Cumulants of QCD Multiplicity Distributions in Small Phase Space Bins

It is shown that, as functions of their rank, cumulants of QCD multiplicity distributions in small phase space bins possess the quasi- oscillating behavior similar to that found for them in the total rapidity range. First minimum moves to lower ranks for smaller bins. For the total rapidity range, it moves to higher ranks with energy increase. The running property of the QCD coupling constant is in charge of these effects which can be verified in experiment.Comment: 7 pages, no Figs, preprint IP-ASTP-19; FIAN-TD 94/

The medium in heavy-ion collisions

The nuclear index of refraction, the density of partons, their free path length and energy loss in the matter created in heavy-ion collisions at RHIC are estimated within the suggestion that the emission of Cherenkov gluons is responsible for the observed two-bump structure of the angular distribution of hadrons belonging to the companion (away-side) jet.Comment: 3 pages, 1 Figur

High energy Cherenkov gluons at RHIC and LHC

The collective effect of emission by the forward moving partons of high energy Cherenkov gluons in nucleus-nucleus collisions at RHIC and LHC energies is considered. It can reveal itself as peaks in the pseudorapidity distribution of jets at midrapidities or as a ring-like structure of individual events in event-by-event analysis. The pseudorapidity distribution of centers of dense isolated groups of particles in HIJING model is determined. It can be considered as the background for Cherenkov gluons. If peaks above this background were found in experiment, they would indicate new collective effects.Comment: 8 pages, 2 figure

A Large Distance Expansion for Quantum Field Theory

Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the Hamiltonian to be reduced to algebraic equations. Applied to Yang-Mills theory this expansion leads to a confining force between quarks.Comment: 5 pages, latex, invited talk at the Second International Sakharov Conference on Physics, May 199

The background for Cherenkov gluons at RHIC and LHC energies

The pseudorapidity distribution of centers of dense isolated groups of particles in HIJING model is determined. It can be considered as the background for Cherenkov gluons. If peaks over this background were found in experiment, they would indicate the onset of new collective effects.Comment: 4 pages, 2 figures, uses espcrc1.sty; QM 2005 contributio

Energy dependence of mean multiplicities in gluon and quark jets at the next-to-next-to-next-to-leading order

Analytic predictions for the energy dependence of the mean multiplicities in gluon and quark jets are presented at the next-to-next-to-next-to-leading order (3NLO) of perturbative QCD and are compared to experiment. The 3NLO correction to the gluon jet multiplicity is found to be small. The corresponding theoretical expression provides a good description of available gluon jet measurements. In contrast, the 3NLO correction to the quark jet multiplicity is large and the theoretical expression does not describe the data accurately. It is shown that the well known success of the next-to-leading order (NLO) approximation in describing the energy evolution of quark jet multiplicity can be attributed to the equivalence of the quark and gluon expressions at NLO to within a constant factor, and to almost constant contributions from higher order terms to the gluon jet result

On distribution of number of trades in different time windows in the stock market

Properties of distributions of the number of trades in different intraday time intervals for five stocks traded in MICEX are studied. The dependence of the mean number of trades on the capital turnover is analyzed. Correlation analysis using factorial and $H_q$ moments demonstrates the multifractal nature of these distributions as well as some peculiar changes in the correlation pattern. Guided by the analogy with the analysis of particle multiplicity distributions in multiparticle production at high energies, an evolution equation relating changes in capital turnover and a number of trades is proposed. We argue that such equation can describe the observed features of the distribution of the number of trades in the stock market.Comment: LaTeX, 6 figure

Comparative Analysis of Multiplicity Distributions in Inelastic Processes for Different Colliding Particles and Nuclei

Theoretical prediction of oscillations of cumulant moments of parton multiplicity distributions inside a jet supported by experimental data in some multiple production processes asks for analysis of the phenomenon for the whole set of available reactions. We have found out that the oscillations persist in any kind of processes and increase for particles with more complicated structure i.e. in the order of ee, eh, hh, hA, AA. The effect is not strongly dependent on the available phase space. Theoretical values of moments for quark and gluon jets up to 5th rank are shown. Zeros of the truncated generating function and singularities of the total generating function are discussed.Comment: revised version -- no changes in the text, corrected 3 references; 10 pages, 4 Postscript figure

Cherenkov Glue in Opaque Nuclear Medium

The spectrum of Cherenkov gluons is calculated within the framework of in-medium QCD. It is compared with experimental data on the double-humped structure around the away-side jet obtained at RHIC. The values of the real and imaginary parts of the nuclear permittivity are obtained from these fits. It is shown that accounting for an additional smearing due to resonance-like production of final hadrons allows to achieve an agreement with experimental data

Fractional Fokker-Planck Equation and Oscillatory Behavior of Cumulant Moments

The Fokker-Planck equation is considered, which is connected to the birth and death process with immigration by the Poisson transform. The fractional derivative in time variable is introduced into the Fokker-Planck equation. From its solution (the probability density function), the generating function (GF) for the corresponding probability distribution is derived. We consider the case when the GF reduces to that of the negative binomial distribution (NBD), if the fractional derivative is replaced to the ordinary one. Formulas of the factorial moment and the $H_j$ moment are derived from the GF. The $H_j$ moment derived from the GF of the NBD decreases monotonously as the rank j increases. However, the $H_j$ moment derived in our approach oscillates, which is contrasted with the case of the NBD. Calculated $H_j$ moments are compared with those given from the data in $p\bar{p}$ collisions and in $e^+e^-$ collisions.Comment: 10 pages, 8 figures, submitted to Phys. Rev.