Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics

Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and shape invariance - two main ingredients of the supersymmetrical quantum mechanics. The first method explores the opportunity to separate variables in the supercharge, and it allows to find a part of spectrum of the Schr\"odinger Hamiltonian. The second method works when the standard separation of variables procedure can be applied for one of the partner Hamiltonians. Then the spectrum and wave functions of the second partner can be found. Both methods are illustrated by the example of two-dimensional generalization of Morse potential for different values of parameters

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

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

Pentaquark decay is suppressed by chirality conservation

It is shown, that if the pentaquark $\Theta^+ = uudd\bar{s}$ baryon can be represented by the local quark current $\eta_{\Theta}$, its decay $\Theta^+ \to n K^+ (p K^0)$ is forbidden in the limit of chirality conservation. The $\Theta^+$decay width $\Gamma$ is proportional to $\alpha^2_s < 0 | \bar{q} q | 0 >^2$, where $$, $q = u,d,s$ is quark condensate, and, therefore, is strongly suppressed. Also the polarization operator of the pentaquark current with isospin 1 is calculated using the operator product expansion and estimation for it mass is obtained .Comment: 4 pages, 1 fig, typos correcte

Comment on "Remark on the external-field method in QCD sum rules"

It is proved, that suggested by Jin modified formalism in the external-field method in QCD sum rules exactly coincides with the formalism used before. Therefore, unlike the claims of ref.1, this formalism cannot improve the predictability and reliability of external-field sum rule calculations in comparison with those, done by the standard approach. PACS number(s): 12.38.Lg, 11.55.HxComment: 5 pages, RevTe

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