Abstract
For a long time, the quark confinement mechanism has been one of the most difficult problems in theoretical physics. In particular, there is no clear correspondence between the confinement and non-Abelian nature of QCD. We study the static interquark potential and its Abelian projection in both mesons and baryons in the maximally Abelian (MA) gauge in SU(3) quenched lattice QCD. Remarkably, we find that the quark confining force in QCD can be perfectly described only with Abelian variables in theMAgauge, which we call “perfect Abelian dominance” of the quark confinement.
Highlights
The mechanism of quark confinement is an important long-standing problem in quantum chromodynamics (QCD)
There are two large gaps between the dual superconductor and the QCD vacuum: (i) the dual superconductor is governed by an Abelian U(1) gauge theory, while QCD is a non-Abelian SU(3) gauge theory; (ii) the dual superconductor requires the condensation of color-magnetic monopoles, while QCD does not have such monopoles as elementary degrees of freedom
We have studied the maximally Abelian (MA) projection of quark confinement in the mesonic quark-antiquark and baryonic three-quark potentials in the SU(3) QCD with several spacings and volume lattices
Summary
The mechanism of quark confinement is an important long-standing problem in quantum chromodynamics (QCD). To obtain σAbel σ, it is necessary to use large-volume lattices of more than about 2 fm [14, 15] These observations of σAbel σ indicate that the Abelianization of QCD can be realized without loss of the quark-confining force via the MA projection. 2, we describe the numerical methods to calculate the MA-projected Abelian theory and the QQand 3Q potentials. The of the link variables QQand 3Q Wilson along loops represent that the gauge-invariant QQor 3Q state is generated at t = 0 and is annihilated at t = T with the quarks spatially fixed in R3 for 0 < t < T. from the Abelian Wilson loop in the MA gauge W uμ(s) and the 3Q one W3Q uμ(s) , respectively. The error bars in each panel denote the statistical errors estimated with the jackknife method
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