Roles of the color antisymmetric ghost propagator in the infrared QCD

The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region is not purely color diagonal as in high energy region. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost-gluon-ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon propagator and the ghost propagator is investigated. Recent Dyson-Schwinger equation analysis suggests the ghost dressing function $G(0)=$ finite and no infrared enhancement or $\alpha_G=0$. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as $_r =-\frac{G(q^2)}{q^2}$ with $G(q^2)\propto q^{-2(1+\alpha_G)}$ with $\alpha_G = 0.5$, if the fixed point scenario is valid. I interpret the $\alpha_G=0$ solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is $\kappa=\alpha_G=-0.5$ and that of MILC is about -0.7. The implication for the Kugo-Ojima color confinement criterion, QCD effective coupling and the Slavnov identity are given.Comment: 13 pages 10 figures, references added and revised. version to be published in Few-Body System

Infrared features of unquenched finite temperature lattice Landau gauge QCD

The color diagonal and color antisymmetric ghost propagators slightly above $T_c$ of $N_f=2$ MILC $24^3\times 12$ lattices are measured and compared with zero temperature unquenched $N_f=2+1$ MILC$_c$ $20^3\times 64$ and MILC$_f$ $28^3\times 96$ lattices and zero temperature quenched $56^4$ $\beta=6.4$ and 6.45 lattices. The expectation value of the color antisymmetric ghost propagator $\phi^c(q)$ is zero but its Binder cumulant, which is consistent with that of $N_c^2-1$ dimensional Gaussian distribution below $T_c$, decreases above $T_c$. Although the color diagonal ghost propagator is temperature independent, the $l^1$ norm of the color antisymmetric ghost propagator is temperature dependent. The expectation value of the ghost condensate observed at zero temperature unquenched configuration is consistent with 0 in $T>T_c$. We also measure transverse, magnetic and electric gluon propagator and extract gluon screening masses. The running coupling measured from the product of the gluon dressing function and the ghost dressing function are almost temperature independent but the effect of $A^2$ condensate observed at zero temperature is consistent with 0 in $T>T_c$. The transverse gluon dressing function at low temperature has a peak in the infrared but it becomes flatter at high temperature. Its absolute value in the high momentum is larger for high temperature and similar to the magnetic gluon dressing function. The electric gluon propagator at high momentum is temperature independent. These data imply that the magnetic gluon propagator and the color antisymmetric ghost propagator are affected by the presence of dynamical quarks and there are strong non-perturbative effects through the temperature dependent color anti-symmetric ghost propagator.Comment: 11 pages 16 figures, version accepted for publication in Phys. Rev.

Numerical Study of the Ghost-Gluon Vertex in Landau gauge

We present a numerical study of the ghost-gluon vertex and of the corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau gauge for SU(2) lattice gauge theory. Data were obtained for three different lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings \beta = 2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called smeared gauge fixing. We also consider two different sets of momenta (orbits) in order to check for possible effects due to the breaking of rotational symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a nonperturbative verification of the so-called nonrenormalization of the Landau ghost-gluon vertex. Finally, we use our data to evaluate the running coupling constant \alpha_s(p^2).Comment: 19 pages, 6 figures, 9 tables, using axodraw.sty; minor modifications in the abstract, introduction and conclusion

Pion wave functions from holographic QCD and the role of infrared renormalons in photon-photon collisions

In this article, we calculate the contribution of the higher-twist Feynman diagrams to the large-$p_T$ inclusive single pion production cross section in photon-photon collisions in case of the running coupling and frozen coupling approaches within holographic QCD. We compare the resummed higher-twist cross sections with the ones obtained in the framework of the frozen coupling approach and leading-twist cross section. Also, we show that in the context of frozen coupling approach a higher-twist contribution to the photon-photon collisions cross section is normalized in terms of the pion electromagnetic form factor.Comment: 21 pages, 15 figures. arXiv admin note: text overlap with arXiv:0709.2072 by other author

The magnetic mass of transverse gluon, the B-meson weak decay vertex and the triality symmetry of octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass $m_{mag}$ becomes approximately equal to $T_c$ at $T=T_c\sim 1.14\Lambda_{\bar{MS}}\sim 260$MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.Comment: 22 pages, 9 figure

Class-Discriminative Weighted Distortion Measure for VQ-based Speaker Identification

We consider the distortion measure in vector quantization based speaker identification system. The model of a speaker is a codebook generated from the set of feature vectors from the speakers voice sample. The matching is performed by evaluating the distortions between the unknown speech sample and the models in the speaker database. In this paper, we introduce a weighted distortion measure that takes into account the correlations between the known models in the database. Larger weights are assigned to vectors that have high discriminating power between the speakers and vice versa

Infrared Features of the Landau Gauge QCD

The infrared features of Landau gauge QCD are studied by the lattice simulation of $\beta=6.0, 16^4, 24^4, 32^4$ and $\beta=6.4, 32^4, 48^4$. We adopt two definitions of the gauge field; 1) $U-$linear 2) $\log U$ and measured the gluon propagator and ghost propagator. Infrared singularity of the gluon propagator is less than that of tree level result but the gluon propagator at 0 momentum remains finite. The infrared singularity of ghost propagator is stronger than the tree level. The QCD running coupling measured by using the gluon propagator and the ghost propagator has a maximum $\alpha_s(p)\simeq 1$ at around $p=0.5GeV$ and decreases as $p$ approaches 0. The data are analyzed in use of formula of the principle of minimal sensitivity(PMS), the effective charge method and the contour-improved perturbation method, which suggest necessity of the resummation of perturbation series in the infrared region together with existence of the infrared fixed point. Kugo-Ojima parameter saturates at about -0.8 in contrast to the theoretically expected value -1.Comment: RevTex4, 9 pages, 10 eps figures, Typos corrected. To be published in Phys. Rev. D(2004

Effects of Symmetry Breaking on the Strong and Electroweak Interactions of the Vector Nonet

Starting from a chiral invariant and quark line rule conserving Lagrangian of pseudoscalar and vector nonets we introduce first and second order symmetry breaking as well as quark line rule violating terms and fit the parameters, at tree level, to many strong and electroweak processes. A number of predictions are made. The electroweak interactions are included in a manifestly gauge invariant manner. The resulting symmetry breaking pattern is discussed in detail. Specifically, for the ``strong'' interactions, we study all the vector meson masses and V -> \phi \phi decays, including isotopic spin violations. In the electroweak sector we study the { rho^0 , omega , phi } -> e^+e^- decays, { pi^+ , K^+ , K^0 } ``charge radii'', K_{l3} ``slope factor'' and the overall e^+e^- -> pi^+ pi^- process. It is hoped that the resulting model may be useful as a reasonable description of low energy physics in the range up to about 1 GeV.Comment: 43 pages (LaTeX), 5 PostScript figures are included as uuencoded-compressed-tar file at the en

The Gribov problem and QCD dynamics

In 1967, Faddeev and Popov were able to quantize the Yang-Mills theory by introducing new particles called ghost through the introduction of a gauge. Ever since, this quantization has become a standard textbook item. Some years later, Gribov discovered that the gauge fixing was not complete, gauge copies called Gribov copies were still present and could affect the infrared region of quantities like the gauge dependent gluon and ghost propagator. This feature was often in literature related to confinement. Some years later, the semi-classical approach of Gribov was generalized to all orders and the so-called GZ action was born. Ever since, many related articles were published. This review tends to give a pedagogic review of the ideas of Gribov and the subsequent construction of the GZ action, including many other toipics related to the Gribov region. It is shown how the GZ action can be viewed as a non-perturbative tool which has relations with other approaches towards confinement. Many different features related to the GZ action shall be discussed in detail, such as BRST breaking, the KO criterion, the propagators, etc. We shall also compare with the lattice data and other non-perturbative approaches, including stochastic quantization.Comment: 121 pages, 12 figures, Review article, references adde

A two-component picture of the <A^2> condensate with instantons

We study the interplay between the condensate and instantons in non-Abelian gauge theory. Therefore we use the formalism of Local Composite Operators, with which the vacuum expectation value of this condensate can be analytically computed. We first use the dilute gas approximation and partially solve the infrared problem of instanton physics. In order to find quantitative results, however, we turn to an instanton liquid model, where we find how the different contributions to the condensate add up.Comment: 9 pages, 1 figur