Fluctuations In High-energy Collisions Research Articles

Pseudorapidity window size dependence of multiplicity fluctuations in high-energy collisions with system size and beam energies

An investigation of the critical behavior of strongly interacting quantum chromodynamics (QCD) matter has been performed by analyzing fluctuation observables on event-by-event (ebe) basis measured in high-energy collision experiments. The fluctuation analysis is performed using nuclear interactions at different target sizes and at different colliding beam energies as a function of varying width of pseudorapidity interval. For the sake of comparison, ebe multiplicity fluctuations in hadronic and heavy ion collisions (p–H, p–A and A–B) are studied within the framework of the Lund Monte Carlo-based FRITIOF model. Charged particle multiplicity and the variance of the multiplicity distribution are estimated for the interactions involving different target sizes and beam momenta, i.e., p–H, p–CNO, p–AgBr at 200 A GeV/c and [Formula: see text]O–AgBr collisions at 14.6 A, 60 A and 200 A GeV/c. Further, multiplicity fluctuations are quantified in terms of intensive quantity, the scaled variances [Formula: see text] and the strongly intensive quantity [Formula: see text] derived from the charged particle multiplicity and the width of the multiplicity distribution. Strongly intensive quantity [Formula: see text] is a quantity of great significance to extract information about short- and long-range multiplicity correlations. Furthermore, the collision centrality and centrality bin width-dependent behavior of the multiplicity fluctuation have been examined in the framework of Lund Monte Carlo-based FRITIOF model. Results based on the fluctuation analysis carried out in this study are interpreted in terms of dynamics of collision process and the possibility of related QCD phase transition.

Entropic Divergence and Entropy Related to Nonlinear Master Equations

We reverse engineer entropy formulas from entropic divergence, optimized to given classes of probability distribution function (PDF) evolution dynamical equation. For linear dynamics of the distribution function, the traditional Kullback–Leibler formula follows from using the logarithm function in the Csiszár’s f-divergence construction, while for nonlinear master equations more general formulas emerge. As applications, we review a local growth and global reset (LGGR) model for citation distributions, income distribution models and hadron number fluctuations in high energy collisions.

Normalization of strongly intensive quantities

Recently, two strongly intensive quantities, $\ensuremath{\Delta}[A,B]$ and $\ensuremath{\Sigma}[A,B]$, designed for the study of event-by-event fluctuations in high-energy collisions were introduced. They are defined in terms of two extensive event observables $A$ and $B$. In this paper a special normalization of the $\ensuremath{\Delta}[A,B]$ and $\ensuremath{\Sigma}[A,B]$ fluctuation measures is proposed. It ensures that they are dimensionless and yields a common scale required for a quantitative comparison of fluctuations of different, in general dimensional, extensive quantities. Namely, the properly normalized strongly intensive measures assume the value one for fluctuations given by the independent particle model, and they are equal to zero when the $A$ and $B$ observables have constant values in all collision events.

Levy Stability Index from Multifractal Spectrum

A method for extracting the Levy stability index μ from the multi-fractal spectrum f(α) in high energy multiparticle production is proposed. This index is an important parameter, characterizing the non-linear behaviour of dynamical fluctuations in high energy collisions. Using the random cascading α model as an example, the validity of this method is tested. It is shown that this method, based on a linear fit, is consistent with and more accurate than the usual method, which gets the Levy index through fitting the ratio of qth to 2nd order multi-fractal (Rényi) dimensions to the Peschanski formula.

Some Analytical Results of Bunching Parameters for Multiplicity Fluctuations in High Energy Collisions

A few analytical results are presented for the bunching parameters analysis applied to study the fluctuations of hadron multiplicity density in high energy collisions. The behaviors of bunching parameters are analyzed in the cases of concatenate and partitioning fluctuations. The effect of pairing in partition is also studied. As the phase-space decreases, the concatenation can be observed as the divergence of one of the bunching parameters, which also implies a strong short range correlation. In the case of a weak short range correlation, both types of binomial partitions lead to saturation for all the bunching parameters. As the phase-space increases, the effects of pair production can be observed as the oscillatory bunching parameters ηq — a function of order q. The characteristics of the observed features are discussed. Comparisons to experimental data are also presented.

Fractal behavior of multiplicity fluctuations in high-energy collisions

It is shown that the multiplicity fluctuations of the particles produced in high-energy hadron collisions can be systematically quantified by the $G$ moments, which can be defined to suppress the statistical contributions. Expansion in terms of a set of basic functions ${B}_{q,k}(M)$ provides simple fractal interpretation for the asymptotic power-law behavior of $〈{G}_{q}〉$. The connection with the scaled factorial moments is investigated. An extension to nonintegral values of $q$ is considered. The generalized fractal dimension ${D}_{q}$ is determined. Calculations of all quantities involving multiplicity fluctuations are done using a Monte Carlo code (ECCO) based on the geometrical branching model, which has previously been shown to yield the correct degree of intermittency as determined by the NA22 experiment on hadronic collisions.

Moments of rapidity distributions as a measure of short-range fluctuations in high-energy collisions

It is proposed to study the dependence of factorial moments of the rapidity distribution on the size δy of the resolution. It is shown that if the fluctuations are purely statistical no variation of moments δy is expected, and thus observation of such a variation indicates the presence of genuine fluctuations of physical origin. The region in which the change occurs corresponds to the size (in rapidity) of the observed fluctuations. Intermittency, i.e. fluctuations of many different sizes, would show up as a power-law behaviour of moments on δy. A good experimental resolution can be obtained from the rapidity distribution of high multiplicity events.

Inclusive Spectra in Deeply InelasticepCollisions

We develop a picture of $\mathrm{ep}$ collisions which is in the spirit of recent speculations concerning multiplicity fluctuations in high-energy collisions. We analyze the implications for experimental studies.