Heavy-quark condensate at zero- and nonzero temperatures for various forms of the short-distance potential

With the use of the world-line formalism, the heavy-quark condensate in the SU(N)-QCD is evaluated for the cases when the next-to-1/r term in the quark-antiquark potential at short distances is either quadratic, or linear. In the former case, the standard QCD-sum-rules result is reproduced, while the latter result is a novel one. Explicitly, it is UV-finite only in less than four dimensions. This fact excludes a possibility to have, in four dimensions, very short strings (whose length has the scale of the lattice spacing), and consequently the short-range linear potential (if it exists) cannot violate the OPE. In any number of dimensions, the obtained novel expression for the quark condensate depends on the string tension at short distances, rather than on the gluon condensate, and grows linearly with the number of colors in the same way as the standard QCD-sum-rules expression. The use of the world-line formalism enables one to generalize further both results to the case of finite temperatures. A generalization of the QCD-sum-rules expression to the case of an arbitrary number of space-time dimensions is also obtained and is shown to be UV-finite, provided this number is smaller than six.Comment: 11 pages, no figure

Accuracy of Auxiliary Field Approach for Baryons

We provide a check of the accuracy of the auxiliary field formalism used to derive the Effective Hamiltonian for baryons in the Field Correlator Method. To this end we compare the solutions for the Effective Hamiltonian with those obtained from the solution of the Salpeter equation. Comparing these results gives a first estimate of the systematic uncertainty due to the use of the auxiliary field formalism for baryons.Comment: 6 pages, 2 tables; published versio

Following Gluonic World Lines to Find the QCD Coupling in the Infrared

Using a parametrization of the Wilson loop with the minimal-area law, we calculate the polarization operator of a valence gluon, which propagates in the confining background. This enables us to obtain the infrared freezing (i.e. finiteness) of the running strong coupling in the confinement phase, as well as in the deconfinement phase up to the temperature of dimensional reduction. The momentum scale defining the onset of freezing is found both analytically and numerically. The nonperturbative contribution to the thrust variable, originating from the freezing, makes the value of this variable closer to the experimental one.Comment: 25 pages, 5 figure

Chiral symmetry breaking in confining theories and asymptotic limits of operator product expansion

The pattern of spontaneous chiral symmetry breaking (CSB) in confining background fields is analyzed. It is explicitly demonstrated how to get the inverse square root large proper time asymptotic of the operator product expansion which is needed for CSB.Comment: LaTeX, 20 pages; minor revision

Induced Universal Properties and Deconfinement

We propose a general strategy to determine universal properties induced by a nearby phase transition on a non-order parameter field. A general renormalizable Lagrangian is used, which contains the order parameter and a non-order parameter field, and respects all the symmetries present. We investigate the case in which the order parameter field depends only on space coordinates and the case in which this field is also time dependent. We find that the spatial correlators of the non-order parameter field, in both cases, are infrared dominated and can be used to determine properties of the phase transition. We predict a universal behavior for the screening mass of a generic singlet field, and show how to extract relevant information from such a quantity. We also demonstrate that the pole mass of the non-order parameter field is not infrared sensitive. Our results can be applied to any continuous phase transition. As an example we consider the deconfining transition in pure Yang-Mills theory, and show that our findings are supported by lattice data. Our analysis suggests that monitoring the spatial correlators of different hadron species, more specifically the derivatives of these, provides an efficient and sufficient way to experimentally uncover the deconfining phase transition and its features.Comment: Added computational details and improved the text. The results are unchange

SU(3) Flux Tubes in a Model of the stochastic Vacuum

We calculate the squared gluon field strengths of a heavy q-$\rm \bar{q}$-pair in the model of the stochastic vacuum. We observe that with increasing separation a chromoelectric flux tube is built. The properties of the emerging flux tube are investigated.Comment: 14, epsf, HD-THEP-94-3

Confinement and Chiral Symmetry Breaking via Domain-Like Structures in the QCD Vacuum

A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the presence of domains are calculated explicitly and their analytical properties are discussed. The Fourier transforms of the propagators are entire functions and thus describe confined dynamical fields.Comment: RevTeX, 48 pages (32 pages + Appendices A-E), new references added [1,2,4,5] and minor formulae corrected for typographical error

Glueballs, gluon condensate, and pure glue QCD below T_c

A quasiparticle description of pure glue QCD thermodynamics at T<T_c is proposed and compared to recent lattice data. Given that a gas of glueballs with constant mass cannot quantitatively reproduce the early stages of the deconfinement phase transition, the problem is to identify a relevant mechanism leading to the observed sudden increase of the pressure, trace anomaly, etc. It is shown that the strong decrease of the gluon condensate near T_c combined with the increasing thermal width of the lightest glueballs might be the trigger of the phase transition.Comment: 5 pages, 5 figures; analysis refined in v2, explanations added; v3 to appear in EPJ

Decomposition of the QCD String into Dipoles and Unintegrated Gluon Distributions

We present the perturbative and non-perturbative QCD structure of the dipole-dipole scattering amplitude in momentum space. The perturbative contribution is described by two-gluon exchange and the non-perturbative contribution by the stochastic vacuum model which leads to confinement of the quark and antiquark in the dipole via a string of color fields. This QCD string gives important non-perturbative contributions to high-energy reactions. A new structure different from the perturbative dipole factors is found in the string-string scattering amplitude. The string can be represented as an integral over stringless dipoles with a given dipole number density. This decomposition of the QCD string into dipoles allows us to calculate the unintegrated gluon distribution of hadrons and photons from the dipole-hadron and dipole-photon cross section via kT-factorization.Comment: 43 pages, 14 figure

Lectures on Chiral Disorder in QCD

I explain the concept that light quarks diffuse in the QCD vacuum following the spontaneous breakdown of chiral symmetry. I exploit the striking analogy to disordered electrons in metals, identifying, among others, the universal regime described by random matrix theory, diffusive regime described by chiral perturbation theory and the crossover between these two domains.Comment: Lectures given at the Cargese Summer School, August 6-18, 200