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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 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 scalar resonances $$X(3915), X(3960), X_0(4140)$$ X ( 3915 ) , X ( 3960 ) , X 0 ( 4140 ) are considered as exotic four-quark states: $$cq\bar{c} \bar{q}, cs\bar{c} \bar{s}, cs\bar{c}\bar{s}$$ c q c ¯ q ¯ , c s c ¯ s ¯ , c s c ¯ s ¯ , while the X(3863) is proved to be the $$c\bar{c}, 2\,^3P_0$$ c c ¯ , 2 3 P 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 ( $$\lesssim 1.0$$ ≲ 1.0 fm). Then the resonance X(3915) appears due to the transitions: $$J/\psi \omega $$ J / ψ ω into $$D^{*+}D^{*-}$$ D ∗ + D ∗ - (or $$D^{*0}\bar{D}^{*0})$$ D ∗ 0 D ¯ ∗ 0 ) and back, while the X(3960) is created due to the transitions $$D_s^+D_s^-$$ D s + D s - into $$J/\psi \phi $$ J / ψ ϕ and back, and the $$X_0(4140)$$ X 0 ( 4140 ) is formed in the transitions $$J/\psi \phi $$ J / ψ ϕ into $$D_s^{*+}D_s^{*-}$$ 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 $$J^P=0^+$$ 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 $$c\bar{c}$$ c c ¯ channel) it is shifted up and lies by (20–30) MeV above the lower threshold. The following masses and widths are calculated: $$M(X(3915))=3920$$ M ( X ( 3915 ) ) = 3920 MeV, $$\Gamma (X(3915))=20$$ Γ ( X ( 3915 ) ) = 20 MeV; $$M(X(3960))=3970$$ M ( X ( 3960 ) ) = 3970 MeV, $$\Gamma (X(3960)=45(5)$$ Γ ( X ( 3960 ) = 45 ( 5 ) MeV, $$M(X_0(4140))= 4120(20)$$ M ( X 0 ( 4140 ) ) = 4120 ( 20 ) MeV, $$\Gamma (X_0(4140))=100$$ Γ ( X 0 ( 4140 ) ) = 100 MeV, which are in good agreement with experiment.

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: 23 pages,3 figures

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: 11 pages,1 figure. arXiv admin note: substantial text overlap with arXiv:2206.14489

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

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

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., 21 pages,2 figures

В работе выявлена четкая взаимосвязь количества и свойств остаточного аустенита, содержащегося в конструкционных легированных сталях после закалки в бейнитной области температур, с их механическими свойствами, и впервые разработан способ неразрушающего контроля качества применяемой термической обработки и уровня ударной вязкости деталей из этих сталей. The work reveals a clear relationship between the amount and properties of retained austenite contained in structural alloy steels after bainite hardening with mechanical properties, and for the first time the nondestructive quality controlling method for the applied heat treatment and the level of impact toughness of parts has been developed. Исследование выполнено в рамках государствен­ного задания Минобрнауки России (темы «Давление» г. р. № АААА­А18-118020190104-3 и «Структура» г. р. № АААА-А18-118020190116-6) при частичной поддержке РФФИ (проект № 20-03-00056). The study was carried out within the framework of the state task of the Ministry of Education and Science of Russia (topics “Pressure”, born in the year no. AAAA18-118020190104-3 and “Structure”, born in the year no. AAAA18-118020190116-6) with partial support of the RFBR (project no. 20-03-0056).

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 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.

The modes of laser surface treatment of VT9 and VT18u titanium alloys were investigated. The microhardness of the surface layers of the samples tested by the Berkovich and Vickers pyramids was calculated. The restored imprint method was used for calculations. An increase in the microhardness of the surface after processing by a series of nanosecond pulses was established. Possible mechanisms contributing to the increase in the microhardness of the surface layers of titanium alloys were analyzed. Рассмотрены режимы лазерной обработки поверхности титановых сплавов ВТ9 и ВТ18у. По методу восстановленного отпечатка рассчитана микротвердость поверхностных слоев образцов при индентировании пирамидками Берковича и Виккерса. Установлено возрастание микротвердости поверхности после обработки сериями наносекундных импульсов. Проанализированы возможные механизмы, способствующие повышению микротвердости приповерхностных слоев титановых сплавов.

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., 10 pages, 3 figures

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 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 $��_q >0.5$ GeV there exists a region in the $(��, T)$ 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., 18 pages , 11 figures

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

3-Acyloxy-7-bromo-5-(2’-chloro)phenyl-1,2-dihydro-3.H-1,4-benzodiazepin-2-ones (2-8) were synthesized by the interaction of the 7-bromo-3-hydroxy-5-(2’-chloro)phenyl-1,2-dihydro-3.H-1,4-benzodiazepin-2-one (1) with chloroanhy-drides of corresponding carboxylic acids. The formation of hydrogen bonds in solutions of the obtained esters was studied by the method of IR spectroscopy. The molecular and crystalline structure of lauroiloxyderivative 5 was determined by the method of X-ray diffraction analysis. It was noted, that enantic ester of 7-bromo-3-hydroxy-5-(2’-chloro)phenyl-1,2-dihydro-3.H-1,4-benzodiazepin-2-one (3) has showed the highest anticonvulsant activity. This activity is observed in half an hour after injection and remain on the level 200% of control values over 24 hours., 3-Ацилокси-7-бром-5-(2’-хлорфеніл)-1,2-дигідро-3.Н-1,4-бенздіазешн-2-они (28) отримано взаємодією 7-бром-3-гідрокси-5-(2’-хлор)феніл-1,2-дигідро-3.Н-1,4-бенздіазепін-2-ону (1) з хлорангідридами відповідних карбонових кислот. Вивчено утворення водневих зв’язків у розчинах отриманих естерів за допомогою ІЧ спектроскопії. Встановлена кристалічна та молекулярна структура лауроїлоксипохідного 5 методом рентгеноструктурного аналізу. Найбільша протисудомна дія була встановлена для енантового естеру 7-бром-3-гідрокси-5-(2’-хлор)феніл-1,2-дигідро-3.Н-1,4-бенздіазешн-2-ону (3), яка проявляється вже за 0,5 год після введення та зберігається на рівні 200% від контрольних значень протягом 24 год.

The standard $SU(2) \times U(1)$ fields are considered in 4D plus one extra compact dimension. As a result two basic effects are obtained. First, four Goldstone-like scalars are produced, three of them are used to create longitudinal modes of the $W,Z$ fields, while the fourth becomes the Higgs-like scalar. Second, $W$ and $Z$ get their masses from the extra compact dimension with the standard pattern of symmetry violation. The resulting theory has the same fields as in the standard model, but without the Higgs vacuum average. The properties of the new Higgs scalar and its interaction with fermions are briefly discussed., Comment: 11 pages

Hadron decay widths are shown to increase in strong magnetic fields as $\Gamma (eB) \sim \frac{eB}{\kappa} \Gamma(0)$. The same mechanism is shown to be present in the production of the sea quark pair inside the confining string, which decreases the string tension with the growing $eB$ parallel to the string . On the other hand, the average energy of the $q\bar q$ holes in the string world sheet increases, when the direction of $\mathbf{B}$ is perpendicular to the sheet. These two effects stipulate the spectacular picture of the $\mathbf{B}$ dependent confinement and $\alpha_s$, discovered on the lattice., Comment: 14 pages; 2 figures; LaTeX2e

Radiative decays of $X(3872)$ are studied in single-channel approximation (SCA) and in the coupled-channel (CC) approach, where the decay channels $D\bar D^*$ are described with the string breaking mechanism. In SCA the transition rate $\tilde{\Gamma}_2=\Gamma(2\,{}^3P_1 \rightarrow \psi\gamma)=71.8$~keV and large $\tilde{\Gamma}_1=\Gamma(2\,{}^3P_1\rightarrow J/\psi\gamma)=85.4$~keV are obtained, giving for their ratio the value $\tilde{R_{\psi\gamma}}=\frac{\tilde{\Gamma}_2}{\tilde{\Gamma}_1}=0.84$. In the CC approach three factors are shown to be equally important. First, the admixture of the $1\,{}^3P_1$ component in the normalized wave function of $X(3872)$ due to the CC effects. Its weight $c_{\rm X}(E_{\rm R})=0.200\pm 0.015$ is calculated. Secondly, the use of the multipole function $g(r)$ instead of $r$ in the overlap integrals, determining the partial widths. Thirdly, the choice of the gluon-exchange interaction for $X(3872)$, as well as for other states above threshold. If for $X(3872)$ the gluon-exchange potential is taken the same as for low-lying charmonium states, then in the CC approach $\Gamma_1= \Gamma(X(3872)\rightarrow J/\psi\gamma) \sim 3$~keV is very small, giving the large ratio $R_{\psi\gamma}=\frac{\mathcal{B}(X(3872)\rightarrow \psi(2S)\gamma)}{\mathcal{B}(X(3872)\rightarrow J/\psi\gamma)}\gg 1.0$. Arguments are presented why the gluon-exchange interaction may be suppressed for $X(3872)$ and in this case $\Gamma_1=42.7$~keV, $\Gamma_2= 70.5$~keV, and $R_{\psi\gamma}=1.65$ are predicted for the minimal value $c_{\rm X}({\rm min})=0.185$, while for the maximal value $c_{\rm X}=0.215$ we obtained $\Gamma_1=30.8$~keV, $\Gamma_2=73.2$~keV, and $R_{\psi\gamma}=2.38$, which agrees with the LHCb data., Comment: 12 pages, no figures

Hadron decay widths are shown to increase in strong magnetic fields as $��(eB) \sim \frac{eB}�� ��(0)$. The same mechanism is shown to be present in the production of the sea quark pair inside the confining string, which decreases the string tension with the growing $eB$ parallel to the string . On the other hand, the average energy of the $q\bar q$ holes in the string world sheet increases, when the direction of $\mathbf{B}$ is perpendicular to the sheet. These two effects stipulate the spectacular picture of the $\mathbf{B}$ dependent confinement and $��_s$, discovered on the lattice., 14 pages; 2 figures; LaTeX2e

Radiative decays of $X(3872)$ are studied in single-channel approximation (SCA) and in the coupled-channel (CC) approach, where the decay channels $D\bar D^*$ are described with the string breaking mechanism. In SCA the transition rate $\tilde��_2=��(2\,{}^3P_1 \rightarrow ����)=71.8$~keV and large $\tilde��_1=��(2\,{}^3P_1\rightarrow J/����)=85.4$~keV are obtained, giving for their ratio the value $\tilde{R_{����}}=\frac{\tilde��_2}{\tilde��_1}=0.84$. In the CC approach three factors are shown to be equally important. First, the admixture of the $1\,{}^3P_1$ component in the normalized wave function of $X(3872)$ due to the CC effects. Its weight $c_{\rm X}(E_{\rm R})=0.200\pm 0.015$ is calculated. Secondly, the use of the multipole function $g(r)$ instead of $r$ in the overlap integrals, determining the partial widths. Thirdly, the choice of the gluon-exchange interaction for $X(3872)$, as well as for other states above threshold. If for $X(3872)$ the gluon-exchange potential is taken the same as for low-lying charmonium states, then in the CC approach $��_1= ��(X(3872)\rightarrow J/����) \sim 3$~keV is very small, giving the large ratio $R_{����}=\frac{\mathcal{B}(X(3872)\rightarrow ��(2S)��)}{\mathcal{B}(X(3872)\rightarrow J/����)}\gg 1.0$. Arguments are presented why the gluon-exchange interaction may be suppressed for $X(3872)$ and in this case $��_1=42.7$~keV, $��_2= 70.5$~keV, and $R_{����}=1.65$ are predicted for the minimal value $c_{\rm X}({\rm min})=0.185$, while for the maximal value $c_{\rm X}=0.215$ we obtained $��_1=30.8$~keV, $��_2=73.2$~keV, and $R_{����}=2.38$, which agrees with the LHCb data., 12 pages, no figures

Magnetic susceptibility in the deconfined phase of QCD is calculated in a closed form using a recent general expression for the quark gas pressure in magnetic field. Quark selfenergies are entering the result via Polyakov line factors and ensure the total paramagnetic effect, increasing with temperature. A generalized form of magnetic susceptibility in nonzero magnetic field suitable for experimental and lattice measurements is derived, showing a good agreement with available lattice data., 5 pages, 1 figure

Nonperturbative treatment of quark-hadron transition at nonzero temperature T and chemical potential mu in the framework of Field Correlator Method is generalized to the case of nonzero magnetic field B. A compact form of the quark pressure for arbitrary B, mu, T is derived. As a result the transition temperature is found as a function of B and mu, which depends on only parameters: vacuum gluonic condensate G_2 and the field correlator D_1^E(x), which defines the Polyakov loops and it is known both analytically and on the lattice. A moderate (25%) decrease of T_c(mu=0) for eB changing from zero to 1 GeV^2 is found. A sequence of transition curves in the (mu, T) plane is obtained for B in the same interval, monotonically decreasing in scale for growing B., Comment: 24 pages, 2 figures, misprints corrected, references added

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., 10 Pages LaTeX, 2 Postscript Figures

Radiative decays of X(3872) with $J^{PC}=1^{++}$ are studied in the coupled-channel approach, where the $c\bar c$ states are described by relativistic string Hamiltonian, while for the decay channels $DD^*$ a string breaking mechanism is used. Within this method a sharp peak and correct mass shift of the $2 {}^3P_1$ charmonium state just to the $D^0D^{*0}$ threshold was already obtained for a prescribed channel coupling to the $DD^*$ decay channels. For the same value of coupling the normalized wave function (w.f.) of X(3872) acquires admixture of the $1 {}^3P_1$ component with the w.f. fraction $c_1=0.153 (\theta=8.8^\circ$), which increases the transition rate $\Gamma(X(3872)\rightarrow J/\psi\gamma)$ up to 50-70 keV, making the ratio $R=\frac{\mathcal{B}(X(3872)\rightarrow \psi^{\prime}\gamma)}{\mathcal{B}(X(3872)\rightarrow J/\psi \gamma)}=0.8\pm 0.20 (th)$ significantly smaller, as compared to $R\simeq 5$ for X(3872) as a purely $2 {}^3P_1$ state., Comment: 14 pages,2 Tables

We study the relativistic quark-antiquark system embedded in magnetic field (MF). The Hamiltonian containing confinement, color Coulomb and spin-spin interaction is derived. We analytically follow the evolution of the lowest neutral meson state as a function of MF strength. Calculating the color Coulomb energy $V_{Coul}$ we have observed the unbounded negative (at least in the limit of large $N_c$) contribution at large MF which makes the mass negative for $eB> eB^{QCD}_{crit}$. We display the $\pi^0$ and $\rho^0$ masses as functions of MF in comparison with recent lattice data., Comment: 16 pages, 1 figure

Radiative decays of X(3872) with $J^{PC}=1^{++}$ are studied in the coupled-channel approach, where the $c\bar c$ states are described by relativistic string Hamiltonian, while for the decay channels $DD^*$ a string breaking mechanism is used. Within this method a sharp peak and correct mass shift of the $2 {}^3P_1$ charmonium state just to the $D^0D^{*0}$ threshold was already obtained for a prescribed channel coupling to the $DD^*$ decay channels. For the same value of coupling the normalized wave function (w.f.) of X(3872) acquires admixture of the $1 {}^3P_1$ component with the w.f. fraction $c_1=0.153 (��=8.8^\circ$), which increases the transition rate $��(X(3872)\rightarrow J/����)$ up to 50-70 keV, making the ratio $R=\frac{\mathcal{B}(X(3872)\rightarrow ��^{\prime}��)}{\mathcal{B}(X(3872)\rightarrow J/����)}=0.8\pm 0.20 (th)$ significantly smaller, as compared to $R\simeq 5$ for X(3872) as a purely $2 {}^3P_1$ state., 14 pages,2 Tables

The QCD string breaking due to quark pair creation in the vacuum confining field, possibly accompanied by vector, scalar or Nambu-Goldstone bosons, is studied nonperturbatively. The scalar light pair creation vertex occurs due to chiral symmetry breaking and has a confining form, which is computed explicitly together with subleading vector contributions. Dependence on light quark mass and flavor is specifically studied. The dominant scalar term is in good agreement with the $^3P_0$ model and experimental data., LaTeX2,17 pages,2 figures

Dynamical equations for fermion masses are derived using high scale universal mass generation and consequent mass evolution due to $SU(3), SU(2)$, and U(1$ gauge interaction. Assuming mass generation at the GUT scale $M=10^{14}$ GeV, one obtains hierarchy and a large spread in fermion masses with roughly correct values of $m_\nu, m_\tau, m_t, m_b$ in the third generation. The smallness of neutrino mass, $\nu_3\sim 10^{-12} m_{t}$, naturally arises in the solution., Comment: 4 pages

The crystal structure of racemate R,S-7-bromo-3-(2-methoxy)ethoxy-5-phenyl-1,2-dihydro-3H-1,4-benzodiazepine-2-one (1) has been compared to the structure of R-enantiomer. It has been determined that crystals of R-enantiomer and R,S-racemate are formed by the similar H-bonded chains. In the crystal of racemate there are two types of chains each built up exclusively from the molecules of the same configuration whereas the crystal of R-enantiomer is formed by identical parallel chains. All the compounds studied have been found to possess a high analgesic activity, which exceeds the activity of the reference medicine. Проведено порівняння кристалічної структури R,S-7-бром-3-(2-метокси)етокси-5-феніл-1,2-дигідро-ЗН-1,4-бенздіазепін-2-ону зі структурою R-енантіомера. Встановлено, що кристали R-енантіомера і R,S-рацемату сформовані ланцюгами, зв'язаними за рахунок водневих зв'язків. У кристалі рацемату утворюються ланцюги, що складаються з молекул тільки R- або S-енантіомера, які формують протилежно спрямовані спіралі, а кристал R-енантіомера утворений ідентичними паралельними ланцюгами. Виявлено, що всі досліджені сполуки мають високу аналгетичну активність, яка перевершує активність препарату порівняння. Проведено сравнение кристаллической структуры R,S-7-бром-5-(2-метокси)этокси-5-фенил-1,2-дигидро-ЗН-1,4-бенздиазепин-2-она со структурой R-энантиомера. Установлено, что кристаллы R-энантиомера и R,S-рацемата сформированы цепями, связанными за счет водородных связей. В кристалле рацемата образуются цепи, состоящие из молекул только R- либо S-энантиомеров, которые формируют противоположно направленные спирали, а кристалл R-энантиомера образован идентичными параллельными цепями. Обнаружено, что все исследуемые соединения обладают высокой анальгетической активностью, превосходящей активность препарата сравнения.

A comprehensive study of the color singlet heavy quark states above T_c is given, using the Field Correlator Method (FCM) for nonperturbative Q{\bar Q} potentials and the screened Coulomb potential with the T-dependent Debye radius. Using these potentials we calculate binding energies and melting temperatures of heavy mesons and baryons in the deconfined phase of quark-gluon plasma and the J/\psi and Upsilon disintegration cross sections via the gluon absorption., Comment: Slightly modified journal version, 2 figures and few references added

We use the screened Coulomb potential with $r$-dependent coupling constant and the non--perturbative quark--antiquark potential derived within Field Correlator Method (FCM) to calculate $J/\psi$ and $\Upsilon$ binding energies and melting temperatures in the deconfined phase of quark-gluon plasma., Comment: Summary of talks given at the 14th Lomonosov Conference on Elementary Particle Physics, August 19-25, 2009, MSU, Moscow, at Session of RAS Nuclear Physics Department, November 23-27, 2009, ITEP, and at XIII International Conference on Hadron Spectroscopy, November 29 - December 4, 2009, FSU, Tallahassee, USA

A new approach to EW composite scalars is developed, starting from the fundamental gauge interaction on high scale. The latter is assumed to have the group structure $SU(2)_L \times SU(2)_R\times SU(4)$ where SU(4) is the Pati-Salam color-lepton group. The topological EW vacuum filled by instantons is explicitly constructed and the resulting equations for fermion masses exhibit spontaneous SU(2) flavor symmetry violation with possibility of very large mass ratios., Comment: LaTeX,31 pages

We use the screened Coulomb potential with $r$-dependent coupling constant and the non--perturbative quark--antiquark potential derived within Field Correlator Method (FCM) to calculate $J/��$ and $��$ binding energies and melting temperatures in the deconfined phase of quark-gluon plasma., Summary of talks given at the 14th Lomonosov Conference on Elementary Particle Physics, August 19-25, 2009, MSU, Moscow, at Session of RAS Nuclear Physics Department, November 23-27, 2009, ITEP, and at XIII International Conference on Hadron Spectroscopy, November 29 - December 4, 2009, FSU, Tallahassee, USA

The mechanism of string creation for light quarks developed earlier is considered for nonzero quark chemical potential. A strong modification of the confining string due to finite quark density (chemical quark potential $\mu$) is observed. As a surprising result in a multiquark system with a common string junction an attractive well appears of radius $\mu/\sigma$ and of an average depth equal to $\mu$, which induces formation of multiquark hadrons. Preliminary estimates predict a new phase transition to multiquark hadron phase at rather high densities (in heavy ion collisions or in neutron stars) when neutron matter is compressed to 3-4 normal nuclear densities., Comment: 12 pages, 1 figure, 2 tables; to be published in Phys. Lett. B

International audience

The $\eta$ production in the $(n,n')$ bottomonium transitions $\Upsilon (n) \to \Upsilon (n') \eta, $ is studied in the method used before for dipion heavy quarkonia transitions. The widths $\Gamma_\eta(n,n')$ are calculated without fitting parameters for $n=2,3,4,5, n'=1$.Resulting $\Gamma_\eta(4,1)$ is found to be large in agreement with recent data., Comment: 10 pages

Two- and three-body decays of $\Upsilon (5S)$ into $BB, $$ BB^*, $ $ B^*B^*,$ $ B_sB_s, $ $B_sB_s^*, $ $B_s^* B_s^*$ and $BB^*\pi, B^*B^*\pi$ are evaluated using the theory, developed earlier for dipion bottomonium transitions. The theory contains only two parameters, vertex masses $M_{br}$ and $M_\omega$, known from dipion spectra and width. Predicted values of $\Gamma_{tot}(5S)$ and six partial widths $\Gamma_k(5S), k=BB, BB^*,...$ are in agreement with experiment. The decay widths $\Gamma_{5S}(\pi BB^*)$ and $\Gamma_{5S}(\pi B^*B^*)$ are also calculated and found to be of the order of 10 keV., Comment: 6 pages

Dipion transitions of $\Upsilon (nS)$ with $n=5, n'=1,2,3$ are studied using the Field Correlator Method, applied previously to dipion transitions with $n=2,3,4$ The only two parameters of effective Lagrangian were fixed in that earlier study, and total widths $\Gamma_{\pi\pi} (5, n')$ as well as pionless decay widths $\Gamma_{BB} (5S), \Gamma_{BB^*} (5S), \Gamma_{B^*B^*}(5S)$ and $\Gamma_{KK} (5, n')$ were calculated and are in a reasonable agreement with experiment. The experimental $\pi\pi$ spectra for $(5,1)$ and (5,2) transitions are well reproduced taking into account FSI in the $\pi\pi$., Comment: 16 pages, 6 figures

In the framework of the coupled channel model the mass shifts of the $P$--wave excitations of $D_s$ and $B_s$ mesons have been calculated. The corresponding coupling to $DK$ and $BK$ channels is provided by the effective chiral Lagrangian which is deduced from QCD and does not contain fitting parameters. The strong mass shifts down for $0^+$ and ${1^+}'$ states have been obtained, while ${1^+}"$ and $2^+$ states remain almost at rest. Two factors are essential for large mass shifts: strong coupling of the $0^+$ and $1^{+'}$ states to the $S$-wave decay channel, containing a Nambu-Goldstone meson, and the chiral flip transitions due to the bispinor structure of both heavy-light mesons. The masses $M(B^*_s(0^+))=5710(15)$ MeV and $M(B_s(1^{+'}))=5730(15)$ MeV are predicted. Experimental limit on the width $\Gamma(D_{s1}(2536)), Comment: to be published in the Proceedings of the Conference QUARKS-2008, Sergiev Posad, Russia, 23rd-29th May 2008

Two- and three-body decays of $��(5S)$ into $BB, $$ BB^*, $ $ B^*B^*,$ $ B_sB_s, $ $B_sB_s^*, $ $B_s^* B_s^*$ and $BB^*��, B^*B^*��$ are evaluated using the theory, developed earlier for dipion bottomonium transitions. The theory contains only two parameters, vertex masses $M_{br}$ and $M_��$, known from dipion spectra and width. Predicted values of $��_{tot}(5S)$ and six partial widths $��_k(5S), k=BB, BB^*,...$ are in agreement with experiment. The decay widths $��_{5S}(��BB^*)$ and $��_{5S}(��B^*B^*)$ are also calculated and found to be of the order of 10 keV., 6 pages

In the deconfinement phase of QCD quarks and gluons interact with the dense stochastic colour-magnetic vacuum. We consider the dynamics of quarks in this deconfinement phase using the Field Correlators Method and derive an effective nonperturbative inter-quark potential, in addition to the usual perturbative short-ranged interaction. We find the resulting angular-momentum-dependent interaction to be attractive enough to maintain bound states and, for light quarks (and gluons), to cause emission of quark and gluon pairs. Possible consequences for the strong interacting quark--gluon plasma are briefly discussed., Comment: LaTeX2e, 12 pages

The 4q effective Lagrangian and the gap equation are derived for light quarks in the confinement phase of QCD. The modification of the confining string due to finite quark density (chemical quark potential \mu) is observed. As a surprising result in a multiquark system with a common string junction an attractive well appears of radius \mu/\sigma and of an average depth equal to \mu. Possible implications for the density phase transition are discussed., Comment: 10 pages

Spin-dependent deconfined interaction in the Q\barQ system is derived from the field correlators known from lattice and analytic calculations. As a result hyperfine splitting is found numerically for charmonium, bottomonium and strangeonium in the range T_c, Comment: 11 pages,in honor of Adriano Di Giacomo on his 70th birthday, to be published in the Festschrift