. Thus, we conclude that low-lying Dirac modes are not essential modes for confinement, and there is no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD., Comment: Proc. of LATTICE2013

We calculate the tensor charge of the quark in the QCD-like theory in the Landau gauge using the Schwinger-Dyson formalism. It is found that the dressed tensor charge of the quark is significantly suppressed against the bare quark contribution, and the result agrees qualitatively with the analyses in the collinear factorization approach and lattice QCD. We also analyze the quark confinement effect with the phenomenological strong coupling given by Richardson, and find that this contribution is small. We show that the suppression of the quark tensor charge is due to the superposition of the spin flip of the quark arising from the successive emission of gluons which dress the tensor vertex. We also consider the relation between the quark and the nucleon electric dipole moments by combining with the simple constituent quark model., Comment: 16 pages, 11 figures. arXiv admin note: text overlap with arXiv:1401.2852

Using the Dirac-mode expansion method, which keeps the gauge invariance, we analyze the Polyakov loop in terms of the Dirac modes in SU(3) quenched lattice QCD in both confined and deconfined phases. First, to investigate the direct correspondence between confinement and chiral symmetry breaking, we remove low-lying Dirac-modes from the confined vacuum generated by lattice QCD. In this system without low-lying Dirac modes, while the chiral condensate $\langle \bar{q} q\rangle$ is extremely reduced, we find that the Polyakov loop is almost zero and $Z_3$-center symmetry is unbroken, which indicates quark confinement. We also investigate the removal of ultraviolet (UV) Dirac-modes, and find that the Polyakov loop is almost zero. Second, we deal with the deconfined phase above $T_c$, and find that the behaviors of the Polyakov loop and $Z_3$-symmetry are not changed without low-lying or UV Dirac-modes. Finally, we develop a new method to remove low-lying Dirac modes from the Polyakov loop for a larger lattice of $12^3 \times 4$ at finite temperature, and find almost the same results. These results suggest that each eigenmode has the information of confinement, i.e., the "seed" of confinement is distributed in a wider region of the Dirac eigenmodes unlike chiral symmetry breaking, and there is no direct correspondence between confinement and chiral symmetry breaking through Dirac-eigenmodes., Comment: 22 pages, 14 figures

In SU(3) lattice QCD, we study diagonal and off-diagonal gluon propagators in the maximally Abelian (MA) gauge with U(1)$_3 \timesU(1)_8$ Landau gauge fixing. These propagators are studied both in the coordinate space and in the momentum space. The Monte Carlo simulation is performed on $16^4$ at $\beta$=6.0 and $32^4$ at $\beta$=5.8 and 6.0 at the quenched level. In the four-dimensional Euclidean space-time, the effective mass of diagonal gluons is estimated as $M_{\mathrm{diag}} \simeq 0.3\mathrm{GeV}$ and that of off-diagonal gluons as $M_{\mathrm{off}} \simeq 1\mathrm{GeV}$ in the region of $r =0.4-1.0$fm. In the momentum space, the effective mass of diagonal gluons is estimated as $M_{\mathrm{diag}} \simeq 0.3\mathrm{GeV}$ and that of off-diagonal gluons as $M_{\mathrm{off}} \simeq 1\mathrm{GeV}$ in the region of $p <1.1$GeV. The off-diagonal gluon propagator is relatively suppressed in the infrared region and seems to be finite at zero momentum, while the diagonal gluon propagator is enhanced. Furthermore, we also study the functional form of these propagators in momentum space. These propagators are well fitted by $Z/(p^2+m^2)^\nu$ with fit parameters, $Z, m$ and $\nu$ in the region of $p <3.0$GeV. From the fit results and lattice calculations, all of the spectral functions of diagonal and off-diagonal gluons would have negative regions., Comment: Continues and extends arXiv:1207.4377

Using the eigen-mode of the QCD Dirac operator $\Slash D=\gamma^\mu D^\mu$, we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculations. Even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking, we find that the Wilson loop obeys the area law, and the string tension or the confinement force is almost unchanged. We find also that the Polyakov loop remains to be almost zero even without the low-lying Dirac modes, which indicates the Z_3-unbroken confinement phase. These results indicate that one-to-one correspondence does not hold between confinement and chiral symmetry breaking in QCD., Comment: 8 pages, 20 figures, Prepared for Conference: Quark Confinement and the Hadron Spectrum X (Confinement X)

In both cases of quark-antiquark (Q-Qbar) and three-quark (3Q) systems, we study ground-state and low-lying excited-state potentials in terms of the gluon-momentum component in the Coulomb gauge in SU(3) quenched lattice QCD. By introducing UV-cut in the gluon-momentum space, we investigate the "UV-gluon sensitivity" of the ground-state and excited-state potentials quantitatively. Such a non-quark-origin excitation is a purely gluonic excitation, which can be interpreted as a stringy excitation in the color flux-tube picture of hadrons. For both Q-Qbar and 3Q systems, the IR part of the ground-state potential is almost unchanged, even after cutting off high-momentum gluon component. On the other hand, we find more significant change of excited-state potential by the cut of UV-gluons. However, even after the removal of UV-gluons, the magnitude of the low-lying gluonic excitation remains to be of the order of 1GeV., Comment: Talk given at Conference: Quark Confinement and the Hadron Spectrum X

In order to investigate the direct relation between confinement and chiral symmetry breaking in QCD, we investigate the Polyakov loop in terms of the Dirac eigenmodes in both confined and deconfined phases. Using the Dirac-mode expansion method in SU(3) lattice QCD, we analyze the contribution of low-lying and higher Dirac-modes to the Polyakov loop, respectively.In the confined phase below T_c, after removing low-lying Dirac-modes, the chiral condensate $< \bar{q} q>$ is largely reduced, however, the Polyakov loop remains almost zero and Z_3-center symmetry is unbroken. These results indicate that the system is still in the confined phase without low-lying Dirac-modes. By higher Dirac-modes cut, the Polyakov loop also remains almost zero below T_c. We also analyze the Polyakov loop in the deconfined phase above T_c. We find that the Polyakov loop and Z_3-symmetry behavior are insensitive to low-lying and higher Dirac-modes in both confined and deconfined phases., Comment: 8 pages, 4 figures, talk given at Quark Confinement and the Hadron Spectrum X, 8-12 October 2012, TUM Campus Garching, Munich, Germany

We investigate gluon propagators and the effective mass of the gluon fields in the MA gauge with U(1)$_3 \times$ U(1)$_8$ Landau gauge fixing in SU(3) lattice QCD. The Monte Carlo simulation is performed on $16^4$ at $\beta$=5.7, 5.8 and 6.0 and $32^4$ at $\beta=$5.8 and 6.0 at the quenched level. To calculate the propagators, we adopt a method to extract gauge fields from link-variables analytically in the SU(3) case. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\rm off} \simeq 1.1 - 1.2 {\rm GeV}$ in the region of $r = 0.3 - 0.8 {\rm fm}$, and the propagation is limited within a short range. On the other hand, the diagonal gluons behave as light vector bosons with $M_{\rm diag}\simeq 0.3 {\rm GeV} $ and the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function ${\rm exp}(-m_{\rm off} r)/r$ with $m_{\rm off} = 1.3 -1.4 {\rm GeV}$ for $r = 0.1- 0.8{\rm fm}$. This also indicates that the spectral function of off-diagonal gluons has the negative-value region., Comment: arXiv admin note: substantial text overlap with arXiv:1211.0116, arXiv:1207.4377

Using SU(3) quenched lattice QCD, we study ground-state and low-lying even-parity excited-state potentials of quark-antiquark systems in terms of the gluon-momentum component in the Coulomb gauge. By introducing UV-cut in the gluon-momentum space, we investigate the "UV-gluon sensitivity" of the ground-state and excited-state potentials and the stringy excitation quantitatively. Even after cutting off high-momentum gluon component above 1.5GeV, the IR part of the ground-state potential is almost unchanged. On the other hand, the change of excited-state potential is more significant by the cut of UV-gluons. However, even after the removal of UV-gluons, the magnitude of the low-lying gluonic excitation remains to be of the order of 1GeV., Comment: Talk given at Conference: Lattice 2012