Deconfinement transition for nonzero baryon density in the Field Correlator Method

Deconfinement phase transition due to disappearance of confining colorelectric field correlators is described using nonperturbative equation of state. The resulting transition temperature $T_c(\mu)$ at any chemical potential $\mu$ is expressed in terms of the change of gluonic condensate $\Delta G_2$ and absolute value of Polyakov loop $L_{fund} (T_c)$, known from lattice and analytic data, and is in good agreement with lattice data for $\Delta G_2 \approx 0.0035$ GeV$^4$. E.g. $T_c(0) =0.27; 0.19; 0.17$ GeV for $n_f=0,2,3$ respectively.Comment: 8 pages, 1 figure, LaTeX2e; some typos correcte

Dynamics of confined gluons

Propagation of gluons in the confining vacuum is studied in the framework of the background perturbation theory, where nonperturbative background contains confining correlators. Two settings of the problem are considered. In the first the confined gluon is evolving in time together with static quark and antiquark forming the one-gluon static hybrid. The hybrid spectrum is calculated in terms of string tension and is in agreement with earlier analytic and lattice calculations. In the second setting the confined gluon is exchanged between quarks and the gluon Green's function is calculated, giving rise to the Coulomb potential modified at large distances. The resulting screening radius of 0.5 fm presents a serious problem when confronting with lattice and experimental data. A possible solution of this discrepancy is discussed.Comment: 17 pages, no figures; v2: minor numerical changes in the tabl

The static QQˉQ\bar Q interaction at small distances and OPE violating terms

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 Let

The matrix Hamiltonian for hadrons and the role of negative-energy components

The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white $q\bar q$ system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied in the example of the heavy-light meson and the standard einbein technic is extended to the case of the matrix Hamiltonian. Comparison with the Dirac equation shows a good agreement of the results. For arbitrary $q\bar q$ system the nondiagonal matrix Hamiltonian components are calculated through hyperfine interaction terms. A general discussion of the role of negative energy components is given in conclusion.Comment: 29 pages, no figure

Analytic calculation of field-strength correlators

Field correlators are expressed using background field formalism through the gluelump Green's functions. The latter are obtained in the path integral and Hamiltonian formalism. As a result behaviour of field correlators is obtained at small and large distances both for perturbative and nonperturbative parts. The latter decay exponentially at large distances and are finite at x=0, in agreement with OPE and lattice data.Comment: 28 pages, no figures; new material added, misprints correcte

Glueballs, gluerings and gluestars in the d=2+1 SU(N) gauge theory

The 3d gluodynamics which governs the large T quark gluon plasma is studied in the framework of the field correlator method. Field correlators and spacial string tension are derived through the gluelump Green's functions. The glueball spectrum is calculated both in C=-1 as well as in C=+1 sectors, and multigluon bound states in the form of "gluon rings" and "gluon stars" are computed explicitly. Good overall agreement with available lattice data is observed.Comment: 19 page

Decay constants of the heavy-light mesons from the field correlator method

Meson Green's functions and decay constants $f_{\Gamma}$ in different channels $\Gamma$ are calculated using the Field Correlator Method. Both, spectrum and $f_\Gamma$, appear to be expressed only through universal constants: the string tension $\sigma$, $\alpha_s$, and the pole quark masses. For the $S$-wave states the calculated masses agree with the experimental numbers within $\pm 5$ MeV. For the $D$ and $D_s$ mesons the values of $f_{\rm P} (1S)$ are equal to 210(10) and 260(10) MeV, respectively, and their ratio $f_{D_s}/f_D$=1.24(3) agrees with recent CLEO experiment. The values $f_{\rm P}(1S)=182, 216, 438$ MeV are obtained for the $B$, $B_s$, and $B_c$ mesons with the ratio $f_{B_s}/f_B$=1.19(2) and $f_D/f_B$=1.14(2). The decay constants $f_{\rm P}(2S)$ for the first radial excitations as well as the decay constants $f_{\rm V}(1S)$ in the vector channel are also calculated. The difference of about 20% between $f_{D_s}$ and $f_D$, $f_{B_s}$ and $f_B$ directly follows from our analytical formulas.Comment: 37 pages, 10 tables, RevTeX

Current correlators in QCD: OPE versus large distance dynamics

We analyse the structure of current-current correlators in coordinate space in large $N_c$ limit when the corresponding spectral density takes the form of an infinite sum over hadron poles. The latter are computed in the QCD string model with quarks at the ends, including the lowest states, for all channels. The corresponding correlators demonstrate reasonable qualitative agreement with the lattice data without any additional fits. Different issues concerning the structure of the short distance OPE are discussed.Comment: LaTeX, 25 pages, 13 figure

Baryon magnetic moments in the effective quark Lagrangian approach

An effective quark Lagrangian is derived from first principles through bilocal gluon field correlators. It is used to write down equations for baryons, containing both perturbative and nonperturbative fields. As a result one obtains magnetic moments of octet and decuplet baryons without introduction of constituent quark masses and using only string tension as an input. Magnetic moments come out on average in reasonable agreement with experiment, except for nucleons and $\Sigma^-$. The predictions for the proton and neutron are shown to be in close agreement with the empirical values once we choose the string tension such to yield the proper nucleon mass. Pionic corrections to the nucleon magnetic moments have been estimated. In particular, the total result of the two-body current contributions are found to be small. Inclusion of the anomalous magnetic moment contributions from pion and kaon loops leads to an improvement of the predictions.Comment: 24 pages Revte

Test of the QCD vacuum with the sources in higher representations

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 page