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We use the nonperturbative quark-antiquark potential derived within the Field Correlator Method and the screened Coulomb potential to calculate binding energies and melting temperatures of heavy mesons and baryons in the deconfined phase of quark-gluon plasma.

The correction to the string junction three-quark potential in a baryon due to the proper moment of inertia of the QCD string is calculated. The magnitudes of the string corrections in P-wave heavy baryons are estimated., Comment: published version

We carry out an investigation of the P-wave hyperons Λ Σ, and ξ employing the field correlator method in QCD. This method allows us to derive the effective Hamiltonian (EH) approach successfully applied to the meson and ground-state baryon spectra. The EH is written in the form of the nonrelativistic three-quark Hamiltonian with perturbative Coulomb-like and nonperturbative string interactions and the specific mass term. We solve the three-quark problem using the hyperspherical approach. With only two parameters, the string tension σ and the strong coupling constant αs, a unified quantitative description of the ground and excited hyperon states is achieved. In particular, we predict that all the hyperon states have the similar cost (in Δ) ∼460 MeV.

We found an additional symmetry hidden in the fermion and Higgs sectors of the Standard Model. It is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the whole Standard Model is constructed that possesses this symmetry., Comment: 6 pages, no figures. Shortened version

From the fact that the nonperturbative self-energy contribution $C_{\rm SE}$ to the heavy meson mass is small: $C_{\rm SE}(b\bar{b})=0$; $C_{\rm SE}(c\bar{c})\cong -40$ MeV \cite{ref.01}, strong restrictions on the pole masses $m_b$ and $m_c$ are obtained. The analysis of the $b\bar{b}$ and the $c\bar{c}$ spectra with the use of relativistic (string) Hamiltonian gives $m_b$(2-loop)$=4.78\pm 0.05$ GeV and $m_c$(2-loop)$=1.39 \pm 0.06$ GeV which correspond to the $\bar{\rm MS}$ running mass $\bar{m}_b(\bar{m}_b)=4.19\pm 0.04$ GeV and $\bar{m}_c(\bar{m}_c)=1.10\pm 0.05$ GeV. The masses $\omega_c$ and $\omega_b$, which define the heavy quarkonia spin structure, are shown to be by $\sim 200$ MeV larger than the pole ones.

The finite temperature lattice QCD with N_f=2 nonperturbatively improved Wilson fermions is studied on 16^3 8 lattice. Using abelian projection after fixing to MA gauge we determine the transition temperature for m_{\pi}/m_{\rho} \sim 0.8., Comment: 4 pages, 3 figures, talk given at the XVI International Conference on Particles and Nuclei, Osaka, Japan, September 30 - October 4, 2002

We have studied the three quark systems in an Effective Hamiltonian approach in QCD. With only two parameters: the string tension sigma and the strong coupling constant alpha_s we obtain a good description of the ground state light and heavy baryons. The prediction of masses of the doubly heavy baryons not discovered yet are also given. In particular, a mass of 3620 MeV for the lightest (ccu) baryon is found by employing the hyperspherical formalism to the three quark confining potential with the string junction., 8 pages, LaTex

We perform the careful study of the gauge copies problem for the direct center projection in SU(2) lattice gauge theory. Our results indicate that this gauge is not appropriate for the investigation of the center vortices. We also show that the point-like objects, nexuses, are important for the confinement dynamics., 7 pages, 2 figures, Latex2e, minor corrections, one reference added

We analyze the static potential of a quark-antiquark pair at $T\,\geq\,T_c$, where $T_c$ is a temperature of a deconfinement phase transition in QCD. We discuss the possibility that the non-perturbative part of this potential can be studied through the modification of the correlation functions, which define the quadratic field correlators of the nonperturbative vaccuum fields. We use the non-perturbative quark-antiquark potential derived in this way and the screened one-gluon-exchange potential with $T$-dependent Debye screening mass to calculate $J/\psi$, $\Upsilon$ and $\Omega_{bbb}$ binding energies and melting temperatures in the deconfined phase of the full 2-flavors QCD., Comment: a slightly extended version of the talk delivered at "Quark Confinement and the Hadron Spectrum IX - QCHS IX" International Conference (30 August - 3 September 2010, Madrid, Spain), a reference added, minor comments added

We use the screened Coulomb potential with r‐dependent coupling constant and the non‐perturbative quark‐ antiquark potential derived within the Field Correlator Method (FCM) to calculate J/ψ and Υ binding energies and melting temperatures in the deconfined phase of quark‐gluon plasma.

We provide an investigation of the P-wave hyperons employing the field correlator method in QCD. This method allows to derive the Effective Hamiltonian successfully applied to the meson and ground state baryon spectra. The hyperon spectrum appears to be expressed through two parameters relevant to QCD, the string tension

We have investigated by Monte Carlo simulation a recently proposed lattice regularization of gauge theories where the gauge fields are noncompact but gauge-invariance is exact. We have found a nonvanishing value of the string tension.

Dipion transitions of the subthreshold bottomonium levels $\Upsilon (nS)\to \Upsilon (n'S) \pi\pi$ with $n>n', n=2,3,4, n'=1,2$ are studied in the framework of the chiral decay Lagrangian, derived earlier. The channels $B\bar B, B\bar B^*+ c.c, B^* \bar B^*$ are considered in the intermediate state and realistic wave functions of $\Upsilon (n S),B$ and $B^*$ are used in the overlap matrix elements. Imposing the Adler zero requirement on the transition matrix element, one obtains 2d and 1d dipion spectra in reasonable agreement with experiment., Comment: 34 pages, 18 figures

The ground and P-wave excited states of nnn, nns and ssn baryons are studied in the framework of the Field Correlator Method using the running strong coupling constant in the Coulomb-like part of the three-quark potential. The running coupling is calculated up to two loops in the background perturbation theory. The three-quark problem has been solved using the hyperspherical functions method. The masses of the S- and P-wave baryons are presented. Our approach reproduces and improves the previous results for the baryon masses obtained for the freezing value of the coupling constant. The string correction for the confinement potential of the orbitally excited baryons, which is the leading contribution of the proper inertia of the rotating strings, is estimated., Comment: 13 pages, 1 figure, 5 tables

The ground and $P$-wave excited states of $nnn$, $nns$ and $ssn$ baryons are studied in the framework of the field correlator method using the running strong coupling constant in the Coulomb-like part of the three-quark potential. The string correction for the confinement potential of the orbitally excited baryons, which is the leading contribution of the proper inertia of the rotating strings, is estimated., Comment: 6 pages, 2 figures. Talk given at APS April Meeting, Denver, Colorado, May 2-5, 2009 and at the Tenth Conference on the Intersections of Particle and Nuclear Physics (CIPANP 2009), San Diego, California, May 26-31, 2009

We have studied a formulation of gauge theories on a lattice by means of gauge-invariant variables by a Monte Carlo simulation. The gauge-invariant variables used appear in a polar representation for the gauge field and they have been defined on the lattice both in compact and noncompact form. We have found a vanishing value of the string tension.

We investigate numerically lattice Weinberg - Salam model without fermions for realistic values of the fine structure constant and the Weinberg angle. We also analyze the data of the previous numerical investigations of lattice Electroweak theory. We have found that moving along the line of constant physics when the lattice spacing $a$ is decreased, one should leave the physical Higgs phase of the theory at a certain value of $a$. Our estimate of the minimal value of the lattice spacing is $a_c = [430\pm 40 {\rm Gev}]^{-1}$., Latex, 21 pages, 3 figures, to appear in JHEP

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., 6 pages, 2 tables; published version

We use the Field Correlator Method in QCD to calculate the masses of $\Sigma_c$, $\Xi_c$ and recently observed $\Sigma_b$, $\Xi_b$ baryons and their orbital excitations., Comment: Contributed talk at the session of Russian Academy of Sciences "Physics of Fundamental Interactions", ITEP, Moscow, November 26-30, 2007

We consider the lattice realization of the Standard Model with an additional $Z_6$ symmetry. Numerical simulations were performed on the asymmetric lattice, which corresponds to the finite temperature theory. Our choice of parameters corresponds to large Higgs masses ($M_H > 90$ Gev). The phase diagram was investigated and has been found to be different from that of the usual lattice realization of the Standard Model. It has been found, that the confinement-deconfinement phase transition lines for the SU(2) and SU(3) fields coincide. The transition line between Higgs and symmetric deconfinement parts of the phase diagram and the confinement-deconfinement transition line meet in a triple point. The transition between Higgs and symmetric parts of the phase diagram corresponds to the finite temperature electroweak transition/crossover. We see for the first time evidence that Nambu monopoles are condensed at $T>T_c$ while at $T, Comment: Latex, 14 pages

An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently. It has a singular nature and is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In this paper we report our results on the numerical simulation of its Electroweak sector., to appear in Yad. Fiz

The static force $F_B(r)$ and the strong coupling $\alpha_F(r)$, which defines the gluon-exchange part of $F_B(r)$, are studied in QCD background perturbation theory (BPT). In the region $r\la 0.6 $ fm $\alpha_F(r)$ turns out to be essentially smaller than the coupling $\alpha_B(r)$ in the static potential. For the dimensionless function $\Phi_B(r) = r^2 F_B(r)$ the characteristic values $\Phi_B(r_1) =1.0$ and $\Phi_B(r_0)=1.65$ are shown to be reached at the following $Q\bar Q$ separations: $r_1\sqrt{\sigma} =0.77, r_0\sqrt{\sigma} =1.09$ in quenched approximation and $r_1\sqrt{\sigma}=0.72, r_0\sqrt{\sigma}=1.04$ for $n_f =3$. The numbers obtained appear to be by only 8% smaller than those calculated in lattice QCD while the values of the couplings $\alpha_F(r_1)$ and $\alpha_F(r_0)$ in BPT are by $\sim 30% (n_f =3)$ and $50% (n_f=0)$ larger than corresponding lattice couplings. With the use of the BPT potential good description of the bottomonium spectrum is obtained., Comment: 21 pages, 1 figure. To be publised in Phys. Atom. Nucl. dedicated to the 70-th birthday of Yu.A. Simonov

The $b\bar b$ spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings $\Delta_1= \Upsilon({\rm 1D})-\chi_b({\rm 1P})$ and other splittings are very sensitive to the QCD constant $\Lambda_V(n_f)$ which occurs in the Vector scheme, and good agreement with the experimental data is obtained for $\Lambda_V(2$-loop, $n_f=5)= 325\pm 10$ MeV which corresponds to the conventional $\Lambda_{\bar{MS}} (2-$loop, $n_f=5)= 238\pm 7$ MeV, $\alpha_s(2-$loop, $M_Z)=0.1189\pm 0.0005,$ and a large freezing value of the background coupling: $\alpha_{\rm crit} (2$-loop, $q^2=0)=\alpha_{\rm crit} (2$-loop, $r\to \infty)=0.58\pm 0.02$. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling $\alpha_{\rm static}=const$ is introduced, as in the Cornell potential, then precise agreement with $\Delta_1({\rm exp})$ and $\Delta_2({\rm exp})$ can be reached for the rather large value $\alpha_{\rm static} =0.43\pm 0.02$. We predict a value for the mass M(2D) = 10451\pm2 MeV., Comment: 17 pages, no figures, 6 tables

The masses of $uudd\bar s $ and $uudd\bar d$ pentaquarks are evaluated in a framework of the Effective Hamiltonian approach to QCD using the Jaffe-Wilczek $[ud]^2\bar q$ approximation. The mass of the $[ud]^2\bar s$ state is found to be $\sim 300-500$ MeV higher than the observed $\Theta^+(1540)$ mass., Comment: 6 pages, 1 figure included, LaTeX2e; several references added; misprints corrected; to appear in Physics Letters B

Results of the study of lattice QCD with two flavors of nonperturbatively improved Wilson fermions at finite temperature are presented. The transition temperature for m_{\pi}/m_{\rho} \sim 0.8 and lattice spacing a \sim 0.12 fm is determined. A two-exponent ansatz is successfully applied to describe the heavy quark potential in the confinement phase., Comment: 3 pages, 1 figure, talk given at the 5th International Conference on Quark Confinement and the Hadron Spectrum, Gargnano, Italy, 10-14 Sep 2002

We present results for QCD with $N_f=2$ flavors of dynamical quarks using nonperturbatively improved Wilson fermions at finite temperature on $16^3 \times 8$ and $24^3 \times 10$ lattices. We determine the transition temperature in the range of quark masses $0.6 \lesssim m_\pi/m_\rho \leq 0.8$. After fixing the Maximal Abelian gauge we investigate the contribution of Abelian monopoles to the Polyakov loop, Polyakov loop susceptibility and confirm Abelian and monopole dominance in full QCD., Comment: Lattice2003(topology), 3 pages, 6 figures

We consider the electroweak theory without fundamental scalar field. The topological excitation of the SU(2)*U(1) theory (the monopole) plays the role of the Higgs field, it carries the SU(2)*U(1) topological charge due to the theta--term of the special type., Lattice2001(confinement), 3 pages, 1 eps figure

We study the spectrum of the domain walls interpolating between different chirally asymmetric vacua in supersymmetric QCD with the SU(3) gauge group and including 2 pairs of chiral matter multiplets in fundamental and anti-fundamental representations. For small enough masses m < m* = .286... (in the units of ��), there are two different domain wall solutions which are BPS-saturated and two types of ``wallsome sphalerons''. At m = m*, two BPS branches join together and, in the interval m* < m < m** = 3.704..., BPS equations have no solutions but there are solutions to the equations of motion describing a non-BPS domain wall and a sphaleron. For m > m**, there are no solutions whatsoever., 10 pages LaTeX, 5 postscript figures

Solving numerically the equations of motion for the effective lagrangian describing supersymmetric QCD with the SU(2) gauge group, we find a menagerie of complex domain wall solutions connecting different chirally asymmetric vacua. Some of these solutions are BPS saturated walls; they exist when the mass of the matter fields does not exceed some critical value m < m* < 4.67059... There are also sphaleron branches (saddle points of the ebergy functional). In the range m* < m < m** \approx 4.83, one of these branches becomes a local minimum (which is not a BPS saturated one). At m > m*, the complex walls disappear altogether and only the walls connecting a chirally asymmetric vacuum with the chirally symmetric one survive., 23 pages, LaTeX, 11 figures

We considered the lattice electroweak theory at realistic values of $\alpha$ and $\theta_W$ and for large values of the Higgs mass. We investigated numerically the properties of topological objects that are identified with quantum Nambu monopoles. We have found that the action density near the Nambu monopole worldlines exceeds the density averaged over the lattice in the physical region of the phase diagram. Moreover, their percolation probability is found to be an order parameter for the transition between the symmetric and the broken phases. Therefore, these monopoles indeed appear as real physical objects. However, we have found that their density on the lattice increases with increasing ultraviolet cutoff. Thus we conclude, that the conventional lattice electroweak theory is not able to predict the density of Nambu monopoles. This means that the description of Nambu monopole physics based on the lattice Weinberg - Salam model with finite ultraviolet cutoff is incomplete. We expect that the correct description may be obtained only within the lattice theory that involves the description of TeV - scale physics., Comment: LATEX

An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently\cite{BVZ2003}. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In \cite{BVZ2004} we have reported our results on the numerical simulation of the Electroweak sector of the model. In this paper we report our results on the numerical simulation of the full ($SU(3)\otimes SU(2) \otimes U(1)$) model. The phase diagram of the model has been investigated using static quark and lepton potentials. Various types of monopoles have been constructed. Their densities appear to be sensitive to the phase transition lines. Differences between the realizations of the Standard Model which do or do not possess the mentioned $Z_6$ symmetry, are discussed., Latex, 14 pages