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

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'' $\vec \phi(x)$ 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 $\vec \phi(x)$ like the NAH theory. This projection is
manifestly gauge-invariant, and is mathematically equivalent to the ordinary MA
projection. Since $\vec \phi(x)$ obeys the adjoint gauge transformation and is
diagonalized in the MA gauge, $\vec \phi(x)$ 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 $\vec
\phi(x)$ in lattice QCD, when the gluon field is continuous as in the SU($N_c$)
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

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

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