What the Gribov copy tells about confinement 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 factorZ1 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 αs(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 αG = 0.20 but there is an exceptional Gribov copy with αG = 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 sample-wise 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 ensemble 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 αs(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.

AdS/QCD, LIGHT-FRONT HOLOGRAPHY, AND THE NONPERTURBATIVE RUNNING COUPLING

“…The AdS/QCD running coupling is in very good agreement with the effective coupling α g 1 extracted from the Bjorken sum rule. Surprisingly, the Furui and Nakajima lattice results [54] also agree better overall with the g 1 scheme rather than the V scheme. Our analysis indicates that light-front holography captures the essential dynamics of confinement.…”

“…5 (b) are the β-functions obtained from phenomenology and lattice calculations. For clarity, we present only the LF holographic predictions, the lattice results from, [54] and the experimental data supplemented by the relevant sum rules. The width of the aqua band is computed from the uncertainty of α g 1 in the perturbative regime.…”

Scaling behavior and positivity violation of the gluon propagator in full QCD

“…A direct observation, however, of a nonpositive gluon correlator, C t , in particular, for full QCD, has been unfeasible for a long time. Nevertheless, in more recent times a nonpositive C t has been observed in studies of the corresponding Dyson-Schwinger equation [35], in quenched SU 2 lattice gauge theory in three dimensions [46] and hinted at in QCD with dynamical quarks [47]. Explicit evidence in quenched and full QCD (cloverimproved Wilson fermions) has been given recently in [28].…”

Infrared behavior of gluon and ghost propagators from asymmetric lattices

“…This would imply that the real-space gluon propagator is positive and negative in equal measure, i.e. reflection positivity is maximally violated [13,14], indicating absence of gluons from the physical spectrum (gluon confinement). These predictions are also valid for the case of pure SU (2) gauge theory and for three space-time dimensions.…”