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

Improved Calculations of Quark Distributions in Hadrons: the case of pion

The earlier introduced method of calculation of quark distributions in hadrons, based on QCD sum rules, is improved. The imaginary part of the virtual photon forward scattering amplitude on some hadronic current is considered in the case, when initial and final virtualities of the current $p^2_1$, and $p^2_2$ are different, $p^2_1\not= p^2_2$. The operator product expansion (OPE) in $p^2_1$, $p^2_2$ is performed. The sum rule for quark distribution is obtained using double dispersion representation of the amplitude on one side in terms of calculated in QCD OPE and on the other side in terms of physical states contributions. Double Borel transformation in $p^2_1$, $p^2_2$ is applied to the sum rule, killing background non-diagonal transition terms, which deteriorated the accuracy in previous calculations. The case of valence quark distribution in pion is considered, which was impossible to treat by the previous method. OPE up to dimension 6 operators is performed and leading order perturbative corrections are accounted. Valence $u$-quark distribution in $\pi^+$ was found at intermediate $x$, $0.15 < x < 0.7$ and normalization point $Q^2=2 GeV^2$. These results may be used as input for evolution equations.Comment: 29 pages, LaTeX 2e, 13 eps figures include

Geometric variational problems of statistical mechanics and of combinatorics

We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a typical Young diagram and of a typical skyscraper.Comment: 10 page

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

Gluon Polarization from QCD Sum Rules

The gluon polarization $\Delta G$ in a nucleon can be defined in a gauge invariant way as the integral over the Ioffe-time distribution of polarized gluons. We argue that for sufficiently regular polarized gluon distributions $\Delta G$ is dominated by contributions from small and moderate values of the Ioffe-time z < 10. As a consequence $\Delta G$ can be estimated with 20% accuracy from the first two even moments of the polarized gluon distribution, and its behavior at small values of Bjorken x or, equivalently, at large Ioffe-times z. We employ this idea and compute the first two moments of the polarized gluon distribution within the framework of QCD sum rules. Combined with the color coherence hypothesis we obtain an upper limit for $\Delta G \sim 2 \pm 0.5$ at a typical scale $\mu^2 \sim 1 GeV^2$.Comment: 12 pages, Latex, 2 figures include

Performance analysis of an interacting quantum dot thermoelectric system

We analyze the nanocaloritronic performance of an interacting quantum dot that is subject to an applied bias and an applied temperature gradient. It is now well known that, in the absence of phonon contribution, a weakly coupled non-interacting quantum dot can operate at thermoelectric efficiencies approaching the Carnot limit. However, it has also been recently pointed out that such peak efficiencies can only be achieved when operated in the reversible limit, with a vanishing current and hence a vanishing power output. In this paper, we point out three fundamental results affecting the thermoelectric performance due to the inclusion of Coulomb interactions: a) The reversible operating point carries zero efficiency, b) operation at finite power output is possible even at peak efficiencies approaching the Carnot value, and c) the evaluated trends of the the maximum efficiency deviate considerably from the conventional {\it{figure of merit}} $zT$ based result. Finally, we also analyze our system for thermoelectric operation at maximum power output.Comment: 10 pages, 6 figures, Resubmission- to be published in Phys. Rev.

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