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

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

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

Nonperturbative mechanisms of strong decays in QCD

Three decay mechanisms are derived systematically from the QCD Lagrangian using the field correlator method. Resulting operators contain no arbitrary parameters and depend only on characteristics of field correlators known from lattice and analytic calculations. When compared to existing phenomenological models, parameters are in good agreement with the corresponding fitted values.Comment: 12 pages, latex2

Confinement and chiral symmetry breaking in heavy-light quark systems

Assuming a Gaussian approximation for the QCD gluodynamics, all the nonperturbative physics can be encoded into two parameters: the gluon correlation length $T_g$ and the gluon condensate $G_2$. These parameters are sufficient in order to describe the heavy-heavy quark nonperturbative interaction. In this work we adopt the same framework in order to study heavy-light bound states in the non-recoil limit. Spontaneous chiral symmetry breaking and a confining chiral non-invariant interaction emerge quite naturally. The gap equation is solved and discussed. In particular a relation between the light quark condensate and $T_g$ is derived. The energy spectrum for the bound state equation is evaluated and commented.Comment: 15 pages, 2 figures, elsart.st

Dynamics of quark-gluon plasma from Field correlators

It is argued that strong dynamics in the quark-gluon plasma and bound states of quarks and gluons is mostly due to nonperturbative effects described by field correlators. The emphasis in the paper is made on two explicit calculations of these effects from the first principles: one analytic using gluelump Green's functions and another using independent lattice data on correlators. The resulting hadron spectra are investigated in the range T_c < T < 2T_c. The spectra of charmonia, bottomonia, light s-sbar mesons, glueballs and quark-gluon states calculated numerically are in general agreement with lattice MEM data. The possible role of these bound states in the thermodynamics of quark-gluon plasma is discussed.Comment: Revised version with new comments and references and corrected tables VII-IX; 34 pages + 6 figure

Quarkonia and Quark Drip Lines in Quark-Gluon Plasma

We extract the $Q$-$\bar Q$ potential by using the thermodynamic quantities obtained in lattice gauge calculations. The potential is tested and found to give dissociation temperatures that agree well with those from lattice gauge spectral function analysis. Using such a $Q$-$\bar Q$ potential, we examine the quarkonium states in a quark-gluon plasma and determine the `quark drip lines' which separate the region of bound color-singlet $Q\bar Q$ states from the unbound region. The characteristics of the quark drip lines severely limit the region of possible bound $Q\bar Q$ states with light quarks to temperatures close to the phase transition temperature. Bound quarkonia with light quarks may exist very near the phase transition temperature if their effective quark mass is of the order of 300-400 MeV and higher.Comment: 24 pages, 13 figures, in LaTe