Quark distributions in QCD sum rules: unexpected features and paradoxes

Some very unusual features of the hadron structure functions, obtained in the generalized QCD sum rules, like the surprisingly strong difference between longitudinally and transversally polarized $\rho$ mesons structure functions and the strong suppression of the gluon sea in longitudinally polarized $\rho$ mesons are discussed. Also the problem of exact zero contribution of gluon condensates to pion and longitudinally polarized $\rho$ meson quark distributions is discussed.Comment: 9 pages, 5 fig

Spontaneous violation of chiral symmetry in QCD vacuum is the origin of baryon masses and determines baryon magnetic moments and their other static properties

A short review is presented of the spontaneous violation of chiral symmetry in QCD vacuum. It is demonstrated, that this phenomenon is the origin of baryon masses in QCD. The value of nucleon mass is calculated as well as the masses of hyperons and some baryonic resonances and expressed mainly through the values of quark condensates -- $, ~q=u,d,s$ -- the vacuum expectation values (v.e.v.) of quark field. The concept of vacuum expectation values induced by external fields is introduced. It is demonstrated that such v.e.v. induced by static electromagnetic field results in quark condensate magnetic susceptibility, which plays the main role in determination of baryon magnetic moments. The magnetic moments of proton, neutron and hyperons are calculated. The results of calculation of baryon octet $\beta$-decay constants are also presented.Comment: 13 pades, 5 figures. Dedicated to 85-birthday of acad. S.T.Belyaev. To be published in Phys.At.Nucl. Few references are correcte

Calculation of the pentaquark width by QCD sum rule

The pentaquark width is calculated in QCD sum rules. Result for $\Gamma_{\Theta}$ show, that $\Gamma_{\Theta}$ can vary in the region less than 1$MeV$. The main conclusion is, that if pentaquark is genuine states then sum rules really predict the narrow width of pentaquark $\theta^+$, and the suppression of the width is both parametrical and numerical.Comment: 8 Ppages, 3 figures,the numerical error was corrected, two figures are modified. In the limit of errors the result did not change significantl

SUSY approach to Pauli Hamiltonians with an axial symmetry

A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix Hamiltonian is analyzed from the point of view of supersymmetric quantum mechanics. Attention is paid to the discrete symmetries of the Hamiltonian and also to the Hamiltonian hierarchies generated by intertwining operators. The spectrum is studied by means of the associated matrix shape-invariance. The relation between the intertwining operators and the second order symmetries is established and the full set of ladder operators that complete the dynamical algebra is constructed.Comment: 18 pages, 3 figure

New Two-Dimensional Integrable Quantum Models from SUSY Intertwining

Supersymmetrical intertwining relations of second order in the derivatives are investigated for the case of supercharges with deformed hyperbolic metric $g_{ik}=diag(1,-a^2)$. Several classes of particular solutions of these relations are found. The corresponding Hamiltonians do not allow the conventional separation of variables, but they commute with symmetry operators of fourth order in momenta. For some of these models the specific SUSY procedure of separation of variables is applied.Comment: 18 page

Chirality violating condensates in QCD and their connection with zero mode solutions of quark Dirac equations

It is demonstrated, that chirality violating condensates in massless QCD arise entirely from zero mode solutions of Dirac equations in arbitrary gluon fields. The model is suggested, where the zero mode solutions are the ones for quarks, moving in the instanton field. Basing on this model were calculated the quark condensate magnetic susceptibilities of dimensions $3(\chi)$ and 5 ($\kappa$ and $\xi$). The good considence of the values $\chi,\kappa$ and $\xi$, obtained in this approach with ones, found from the hadronic spectrum ia a serious argument in favour, that instantons are the only source of chirality violating condensates in QCD. The temperature dependence of the quark condensate is discussed. It is shown that the phase transition, corresponding to the $T$-dependence of the quark condensate $\alpha(T)$ as an order parameter, is of the type of crossover.Comment: The talk presented of Gribov-80 Workshop, May 28-30, 2010, Trieste, 8 pages, minor change

On the theory of diamagnetism in granular superconductors

We study a highly disordered network of superconducting granules linked by weak Josephson junctions in magnetic field and develop a mean field theory for this problem. The diamagnetic response to a slow {\it variations} of magnetic field is found to be analogous to the response of a type-II superconductor with extremely strong pinning. We calculate an effective penetration depth $\lambda_g$ and critical current $j_c$ and find that both $\lambda_g^{-1}$ and $j_c$ are non-zero but are strongly suppressed by frustration.Comment: REVTEX, 12 pages, two Postscript figure

Combination Rules, Charge Symmetry, and Hall Effect in Cuprates

The rule relating the observed Hall coefficient to the spin and charge responses of the uniform doped Mott insulator is derived. It is essential to include the contribution of holon and spinon three-current correlations to the effective action of the gauge field. In the vicinity of the Mott insulating point the Hall coefficient is holon dominated and weakly temperature dependent. In the vicinity of a point of charge conjugation symmetry the holon contribution to the observed Hall coefficient is small: the Hall coefficient follows the temperature dependence of the diamagnetic susceptibility with a sign determined by the Fermi surface shape. NOTE: document prepared using REVTEX. (3 Figs, not included, available on request from: [email protected])Comment: 8 page

Hall Voltage Fluctuations as a Diagnostic of Internal Magnetic Field Fluctuations in High Temperature Superconductors and the Half-filled Landau Level

Fluctuations of the Hall voltage reveal information about long wavelength magnetic field fluctuations. If gauge theories of strongly correlated electrons are correct, such fluctuations are particularly large in the half-filled Landau level and in high $T_c$ superconductors. We present estimates for the magnitude, system size and frequency dependence of these fluctuations. The frequency dependence contains information about instantons in the gauge field.Comment: 4 pages, LATEX file and 1 PostScript figur