410 research outputs found

    Gluonic Higgs Scalar, Abelianization and Monopoles in QCD -- Similarity and Difference between QCD in the MA Gauge and the NAH Theory

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    We study the similarity and the difference between QCD in the maximally abelian (MA) gauge and the nonabelian Higgs (NAH) theory by introducing the ``gluonic Higgs scalar field'' ϕ(x)\vec \phi(x) corresponding to the ``color-direction'' of the nonabelian gauge connection. The infrared-relevant gluonic mode in QCD can be extracted by the projection along the color-direction ϕ(x)\vec \phi(x) like the NAH theory. This projection is manifestly gauge-invariant, and is mathematically equivalent to the ordinary MA projection. Since ϕ(x)\vec \phi(x) obeys the adjoint gauge transformation and is diagonalized in the MA gauge, ϕ(x)\vec \phi(x) behaves as the Higgs scalar in the NAH theory, and its hedgehog singularity provides the magnetic monopole in the MA gauge like the NAH theory. We observe this direct correspondence between the monopole appearing in the MA gauge and the hedgehog singularity of ϕ(x)\vec \phi(x) in lattice QCD, when the gluon field is continuous as in the SU(NcN_c) Landau gauge. In spite of several similarities, QCD in the MA gauge largely differs from the NAH theory in the two points: one is infrared monopole condensation, and the other is infrared enhancement of the abelian correlation due to monopole condensation.Comment: Talk given at 16th International Conference on Particles and Nuclei (PANIC 02), Osaka, Japan, 30 Sep - 4 Oct 200

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

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    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 Moff1GeVM_{\rm off} \simeq 1 {\rm GeV} in the intermediate distance as 0.2fmr0.8fm0.2{\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 BμB_\mu in the MA gauge, and find longitudinal magnetic screening with mBm_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

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    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(2d1)(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

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    The ground-state three-quark (3Q) potential V3Qg.s.V_{\rm 3Q}^{\rm g.s.} and the excited-state 3Q potential V3Qe.s.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 V3Qg.s.V_{\rm 3Q}^{\rm g.s.} is investigated in detail in lattice QCD with 123×2412^3\times 24 at β=5.7\beta=5.7 and with 163×3216^3\times 32 at β=5.8,6.0\beta=5.8, 6.0. As a result, the ground-state potential V3Qg.s.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-Qˉ\rm\bar Q potential, we find the universality of the string tension as σ3QσQQˉ\sigma_{\rm 3Q}\simeq\sigma_{\rm Q\bar Q} and the one-gluon-exchange result as A3Q12AQQˉA_{\rm 3Q}\simeq\frac12 A_{\rm Q\bar Q}. The excited-state potential V3Qe.s.V_{\rm 3Q}^{\rm e.s.} is also studied in lattice QCD with 163×3216^3\times 32 at β=5.8\beta=5.8 for 24 patterns of the 3Q systems.The energy gap between V3Qg.s.V_{\rm 3Q}^{\rm g.s.} and V3Qe.s.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

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    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 moff1.2GeVm_{\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 BμB_\mu. We evaluate the dual gluon mass as mB=0.4m_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

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    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
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