What the Gribov copy tells on the confinment and the theory of dynamical chiral symmetry breaking

Abstract

We performed lattice Landau gauge QCD simulation on β=6.0, 16^4, 24^4, 32^4 and β=6.4, 32^4, 48^4 and 56^4 by adopting the gauge fixing that minimizes the norm of the gauge field, and measured the running coupling by using the gluon propagator and the ghost propagator. In view of ambiguity in the vertex renormalization factor \tilde Z_1 in the lattice, we adjust the normalization of the running coupling by the perturbative QCD results near the highest momentum point. It has a maximum α_s(q)~ 2.1(3) at around q=0.5 GeV and decreases as q approaches 0, and the Kugo-Ojima parameter reached -0.83(2). The infrared exponent of the ghost propagator at 0.4GeV region is α_G=0.20 but there is an exceptional Gribov copy with α_G=0.27. The features of the exceptional Gribov copy are investigated by measuring four one-dimensional Fourier transform(1-d FT) of the gluon propagator transverse to each lattice axis. We observe, in general, correlation between absolute value of the Kugo-Ojima parameter and the degree of reflection positivity violation in the 1-d FT of the gluon propagator. The 1-d FT of the exceptional Gribov copy has an axis whose gluon propagator manifestly violates reflection positivity, and the average of the Cartan subalgebra components of the Kugo-Ojima parameter along this axis is consistent to -1. The running coupling of the enemble average shows a suppression at 0 momentum, but when the ghost propagator of the exceptional Gribov copy is adopted, the suppression disappears and the data implies presence of the infrared fixed point α_s(0)~ 2.5(5) and κ=0.5 suggested by the Dyson-Schwinger approach in the multiplicative renormalizable scheme. Comparison with the SU(2) QCD and N_f=2 unquenched SU(3) QCD are also made.

10 pages, 10 figures. Some clarifications are made and references are added. Representing the final version to appear in Physical Review D

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Cited by in corpus (34)

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• Nonperturbative QCD Coupling and its $\beta$ function from Light-Front Holography
• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
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• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
• Positivity violation for the lattice Landau gluon propagator
• Numerical Study of the Ghost-Gluon Vertex in Landau gauge
• Experimental determination of the effective strong coupling constant
• Determination of the effective strong coupling constant alpha_{s,g_1}(Q^2) from CLAS spin structure function data
• Positivity violations in QCD
• Asymptotic behavior of the ghost propagator in SU3 lattice gauge theory
• anQCD: a Mathematica package for calculations in general analytic QCD models
• BRST symmetry vs. Horizon condition in Yang-Mills theories
• On the computation of the spectral density of two-point functions: complex masses, cut rules and beyond
• SU(3) Landau gauge gluon and ghost propagators using the logarithmic lattice gluon field definition
• Infrared behavior of gluon and ghost propagators from asymmetric lattices
• Effects of the quark field on the ghost propagator of Lattice Landau Gauge QCD
• Infrared features of unquenched finite temperature lattice Landau gauge QCD
• Ghost sector and geometry in minimal Landau gauge: further constraining the infinite-volume limit
• Ghost condensation on the lattice
• The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator $Tr\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in the Landau gauge
• Conformal Symmetry as a Template for QCD
• A Closer Look at Gluons
• Infrared fixed point of QCD, critical flavor number and triality automorphism of octonions
• Roles of the color antisymmetric ghost propagator in the infrared QCD
• Non-perturbative aspects of Yang-Mills theories
• The self-dual gauge fields and the domain wall fermion zero modes
• Study of spin sum rules (and the strong coupling constant at large distances)