Search

Field distributions generated by static quark-antiquark and QQQ sources are calculated analytically in the framework of the Field Correlator Method (FCM) using Gaussian (bilocal) correlator. In both cases the string consists mostly of longitudinal color electric field, while transverse electric field contributes locally less then 3%, in agreement with earlier lattice studies. In the QQQ case the profile of the Y shape was calculated for the first time and found to have a complicated structure with a deep well at the string junction position. Possible consequences of this form for the baryon structure are discussed., Comment: LaTeX2e, 11 pages, 4 Postscript figures, 2 GIF images, version to appear in Physics Letters B

Spectrum of gluons in the adjoint source field is computed analytically using the QCD string Hamiltonian, containing only one parameter - string tension, fixed by meson and glueball spectrum. Spin splitting is shown to be small. A good agreement is observed with spatially generated gluelump states measured on the lattice. Important role of gluelumps defining the behaviour of field-strength correlators is stressed and correspondence with earlier computations of the latter is established., Comment: LaTeX, 18 pages, no figures, references and comments added

Recent accurate measurements of static potentials between sources in various representations of the gauge group SU(3) performed by G.Bali provide a crucial test of the QCD vacuum models and different approaches to confinement. The Casimir scaling of the potential observed for all measured distances implies strong suppression of higher cumulant contributions. The consequences for the instanton vacuum model and the spectrum of the QCD string are also discussed., Comment: LaTeX, 15 pages, 1 figure

Recent accurate measurement by G.Bali of static potentials between sources in various SU(3) representations provides a crucial test of the QCD vacuum and of different theoretical approaches to the confinement. In particular, the Casimir scaling of static potentials found for all measured distances implies a strong suppression of higher cumulants and a high accuracy of the Gaussian stochastic vacuum. Most popular models are in conflict with these measurements., Comment: LaTeX, 7 pages

Magnetic moments of baryons composed of light and strange quarks are computed for the first time through the only parameter of the model -- string tension $\sigma$. Resulting theoretical values differ from the experimental ones typically by about 10%., Comment: LaTeX, 13 pages; misprints are corrected

The effective quark Lagrangian is written for a light quark in the field of a static antiquark, explicitly containing field correlators as coefficient functions of products of quark operators. At large N_c the closed system of equations for the gauge-invariant quark Green's function in the field of static source is examined analytically. The formation of the string connecting the light quark to the static source is observed numerically. The scalar Lorentz nature of the resulting confinement is shown to hold for the considered case, implying chiral symmetry breaking. The resulting spectrum with and without perturbative gluon exchanges is obtained numerically and compared to the B and D meson masses and HQET., Comment: 17 pages Revtex, 3 figures

Using a nonperturbative method based on asymptotic behaviour of Wilson loops we calculate masses of glueballs and corresponding Regge-trajectories. The method contains no fitting parameters and the mass scale is fixed by the meson Regge slope. Theoretical predictions for lowest glueball states are in a perfect agreement with lattice results. The leading glueball trajectory and its relation to the Pomeron is discussed in details. Important role of mixing between glueball and q\bar q trajectories is emphasized., Comment: 13 pages, 1 EPS figure included using epsf.sty; minor changes in the text and table, figure is replaced

New equations are derived for meson and baryon Green's functions in a systematic method using the QCD Lagrangian and large N_c approximation as a starting point. The equations are shown to contain both confinement dynamics and chiral symmetry breaking. Linear Regge trajectories are demonstrated for the solutions., Comment: LaTeX, 8 pages

Using a nonperturbative method based on asymptotic behaviour of Wilson loops we calculate masses of glueballs and corresponding Regge-trajectories. The only input is string tension fixed by meson Regge slope, while perturbative contributions to spin splittings are defined by standard alpha_s values. The masses of lowest glueball states are in a perfect agreement with lattice results. The leading glueball trajectory which is associated with Pomeron is discussed in details and its mixing with f and f' trajectories is taken into account., Comment: LaTeX2e, 49 pages, 2 figures

Nonperturbative QCD approach is systematically derived starting from the QCD Lagrangian. Treating spin effects as a perturbation, one obtains the universal effective Hamiltonian describing mesons, hybrids and glueballs. Constituent mass of quark and gluon is calculated via string tension. The resulting spectrum of mesons, hybrids and glueballs obtained is in good overall agreement with lattice data and experiment., Comment: LaTeX2e, 51 pages, 6 figures, Lectures given at the XVII International School of Physics "QCD: Perturbative or Nonperturbative", Lisbon, 29 September - 4 October 1999

The spectra of light-light and heavy-light mesons are described by spinless Salpeter equation and Dirac equation respectively, which predict linear dependence of the meson mass squared M^2 on angular momentum J and number of radial nodes n. Both spectra are computed by the WKB method and shown to agree with exact numerical data within few percent even for the lowest levels. The drawback of Salpeter and Dirac equation is that (inverse) Regge slopes do not coincide with the string ones, 2\pi\sigma and \pi\sigma respectively, because the string dynamics is not taken into account properly. The lacking string rotation is introduced via effective Hamiltonian derived from QCD which generates linear Regge trajectories for light mesons with the correct string slope., Comment: LaTeX2e, 11 pages, 2 EPS figures, uses epsf.sty

The asymptotics of n-point Green's function at large external momenta is obtained in the exponentiated form using the Fock-Feynman-Schwinger representation for propagators in the external field. The method is applied to gauge theories such as QCD and QED, and the Sudakov form-factor is calculated as an example in QED and meson form-factor in QCD. Nonperturbative contributions can be conveniently included, as it is demonstrated in the example of the confinement correction to the form-factor., Comment: LaTeX, 15 pages, 3 figures

Nonperturbative contribution to the one-gluon exchange produces a universal linear term in the static potential at small distances $\Delta V=\frac{6N_c \alpha_s \sigma r}{2\pi}$. Its role in the resolution of long--standing discrepancies in the fine splitting of heavy quarkonia and improved agreement with lattice data for static potentials is discussed, as well as implications for OPE violating terms in other processes., Comment: Latex, 5 pages, to be published in JETP Lett

Short distance static quark--antiquark interaction is studied systematically using the background perturbation theory with nonperturbative background described by field correlators. A universal linear term $\frac{6N_c\alpha_s\sigma r}{2\pi}$ is observed at small distance $r$ due to the interference between perturbative and nonperturbative contributions. Possible modifications of this term due to additional subleading terms are discussed and implications for systematic corrections to OPE are formulated., Comment: LaTeX, 13 pages, references added

This paper is an extended version of hep-th/9802134. Dual QCD Lagrangian is derived by making use of the generalized coordinate gauge, where 1-form (vector potential) is expressed as an integral of the 2-form (field strength) along an (arbitrary) contour. As another application a simple proof of the nonabelian Stokes theorem is given., Comment: LaTeX 13 pages, no figures

The cancellation of perturbative contributions to the string tension in gluodynamics in the framework of vacuum field correlators method is shown at the order $O(g^4)$ by explicit calculation. The general pattern of these cancellations at all orders and relation with the renormalization properties of the Wilson loop is discussed., Comment: LaTeX 13 pages, no figures

A contour gauge of general type is analysed where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour $C$. For a special class of contours the gauge condition reduces to $k_{\mu}(x) A_{\mu}(x) = 0 $ where $k_{\mu}(x)$ is a tangent vector to the contour $C$. A simple proof of the nonabelian Stokes theorem is given demonstrating the advantage of the gauge., Comment: LaTeX, revised version, comments added

Field strength correlators are semi-classically evaluated in the dilute gas model of non-Abelian sources (instantons) and compared with lattice data for QCD at zero temperature. We show that one of the Euclidean invariant, tensorial structures vanishes for configurations being purely selfdual or anti-selfdual. We compute the invariant functions contributing to the correlators within the two lowest orders in an instanton density expansion. Fitting instanton size and density for quenched and full QCD, we obtain a reasonable description., Comment: 29 pages (revtex) including 3 figures, revised for publication in Phys. Rev. D

The effective quark Lagrangian is derived from the QCD action by means of averaging over the vacuum fields. In the limit of large N_c and keeping for simplicity the lowest order gluonic correlator one obtains nonlinear equations for the quark propagator, exhibiting scalar confinement. Connection to the quark zero mode density is discussed., Comment: LaTeX, 14 pages, no figures

New nonlinear equations for field correlators in the large $N_c$ gluodynamics are derived. Nonperturbative confining correlators are shown to satisfy a system of nonlinear scale-invariant equations. Keeping only the simplest, bilocal correlators one can find the exponential large distance behaviour for both independent correlators $D$ and $D_1$ and express coefficients in the exponentials -- the gluonic correlation length $T_g$ -- through the string tension. Numerically these results are in agreement with lattice data., Comment: LaTeX, 14 pages, no figures

Numerous aspects and mechanisms of color confinement in QCD are surveyed. After a gauge-invariant definition of order parameters, the phenomenon is formulated in the language of field correlators, to select a particular correlator responsible for confinement. In terms of effective Lagrangians confinement is viewed upon as a dual Meissner effect and a quantitative correspondence is established via the popular abelian projection method, which is explained in detail. To determine the field configurations possibly responsible for confinement, the search is made among the classical solutions, and selection criterium is introduced., Comment: LaTeX 63 pages, figures are not included; published in Physics-Uspekhi 39 (4) 313-336 (1996)

The light quark propagation in the confining vacuum, described by an (infinite) set of gauge-invariant vacuum correlators, is studied in detail. To keep gauge invariance at each step the system of light quark and heavy antiquark is considered, and the nonlinear equations are written explicitly for the quark propagator in the limit of large $N_c$. For the lowest (Gaussian) correlator the system is studied in various approximations, and the relativistic WKB method is used to demonstrate the scalar confining interaction of light quarks, which implies chiral symmetry breaking. The chiral condensate is estimated by the relativistic WKB method, and connection to the density of global zero modes is clarified. The higher even order correlators are shown to yield the same properties of scalar confining interaction for light quarks. No attempt was made to solve the obtained nonlinear equations numerically, but the qualitative conclusion on connection between confinement and chiral symmetry breaking is drawn, and an estimate of the chiral condensate is performed., Comment: 54 pages, LaTeX, no figures

The light-cone Hamiltonian, incorporating the nonperturbative dynamics of the $q\bar q$ system connected by the string is solved numerically. The spectrum is shown to coincide with that of the center-of-mass Hamiltonian within the accuracy of computation, displaying the expected degeneracies of the string states, but an overall shift due to different treatment of Z-graphs is obtained. The nonperturbative wave functions are calculated directly from the light-cone Hamiltonian for the first time, thus allowing the explicit estimation of nonperturbative effects in the parton model language. In this way one obtains the string contribution to the parton distributions and in the formfactors and structure functions., Comment: RevTeX 13 pages, 9 figures, in ps format, Submitted to Phys.Rev.D

A straightforward derivation of the effective quark Lagrangian is presented for the topologically neutral chiral broken phase of the dilute instanton gas. The resulting quark Lagrangian is a nonlocal NJL-type and contains 4q, 6q,... vertices for any number of flavours. Correspondence of this result with previously known in literature is discussed in detail., Comment: 15 pages, LaTeX 2.09

A new approach to effective theory of quarks in the instanton vacuum is presented. Exact equations for the quark propagator and Lagrangian are derived which contain contributions of all quark modes with known coefficients. The resulting effective Lagrangian differs from the standard one and resembles that of the Nambu-Jona-Lasinio model., Comment: 5 pages

Exact relations between gauge-invariant vacuum correlators in QCD are derived. Derivatives of the correlators are expressed in terms of higher orders correlators. The behaviour of the correlators at large and small distances due to these relations is discussed., Comment: 11 pages, LaTeX

A new approach to effective theory of quarks in the instanton vacuum is presented. Exact equations for the quark propagator and Lagrangian are derived which contain contributions of all quark modes with known coefficients. The resulting effective Lagrangian resembles that of the Nambu--Jona--Lasinio model. The commonly used zero--mode approximation is shown to be invalid in the chiral limit., Comment: 5 pages, no figures

Using cumulant expansion for an averaged Wilson loop we derive an action of the gluodynamics string in the form of a series in powers of the correlation length of the vacuum. In the lowest orders it contains the Nambu-Goto term and the rigidity term with the coupling constants computed from the bilocal correlator of gluonic fields. Some higher derivative corrections are calculated., Comment: 10 pages

Dyonic classical solutions of $SU(2)$ gluodynamics are discussed. Exact form of dyonic solutions in different gauges is presented and the nontrivial problem of composition of the dilute gas of dyons is settled. Classical interaction between (anti)dyons is considered both analytically and numerically. Confinement in the dyonic gas is discussed in connection with the topological properties of individual dyon solution. Fermionic zero modes of dyonic are displayed and the chiral symmetry breaking in the dyonic gas is demonstrated., Comment: 28 pages, LaTeX, figures are available upon the special request; PS file can be found at http://venus.itep.ru/preprints/1995/95038.ps.gz Lecture at the International School of Physics "Enrico Fermi", Varenna, 27 June--7 July 1995. Revised due to transmission errors

Dyonic classical solutions of $SU(2)$ gluodynamics are discussed. Exact form of dyonic solutions in different gauges is presented and the nontrivial problem of composition of the dilute gas of dyons is settled. Classical interaction between (anti)dyons is considered both analytically and numerically. Confinement in the dyonic gas is discussed in connection with the topological properties of individual dyon solution. Fermionic zero modes of dyonic are displayed and the chiral symmetry breaking in the dyonic gas is demonstrated., Comment: 21 pages, LaTeX, figures are available upon the special request; PS file can be found at http://venus.itep.ru/preprints/1995/95037.ps.gz Lecture at the International School of Physics "Enrico Fermi", Varenna, 27 June--7 July 1995. Revised due to transmission errors

Confined and deconfined phases are defined through nonperturbative correlators and nonperturbative background perturbation theory is used to compute the critical temperature $T_c$ and spatial string tension. Taking evolution along one of the spatial axes the set of Hamiltonians $H(n_1,n_2)$ with different Matsubara frequencies is obtained. Meson and glueball screening masses and wave functions are computed for $H(0,0)$ and compared with available lattice data., Comment: 10 Pages LaTeX, 2 Postscript Figures

Stochastic quantization is used to derive exact equations, connecting multilocal field correlators in the phi^3 theory and gluodynamics. Perturbative expansion of the obtained equations in the lowest orders is presented., Comment: 9 pages

Dyonic classical solutions of Yang-Mills theory are considered and the complete set of fermionic zero modes of these solutions are studied. Representing the QCD vacuum as a gas of dyons, one obtains chiral symmetry breaking due to zero modes similarly to the case of instantonic vacuum., Comment: 23 pages, no figures, PostScript

Bound states of heavy quarks are considered. Using the path integral formalism we are able to rederive, in a gauge invariant way, the Leutwyler-Voloshin short distance analysis as well as a long distance linear potential. At all distances we describe the states in terms of nonperturbative field correlators, and we include radiative corrections at short and intermediate distances. For intermediate distance states (particularly $b\bar {b}$ with $n=2$) our results improve, qualitatively and quantitatively, standard analyses, thanks mostly to being able to take into account the finiteness of the correlation time., Comment: 12 pages, 1 postscript figure, typeset with Plain TeX

Chiral symmetry breaking due to instanton-produced fermion zero modes in the confining vacuum is considered. Zero modes provide 'tHooft-type determinant quark interaction, which is bosonized by introduction of auxiliary fields. For three flavours this procedure becomes nontrivial and a method is suggested which allows to derive effective Lagrangian for massless Nambu--Goldstone modes., Comment: 10 pages

The light-cone Hamiltonian is derived from the general gauge -- and Lorentz -- invariant expression for the $q\bar{q}$ Green's function, containing confinement via the area law for the Wilson loop.The resulting Hamiltonian contains in a nonadditive way contributions from quark and string degrees of freedom. Different limiting dynamical regimes of the system of quarks connected by the string are found. In the limit of no transverse motion one recovers the t'Hooft's 1+1 QCD Hamiltonian. The correspondence with the rest frame Hamiltonian spectrum is established. The important notion of the light-cone string, contributing significantly to the energy--momentum is discussed., Comment: 28 pages, preprint ITEP 45-94

We measure field-strength and their correlators in presence of a static $q \bar q$ pair by numerical simulations. We give an interpretation of these data in terms of quadratic and quartic cumulants., Comment: 16 pages, IFUP-TH 11/94 (3 figures available as .ps files from the authors)

Confining configurations are introduced into the standard instanton vacuum model. This drastically improves theoretical properties of the vacuum: instanton size density $d(\rho)$ stabilizes at $\rho\sim 0.2 fm$, all chiral effects are formulated in a gauge-invariant way and quarks are confined. An interesting interplay of chiral and confining dynamics is observed; for the realistic values of parameters the Georgi-Manohar picture emerges with chiral radius $R_{ch}\sim \rho\sim 0.2 fm$ much less than confining radius $R_c\sim$ hadron radius $\sim 1 fm$. In the limit $R_{ch}\ll R_c$ the chiral mass $M_{ch}(p)$ is unaffected by confinement and can be taken in the local limit $M_{ch}(p=0)$. Different types of effective chiral Lagrangians (ECL) are obtained, containing all or a part of gluon, quark and Nambu--Goldstone--meson fields. The ECL are manifestly gauge--invariant and in the limit of no gluon fields coincide with those found previously. The problem of the double role of the pion -- as a Goldstone meson or as a $q\bar{q}$ system is briefly disscussed using confining ECL with quarks, mesons and gluons., Comment: 40 pages, preprint ITEP-83-93

Starting from the QCD Lagrangian and taking into account both perturbative and nonperturbative effects, we use the method of vacuum correlators to derive the Dirac equation (rigorously for the Coulomb interaction and heuristically for the confining potential) for a system consisting of a light quark and heavy antiquark. As a result the confining potential is a Lorentz scalar, and the Coulomb part the fourth component of a 4-vector. The energy spectrum of the Dirac equation is considered for these potentials. Numerical calculations of energy eigenvalues $E=E_{n\kappa}$ are performed, and some exact solutions of the Dirac equation in the case $E=0$ are found. An effective-potential method convenient for qualitative study of the solutions of the Dirac equation is developed. The connection with experimental spectra of $D$- and $B$-mesons is briefly discussed., Comment: 35 pages, preprint ITEP 83-92

Starting from the QCD Lagrangian we derive the effective action for massive quark and antiquark at large distances, corresponding to the minimal area low of the Wilson loop. The path integral method is used to quantize the system and the spectrum is obtained with asymptotically linear Regge trajectories. Two dynamical regimes distinguished by the string energy--momentum distribution are found: at large orbital excitations ($l\gg 1$) the system behaves as a string and yields the Regge slope of $\frac{1}{2 \pi \sigma}$, while at small $l$ one obtains a potential-like regime for relativistic or nonrelativistic system . The problem of relative time is clarified. It is shown that in the valence quark approximation one can reduce the initial four-dimensional dynamics to the three-dimensional one. The limiting case of a pure string (without quark kinetic terms) is studied and the spectrum of the straight-line string is obtained., Comment: 36 pages, preprint ITEP 17-93

Perturbative expansion in the nonperturbative confining QCD background is formulated. The properly renormalized $\alpha_S(R)$ is shown to be finite at large distances, with the string tension playing the role of an infrared regulator. The infra--red renormalons are shown to be absent in the new perturbation series., Comment: 38 pages, preprint HD-THEP-93-16

The background field formalism is used to implement nonperturbative QCD contributions into diagrammatic technic at $T>0$. The leading terms both in the confining and nonconfining phase are identified at large $N_c$ and the transition temperature is calculated in this limit, which appears to be in good agreement with the Monte Carlo calculations., Comment: 22 pages, preprint ITEP-03-93

The structure of the hadron spectrum is discussed in connection with the main phenomena of nonperturbative QCD: confinement and chiral symmetry breaking (CSB). For the higher part of the spectrum ($M \ge 2 GeV$) spin and chiral effects are unimportant; spectrum of $q\bar{q}$ system is described by an effective Hamiltonian deduced from QCD. The Hamiltonian reduces to relativistic quark potential model or to the open string model in two opposite limits. Hybrids are shown to appear naturally in theory and enter the multiplets which are compared to experiment and bosonic string theory. The phenomenon of conspiracy of the spectrum of radial excited states producing operator product expansion is discussed. The lower part of the spectrum $(M< 2 GeV)$ is influenced by spin and chiral effects. CSB and the chiral quark mass are deduced for the vacuum containing instantons and confining background. Main points are summarized in conclusion., Comment: Invited Talk at the International conference Hadron--93, 21--25 June Como (Italy), 15 pages, preprint ITEP-84-93

In this work the Feynman-Schwinger representation for the two-body Greens function is studied. After having given a brief introduction to the formalism, we report on the first calculations based on this formalism. In order to demonstrate the validity of the method, we consider the static case where the mass of one of the particles becomes very large. We show that the heavy particle follows a classical trajectory and we find a good agreement with the Klein-Gordon result., Comment: 4 pages LaTeX and 2 uuencoded figures in PostScript; requires epsf.sty. Contributed talk at `Few Body XIV', August 23-27 1993, Amsterdam, Netherlands. Utrecht preprint THU-93/21