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The basic properties of the confinement mechanism in QCD -- the temperature dependence of the spatial and temporal string tensions ($\sigma_s(T)$ and $\sigma_E(T)$) -- are studied in the framework of the Field Correlator Method (FCM). It is shown that both functions are connected respectively to the spatial and temporal parts of the vacuum gluon energy $\epsilon_s$ and $\epsilon_E$ which define their equal values at $T=0$. However at $T>0$ the spatial part is growing with $T$ while the temporal part is destroyed by the hadronic pressure at $T=T_c$ (the deconfinement). Both properties are derived within the same method and are in a good agreement with the corresponding lattice data., Comment: v1: LaTeX, 9 pages, 4 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:2305.00558

The recent development of the Field Correlator Method (FCM) is discussed, with applications to the most interesting areas of QCD physics obtained in the lattice data and experiment. These areas include: a) the connection of colorelectric confinement with the basic quark and gluon condensates; b) the explicit form of the colorelectric deconfinement at a growing temperature $T$; c) the theory of the colormagnetic confinement at all temperatures; d) the theory of strong decays, the theory of pdf and jets in the instantaneous formalism with confinement. We demonstrate that the FCM with instantaneous formalism and confinement (instead of the light cone formalism and pure perturbation theory) can provide the way to the theory of QCD, which helps to describe world data without phenomenological parameters., Comment: v2: LaTeX, 26 pages, 2 figures, 2 tables; some typos corrected

The phenomenon of the deconfinement -- the spectacular drop of the colorelectric string tension at the critical temperature $T_c$ -- is studied within the method of field correlators (FCM) taking into account directly the contribution of the gluon condensate into the hadronic free energy. Using the resulting expressions for the free energy as a sum of the gluon condensate (the vacuum energy) and the hadronic pressure one obtains the possibility to calculate the deconfinement temperature $T_c$ and the temperature behavior of the string tension $\sigma_E(T)$ and the gluonic condensate $G_2(T)$ below $T_c$. The connection between the string tension and the quark condensate found in the framework of FCM allows the predict also the latter as a function of $T$ . These results are compared to the known lattice data of $T_c$, $\sigma_E(T)$, $\langle \bar{q}q \rangle(T)$ for hadronic media with different $n_f$ and $m_q$ and in the external magnetic field $eB$. The good agreement of the results of this approach with lattice data is demonstrated., Comment: v2: 23 pages, 3 figures; additional remarks and explanations are added, misprints corrected

The phenomenon of the almost linear growth of the square root of spatial string tension $\sqrt{\sigma_s(T)}= c_{\sigma} g^2 T$ was found both in lattice and in theory, based on the Field Correlator Method (FCM). In the latter the string tension (both spatial and colorelectric) is expressed as an integral of the two gluon Green's function calculated with the same string tension: $\sigma= \int G^{(2g)}_{\sigma}$. This relation allows to check the selfconsistency of the theory. However at nonzero temperature $T$ in the two-gluon Green's function in the space-like region appear terms which create in $\sigma_s$ quadratic in T behavior. We calculate below in the paper the $\sigma_s$ numerically in the whole temperature region $T_c< T < 5 T_c$ using the FCM method and compare the results with lattice data finding a good agreement. This justifies the use of the FCM in the space-like region and in high T thermodynamics without extra parameters., Comment: 18 pages,4 figures

The scalar resonances $X(3915), X(3960), X(4140)$ are considered as exotic four-quark states: $cq\bar c \bar q, cs\bar c \bar s, cs\bar c\bar s$, while the $X(3863)$ is proved to be the $c\bar c, 2\,^3P_0$ state. The masses and the widths of these resonances are calculated in the framework of the Extended Recoupling Model, where a four-quark system is formed inside the bag and has relatively small size ($\la 1.0$~fm). Then the resonance $X(3915)$ appears due to the transitions: $J/\psi\omega$ into $D^{*+}D^{*-}$ (or $D^{*0}\bar D^{*0})$ and back, while the $X(3960)$ is created due to the transitions $D_s^+D_s^-$ into $J/\psi\phi$ and back, and the $X(4140)$ is formed in the transitions $J/\psi\phi$ into $D_s^{*+}D_s^{*-}$ and back. The characteristic feature of the recoupling mechanism is that this type of resonances can be predominantly in the $S$-wave decay channels and has $J^P=0^+$. In two-channel case the resonance occurs to be just near the lower threshold, while due to coupling to third channel (like the $c\bar c$ channel) it is shifted up and lies by (20--30)~MeV above the lower threshold. The following masses and widths are calculated: $M(X(3915))=3920$~MeV, $\Gamma(X(3915))=20$~MeV; $M(X(3960))=3970$~MeV, $\Gamma(X(3960)=45(5)$~MeV, $M(X(4140))= 4120(20)$~MeV, $\Gamma(X(4140))=100$~MeV, which are in good agreement with experiment., Comment: 16 pages

The phenomenon of a narrow peak X(3875), discovered recently by the LHCb in the $D^*D$ system, and the absence of resonances in the $D_sD_s$ and $D_s^*D_s^*$ systems is discussed within the new extended version of the Recoupling Model, where the resonance is the result of infinite recoupling transitions of confining strings between quarks and antiquarks. We show that existence of the resonance in the $D^*D$ and its absence in $D_sD_s$ and $D_s^*D_s^*$ systems are the natural results of the Recoupling Mechanism. The application of this mechanism to the $D\bar D^*$ system allows to obtain the resonance $Z_c(3900)$ with larger width in agreement with experimental data., Comment: 12 pages, 2 tables

The phenomenon of the almost linear growth of the square root of spatial string tension $\sqrt{\sigma_s(T)}= c_{\sigma} g^2 T$ and of the Debye mass $m_D(T)$ was found both in lattice and in theory, based on the Field Correlator Method (FCM). In the latter the string tension (both spatial and colorelectric) is expressed as an integral of the two gluon Green's function calculated with the same string tension: $\sigma= \int G^{(2g)}_{\sigma}$. This relation allows to check the selfconsistency of the theory and at high T it allows also to calculate $c_{\sigma}$ and hence $\sigma_s$. We calculate below in the paper the corresponding coefficients $c_{\sigma}$ and $c_D$ numerically in the FCM method and compare the results with lattice data finding a good agreement. This justifies the use of the FCM in the space-like region and in high T thermodynamics without extra parameters., Comment: 11 pages,no figs

The resonances, containing $c\bar c$ plus $s\bar s$ (or light $q\bar q$) quarks in the mass region $(3900-4700)$ MeV, are analyzed in the relativistic strong coupling theory, with and without channel coupling phenomena. The conventional charmonium spectrum is presented, being calculated with the relativistic string Hamiltonian, which does not contain fitting parameters, while for high excitations the universal flattened confining potential is used. It is shown that $X(4274),X(4500),X(4700)$ can be identified as $3\,^3P_1, 4\,^3P_0, 5\,^3P_0$ states. The exotic states are considered using the coupled-channel (recoupling) theory, when two mesons $m_1,m_2$ transfer into another two mesons $m_3, m_4$ and back (infinite number of times), creating the four-quark systems. The resonances $X(3875), X(3915), Z_{cs}(3985), X(4140)$ can be explained in this way as the exotic four-quark states in the $S$-wave decay channels., Comment: 19 pages

Colormagnetic confinement as a natural component of the QCD confinement is explained and treated in the framework of the Field Correlator Method. For quarks and gluons in hadrons the effects of the colormagnetic confinement are discussed at zero temperature, where it contributes to the spectrum properties and can create its own bound states, while at nonzero temperature in the EoS of the quark gluon plasma the colormagnetic confinement plays a dominating role. Its properties in the QCD thermodynamics are discussed in detail., Comment: 21 pages,2 figures

The basic form of the quark condensate for arbitrary values of external magnetic field and temperature, is derived using the field equations with account of confinement. The resulting expression of the chiral condensate is shown to be proportional to square of the singlet $q\bar q$ ground state wave function at origin, $|\phi_0(0)|^2$. For light quarks without magnetic field the condensates are proportional to $\sigma^{3/2}$ ($\sigma$ is the string tension). Numerical results are presented in 5 Tables and shown to be in good agreement with the lattice data, both for nonzero magnetic field $eB$ and temperature $T$ in the range $0

The scalar confinement in QCD is shown to produce the nonzero quark condensate for any current quark mass. Mechanisms for the Chiral Symmetry breaking and for the nonzero quark condensates are revealed. For the light and strange flavors the condensates are essentially chiral (proportional to (string tension)$^{3/2}$). The expressions for the quark condensates are obtained as a sum over non-chiral meson states, and, using the operator product expansion, as an explicit expression that involves the confining string tension and the current quark mass. The numerical results are fairly close to the lattice data.

Chiral dynamics is investigated using the chiral confining Lagrangian (CCL), previously derived from QCD with confinement interaction. Based on the calculations of the quark condensate, which is defined entirely by confinement in the zero quark mass limit, one can assert that chiral symmetry breaking occurs not spontaneously but is predetermined by confinement. The expansion of the CCL provides the GMOR relations and the effective chiral Lagrangian, which is used to provide the masses and decay constants of all chiral mesons, including $\eta,\eta'$. For the latter one needs to define a non-chiral component due to confinement, while the orthogonality condition defines the wave functions and the eigenvalues. The resulting masses and decay constants of all chiral mesons are obtained in good agreement with experimental and lattice data., Comment: 16 pages

We study the class of processes where the dynamics depends essentially on the properties of the hadron wave functions involved in the reactions. In this case the momentum dependence of the form of wave functions imposed by Lorentz invariance and in particular by the Lorentz contraction can be tested in the experiment and may strongly influence the resulting cross sections. One example of such observables is given by the hadron form factors, where it was shown that the large Q behavior is mostly frozen, when the Lorentz contraction of the hadron wave functions is taken into account. Another example considered previously is the strong hadron decay with high energy emission. In this paper we study the role of the Lorentz contraction in the high-energy hadron-hadron scattering process at large momentum transfer. For the $pp$ and $p\bar p$ scattering at large $s$ it is shown that at small $-t << s$ the picture of two exponential slopes in the differential cross section explained previously by the author is stable while the backward scattering cross section is strongly increased by the Lorentz contraction., Comment: 20 pages

There are several scales in the QCD as the theory of strong interaction: the vacuum gluonic condensate (as the divergence of the dilatation current), the nucleon mass as the basic mass scale in our universe, which is connected to the string tension $\sigma$, and the perturbative QCD scale $\Lambda_{\rm QCD}$, which defines the scale of the renormalized perturbative expansions. In this paper we connect all these scales to the vacuum condensate, using the field correlator method, where the string tension is expressed in terms of nonlocal field correlators, which are connected to the local condensates, while the perturbative $\Lambda_V$ is connected to $\sigma$ in the framework of the Background Perturbation Theory (BPT). We also demonstrate how the IR singularities and IR renormalons disappear in BPT making the resulting theory internally consistent., Comment: 17 pages,3 figures

Recent experiments have discovered two exponents in the $pp$ elastic differential cross sections with two different slope parameters, of the order $(16-20)$~GeV$^{-2}$ and $(4-4.8)$~GeV$^{-2}$ in the regions $ -t \la 0.5 $~GeV$^2$ and $ -t \ga 1$~GeV$^2$, respectively. We suggest a simple model of the $pp$ elastic scattering with two types of particle exchanges: 1) when the exchanged particle transfers the momentum $\veQ$ from a quark of the proton $p_1$ to one quark in another proton $p_2$, producing the slope $B_1$; 2) when the transfer occurs from two quarks in the $p_1$ to two quarks in the $p_2$, giving the exponent with the slope $B_2$. The resulting amplitude is proportional to the product of the form factors of two protons, depending on $\veQ$, but with different coefficients in the cases 1) and 2). Using the only parameter - the proton charge radius $r^2_{ch}= 0.93$~fm$^2$, one obtains $B_1 = 16$~GeV$^{-2}$,~$ B_2 = 4$~GeV$^{-2}$ with the strict value of the ratio, $\frac{B_1}{B_2} = 4.0$, independent of $r_{ch}$. These predictions are surprisingly close to the data both in the $pp$ and in the $\bar p p$ differential cross sections. Comparison to experimental data and theoretical approaches is discussed, together with possible implications for the future development of the theory., Comment: 9 pages,1 table

The infinite chain of transitions of one pair of mesons (channel I) into another pair of mesons (channel II) can produce bound states and resonances in both channels even if no interactions inside channels exist. These resonances which can occur also in meson-baryon channels are called channel-coupling (CC) resonances. A new mechanism of CC resonances is proposed where transitions occur due to a rearrangement of confining strings inside each channel -- the recoupling mechanism. The amplitude of this recoupling mechanism is expressed via overlap integrals of the wave functions of participating mesons (baryons). The explicit calculation with the known wave functions yields the peak at $E= 4.12$ GeV for the transitions $J/\psi + \phi \leftrightarrow D^*_s + \bar D^*_s $, which can be associated with $\chi_{c1}(4140)$, and a narrow peak at $3.98$ GeV with the width $10$ MeV for the transitions $D^{-}_s + D^*_0 \leftrightarrow J/\psi + K^{*-},$ which can be associated with the recently discovered $Z_{cs}(3985)$., Comment: 24 pages, 2 figures, 6 tables

Nucleon form factors play an especially important role in studying the dynamics of nucleons and explicit structure of the wave functions at arbitrary nucleon velocity. The purpose of the paper is to explain theoretically all four nucleon form factors measured experimentally in the cross section measurements (by the Rosenbluth method), yielding almost equal normalized form factors $G^p_E,G^p_M,G^n_M$, as well as in the polarization transfer experiments, where a strongly decreasing proton electric form factor has been discovered. It is shown, using relativistic hyperspherical formalism, that the nucleon wave functions in the lowest approximation provide almost equal normalized form factors as seen in the Rosenbluth cross sections, but in the higher components they contain a large admixture of the quark orbital momenta, which strongly decreases $G^p_E$ and this effect is possibly detected in the polarization transfer method (not seen in the classical cross section experiments). Moreover, the same admixture of the higher components explains the small positive form factor $G^n_E$. The resulting form factors, $G^p_M(Q),G^p_E(Q),G^n_M(Q)$ are calculated up to $Q^2\approx 10$ GeV$^2$, using the standard and the Lorentz contracted wave functions and shown to be in reasonable agreement with experimental data., Comment: 24 pages,3 tables, no figures

Strong decay probabilities are calculated using the Lorentz contracted wave functions of decay products, determined in the arbitrary dynamical scheme with the instantaneous interaction. It is shown that the decay width obtains an additional factor defined by the contraction coefficient $C_m(s)$, which for two-body equal mass decays is $C^2_m(s)= 4m^2/s$ , $s= E^2$. The resulting decay widths are compared to the experimental data, where in particular the $\rho(770),\rho(1450) $ decay data require an additional $1/s$ dependence of the width to fit the data. Important consequences for the dynamics of hadron decays and scattering are shortly discussed., Comment: 11 pages, no figures. arXiv admin note: text overlap with arXiv:2004.11466

Hadron form factors are calculated using the Lorentz contracted wave functions, determined in the arbitrary dynamical scheme with the instantaneous interaction. It is shown that the large $Q$ asymptotics of the form factors is defined by the contraction coefficient $C_m(Q^2) = \frac{m}{\sqrt(m^2+ Q^2/4)}$, where $m$ is the meson mass, and weakly depends on the interaction used. The resulting form factors $F_\pi$ and $F_K$ are obtained in good agreement with the lattice and experimental data. Important consequences for the dynamics of hadron decays and scattering are shortly discussed., Comment: v2: 15 pages, 4 tables

The formalism of the coupled $q\bar q$ and the $\varphi\varphi ( \pi-\pi$, $K\bar K, \pi K,...$) scalar channels is formulated, taking into account the ground and radial excited $q\bar q$ poles. The basic role is shown to be played by the transition coefficients $k^{(I)} (q\bar q, |\varphi\varphi)$, which are calculated using the quark-chiral Lagrangian without free parameters. The resulting method, called the pole projection mechanism (PPM), ensures: 1) one resonance for each $\varphi\varphi$ channel from the basic $q\bar q$ pole, e.g. the $f_0 (500)$ resonance in the $\pi\pi$ channel; 2) a possibility to have two $\varphi\varphi$ resonances, coupled to the same $q\bar q$ state, when the channel coupling is taken into account in the meson-meson channels, which yields $f_0 (500)$ and $f_0(980)$ from the same $n\bar n$ pole around 1 GeV; 3) the strong pole shift down for special ($\pi\pi, \pi K)$ channels due to large transition coefficients $k^{(I)}$, computed in this formalism without free parameters. The parameters of calculated complex poles are in reasonable agreement with the experimental data of the resonances $f_0(500)$, $f_0(980)$, $a_0(980)$, $a_0(1450)$, $K^*_0(700)$, $K^*_0(1430)$, $f_0(1370)$ and $f_0(1710)$., Comment: v2: 22 pages, 5 figures; new explanations are added, several important insertions are made, the list of references is enlarged

The Chiral Confining Lagrangian, based on the chiral theory with quark degrees of freedom, is used to study the spectroscopy of scalar mesons. The formalism does not contain arbitrary fitting parameters and takes into account infinite number of transitions from meson-meson to quark-antiquark states. Starting from known $q\bar q$ poles the transition coefficients ensure the strong shift of the poles for the $\pi\pi$ and much smaller shift for the $K\bar K$ systems. The resulting amplitudes $f_{\pi\pi}$ and $f_{K\bar K}$ are calculated in terms of the $q\bar q$ and the free meson Green's functions. With the account of the $\pi\pi/K\bar{K}$ channel coupling one obtains two resonances: a wide resonance $E_1$ in the range 500-700 MeV and narrow $E_2 $ near 1 GeV, which can be associated with $f_0(500)$ and $f_0(980)$. A similar analysis, applied to the $I=1$ channel, shows that in this case two very close poles in different sheets appear near $E=980$ MeV, which can be associated with the $a_0 (980)$ resonance. The obtained $\pi\pi$ interaction amplitudes, $\operatorname{Re} f_{\pi\pi} (E)$ and $\operatorname{Im} f_{\pi\pi}(E)$ are compared with the known data., Comment: v5: 29 pages, 6 figures; version accepted to PRD, new equations with explanations are added, several important insertions are made, the list of references is correspondingly enlarged

A non-perturbative (np) method of Field Correlators (FCM) was applied to study QCD at temperatures above the deconfinement transition ($1

Properties of the quark-gluon plasma(QGP) in the presence of the baryon chemical potential $\mu_B$ are studied using the Field Correlator Method(FCM). The nonperturbative FCM dynamics includes the Polyakov line, computed via colorelectric string tension $\sigma^E(T)$ and the quark and gluon Debye masses, defined by the colormagnetic string tension $\sigma^H(T)$. The resulting QGP thermodynamics at $\mu_B \le 400$ MeV is in a good agreement with the available lattice data,both pressure and the sound velocity do not show any sign of a critical behavior in this region., Comment: 18 pages,7 figures. arXiv admin note: substantial text overlap with arXiv:1811.08970

Relativistic formalism of Green's functions is dicussed in QCD and QED,where the relativistic Green's functions are constructed using the Schwinger proper time formalism and the Fock-Feynman-Schwinger method.As a result a simple and exact method is found for the relativistic systems,where the interaction can be written in a time-independent form.In this case one can write the relativistic Green's function as a one-dimensional integral of the corresponding nonrelativistic Green's function.The explicit example for the problem of a charge in the constant magnetic field is discussed in detail,and the exact agreement with the Schwinger relativistic form is demonstrated. A similar analysis is performed in the relativistiv Coulomb probem,supporting the accuracy of the proposed relativistic formalism., Comment: 24 pages,1 figure,new refs added

A non-perturbative method of Field Correlators is applied to calculate the Polyakov loop dependence on temperature, $L(T)$, in the 2+1 flavor QCD with small quark masses, so the only relevant scale is the color-electric string tension $\sigma(T)$. Polyakov loop in the temperature range 100 MeV $\lesssim T\lesssim$ 400 MeV is expressed via the heavy-light meson mass that decreases with $T$ as $\sqrt{\sigma (T)}$. The latter is deduced from a gradually vanishing chiral condensate. The resulting $L(T)$ is in good agreement with recent lattice data., Comment: 16 pages, 2 figures

The properties of the quark-gluon plasma(QGP) in the presence of baryon chemical potential are studied using the Field Correlator Method(FCM). At low densities the QGP thermodynamics with the colormagnetic confinement and the Polyakov line interaction is in good agreement with lattice data,and the speed of sound satisfies $C_s^2\leq \frac13$,but in the intermediate range of densities the speed of sound displays a singular behaviour and one needs density modifications of the Polyakov line interaction to avoid instabilities. In particular for $\mu_q >0.5$ GeV there exists a region in the $(\mu, T)$ plane where $C^2_s$ violates the conformal limit. This behaviour is strongly connected to the properties of the Polyakov loop and its density dependence., Comment: 18 pages , 11 figures

The speed of sound $C_{s}$ in the SU(3) and (2+1)QCD is calculated within the Field Correlator Method using the nonperturbative colour magnetic confinement and Polyakov loop interaction in the deconfined region.The resulting $C_{s}$ displays a discontinuity at $T=T_{c}$ in the SU(3) case. It is shown numerically and analytically that $ C^{2}_{s}$ never exceeds $\frac{1}{3}$ both for SU(3) and (2+1) QCD for vanishing chemical potential.A good agreement is found of our numerical results with the corresponding lattice data., Comment: 10 pages, 3 figures

The standard chiral perturbation theory is known to predict much weaker effects in magnetic field, than found in numerical lattice data. To overcome this disagreement we are using the effective chiral confinement Lagrangian, $L_{ECCL}$, containing both chiral and quark degrees of freedom, in the presence of external magnetic field. Without magnetic fields $L_{ECCL}$ reduces to the ordinary chiral Lagrangian $L_{EC L}$, yielding in the lowest order $O(\partial_\mu \varphi)^2$ all known relations, and providing explicit numerical coefficients in the higher $O(p^4, p^6)$ orders. The inclusion of the magnetic field in $L_{ECCL}$ strongly modifies ECL results for chiral condensates, coupling constants $f_\pi, f_K$ and masses of chiral mesons. The resulting behavior contains the only parameter -- the string tension $\sigma$, is roughly proportional to $O\left( \frac{eB}{\sigma}\right)$ and agrees very well with lattice data. These results show that the magnetic field acts not only on the chiral degrees of freedom $(\varphi_\pi)$, but also on quarks in the quark-chiral Lagrangian, which produce much stronger effect., Comment: 24 pages, 6 figures

The theory of confinement based on the stochastic field mechanism, known as the Field Corrleator Method (FCM) is discussed in detail. Experimental and lattice data have accumulated a vast amount of material on the properties of confinement in QCD. We enumerateall these properties as 1)-7), and discuss beyond FCM two existing approaches: monopole based Dual Ginzburg-Landau (DGL) theory,and Gribov-Zwanziger model, from this point of view. It is shown that the FCM satisfies all required criteria. We also prove its selfconsistency; in particular, it is shown that the string tension {\sigma} is the only scaleful parameter in the theory beyond fermion masses, and {\Lambda}_QCD is calculated explicitly to the lowest order in terms of {\sigma}. We also formulate physical consequences of confinement, such as string breaking,Regge trajectories, role of confinement in the perturbation theory, chiral symmetry breaking, confinement in the boosted systems etc. It is demonstrated that the FCM is a suitable tool for the solution of these problems., Comment: 47 pages,11 figures,accepted for publication in Phys.Rev.D

The dynamics of fermion generations is treated in the framework of the fractional Lagrangian and Hamiltonian in the compact extra dimension. The resulting spectra for u, d, e generations are described by the only mass parameter and slightly different fractional numbers, while the neutrino spectra need another mass parameter and a single fractional number for all neutrino species. New definitions of CKM and PMNS mixing matrices with standard data are given as the interference integrals in the extra dimension. A possibility of higher fermion states as dark matter candidates is shortly discussed., Comment: 22 pages, 4 tables, no figures,new eqs and refs added

The thermodynamics of quarks and gluons strongly depends on the vacuum colormagnetic field, which grows with the temperature $T$, so that spatial string tension $\sigma_s ={\rm const}~ g^4 (T) T^2$. We investigate below what happens when one imposes in addition constant magnetic field and discover remarkable structure of the resulting thermodynamic potential., Comment: 10 pages, 2 figures

Thermodynamics of the quark-gluon plasma at finite density is studied in the framework of the Field Correlator Method, where thermodynamical effects of Polyakov loops and colormagnetic confinement are taken into account. Having found good agreement with numerical lattice data for zero density, we calculate pressure $P(T,\,\mu)$ for $0 <\mu< 400$ MeV and $150

Colorelectric and Colormagnetic structure of the flux tubes, connecting heavy quark and antiquark, is investigated in the framework of the Field Correlator method which describes all resulting fields in terms of correlators $D^E$ and $D^E_1$. The latter have been computed via gluelumps, which allows to predict the resulting distribution of color fields $\mathbf{E} (\mathbf{r}),$ and colormagnetic currents $\mathbf{k} (\mathbf{r})$ in the flux tubes. It is shown, that at large distances $r\gg \lambda \approx 0.2$ fm the whole structure of fields and relations between them is similar to that of the dual superconductor theory, but the basic dynamics, including small distances, is given by field correlators of the real stochastic vacuum. The important contradiction between the strong screening of color fields in the width of flux tubes and almost no screening in the perturbative $Q\bar Q$ potential is resolved., Comment: 1+15 pages, 10 figures

Nonperturbative effects in the quark-gluon thermodynamics are studied in the framework of Vacuum Correlator Method. It is shown, that two correlators: colorelectric $D_1^E(x)$ and colormagnetic $D^H(x)$, provide the Polyakov line and the colormagnetic confinement in the spatial planes respectively. As a result both effects produce the realistic behavior of $P(T)$ and $s(T)$, being in good agreement with numerical lattice data., Comment: 1+8 pages, 2 figures