Abelianization of QCD in the Maximally Abelian Gauge and the Nambu-'t Hooft Picture for Color Confinement

We study the Nambu-'t Hooft picture for color confinement in terms of the abelianization of QCD and monopole condensation in the maximally abelian (MA) gauge. In the MA gauge in the Euclidean metric, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to rapid reduction of the off-diagonal gluon correlation. In SU(2) and SU(3) lattice QCD in the MA gauge with the abelian Landau gauge, the Euclidean gluon propagator indicates a large effective mass of the off-diagonal gluon as $M_{\rm off} \simeq 1 {\rm GeV}$ in the intermediate distance as $0.2{\rm fm} \le r \le 0.8{\rm fm}$. Due to the infrared inactiveness of off-diagonal gluons, infrared QCD is well abelianized like nonabelian Higgs theories in the MA gauge. We investigate the inter-monopole potential and the dual gluon field $B_\mu$ in the MA gauge, and find longitudinal magnetic screening with $m_B \simeq$ 0.5 GeV in the infrared region, which indicates the dual Higgs mechanism by monopole condensation. We define the ``gluonic Higgs scalar field'' providing the MA projection, and find the correspondence between its hedgehog singularity and the monopole location in lattice QCD.Comment: Invited talk given at QCD02: High-Energy Physics International Conference in Quantum Chromodynamics, Montpellier, France, 2-9 Jul 200

The Role of Monopoles for Color Confinement

We study the role of the monopole for color confinement by using the monopole current system. For the self-energy of the monopole current less than ln$(2d-1)$, long and complicated monopole world-lines appear and the Wilson loop obeys the area law, and therefore the monopole current system almost reproduces essential features of confinement properties in the long-distance physics. In the short-distance physics, however, the monopole-current theory would become nonlocal due to the monopole size effect. This monopole size would provide a critical scale of QCD in terms of the dual Higgs mechanism.Comment: 3 pages LaTeX, 3 figures, uses espcrc2.sty, Talk presented at lattice97, Edinburgh, Scotland, July. 199

Behind the success of the quark model

The ground-state three-quark (3Q) potential $V_{\rm 3Q}^{\rm g.s.}$ and the excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ are studied using SU(3) lattice QCD at the quenched level. For more than 300 patterns of the 3Q systems, the ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ is investigated in detail in lattice QCD with $12^3\times 24$ at $\beta=5.7$ and with $16^3\times 32$ at $\beta=5.8, 6.0$. As a result, the ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ is found to be well described with Y-ansatz within the 1%-level deviation. From the comparison with the Q-$\rm\bar Q$ potential, we find the universality of the string tension as $\sigma_{\rm 3Q}\simeq\sigma_{\rm Q\bar Q}$ and the one-gluon-exchange result as $A_{\rm 3Q}\simeq\frac12 A_{\rm Q\bar Q}$. The excited-state potential $V_{\rm 3Q}^{\rm e.s.}$ is also studied in lattice QCD with $16^3\times 32$ at $\beta=5.8$ for 24 patterns of the 3Q systems.The energy gap between $V_{\rm 3Q}^{\rm g.s.}$ and $V_{\rm 3Q}^{\rm e.s.}$, which physically means the gluonic excitation energy, is found to be about 1GeV in the typical hadronic scale, which is relatively large compared with the excitation energy of the quark origin. This large gluonic excitation energy justifies the great success of the simple quark model.Comment: Talk given at 16th International Conference on Particles and Nuclei (PANIC 02), Osaka, Japan, 30 Sep - 4 Oct 200

Quark Confinement Physics from Quantum Chromodynamics

We show the construction of the dual superconducting theory for the confinement mechanism from QCD in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. We find that essence of infrared abelian dominance is naturally understood with the off-diagonal gluon mass $m_{\rm off} \simeq 1.2 {\rm GeV}$ induced by the MA gauge fixing. In the MA gauge, the off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon phase tends to be random. As the mathematical origin of abelian dominance for confinement, we demonstrate that the strong randomness of the off-diagonal gluon phase leads to abelian dominance for the string tension. In the MA gauge, there appears the macroscopic network of the monopole world-line covering the whole system. We investigate the monopole-current system in the MA gauge by analyzing the dual gluon field $B_\mu$. We evaluate the dual gluon mass as $m_B = 0.4 \sim$ 0.5GeV in the infrared region, which is the lattice-QCD evidence of the dual Higgs mechanism by monopole condensation. Owing to infrared abelian dominance and infrared monopole condensation, QCD in the MA gauge is describable with the dual Ginzburg-Landau theory.Comment: Invited talk given at KEK-Tanashi International Symposium on Physics of Hadrons and Nuclei, Tokyo, Japan, 14-17 Dec 199

Monopole Current Dynamics and Color Confinement

Color confinement can be understood by the dual Higgs theory, where monopole condensation leads to the exclusion of the electric flux from the QCD vacuum. We study the role of the monopole for color confinement by investigating the monopole current system. When the self-energy of the monopole current is small enough, long and complicated monopole world-lines appear, which is a signal of monopole condensation. In the dense monopole system, the Wilson loop obeys the area-law, and the string tension and the monopole density have similar behavior as the function of the self-energy, which seems that monopole condensation leads to color confinement. On the long-distance physics, the monopole current system almost reproduces essential features of confinement properties in lattice QCD. In the short-distance physics, however, the monopole-current theory would become nonlocal and complicated due to the monopole size effect. This monopole size would provide a critical scale of QCD in terms of the dual Higgs mechanism.Comment: 6 pages LaTeX, 5 figures, uses espcrc1.sty, Talk presented at International Conference on Quark Lepton Nuclear Physics, Osaka, May. 199

Y-type Flux-Tube Formation in Baryons

For more than 300 different patterns of the 3Q systems, the ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is investigated using SU(3) lattice QCD with $12^3\times 24$ at $\beta=5.7$ and $16^3\times 32$ at $\beta=5.8, 6.0$ at the quenched level. As a result of the detailed analyses, we find that the ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ is well described with so-called Y-ansatz as $V_{\rm 3Q}=-A_{\rm 3Q}\sum_{i<j}\frac1{|{\bf r}_i-{\bf r}_j|} +\sigma_{\rm 3Q} L_{\rm min}+C_{\rm 3Q}$, with the accuracy better than 1%. Here, $L_{\rm min}$ denotes the minimal value of total flux-tube length. We also studythe excited-state potential $V_{\rm 3Q}^{\rm e.s.}$ using lattice QCD with $16^3\times 32$ at $\beta=5.8, 6.0$ for more than 100 patterns of the 3Q systems. The energy gap between $V_{\rm 3Q}^{\rm g.s.}$ and $V_{\rm 3Q}^{\rm e.s.}$, which physically means the gluonic excitation energy, is found to be about 1 GeV in the typical hadronic scale. Finally, we suggest a possible scenario which connects the success of the quark model to QCD.Comment: Talk given at Color Confinement and Hadrons in Quantum Chromodynamics (Confinement 2003), Saitama, Japan, 21-24 July 2003; 5 pages, 4 figure

Infrared Abelian Dominance and Dual Higgs Mechanism in Maximally Abelian Gauge

We study infrared abelian dominance and the dual Higgs mechanism in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. In the MA gauge, the off-diagonal gluon phase tends to be random, and the off-diagonal gluon $A_\mu^\pm$ acquires the effective mass as $M_{\rm off} \simeq$ 1.2 GeV. From the monopole current in the MA gauge, we extract the dual gluon field $B_\mu$ and estimate the dual gluon mass as $m_B \simeq$ 0.5 GeV. The QCD-monopole structure is also investigated in terms of off-diagonal gluons. From the lattice QCD in the MA gauge, the dual Ginzburg-Landau (DGL) theory can be constructed as a realistic infrared effective theory based on QCD.Comment: Talk given at 17th International Symposium on Lattice Field Theory (LATTICE 99), Pisa, Italy, 29 Jun - 3 Jul 199