arXiv subjects
Publications and source records attributed to S. Hegyi.
The L\'evy $\alpha$-stable generalization of the ReBB model of elastic proton-proton and proton-antiproton scattering is presented. The motivation for the future use of this model in describing experimental data is discussed.
A simple Lévy-$α$ stable (SL) model is used to describe the data on elastic $pp$ and $p\bar p$ scattering at low-$|t|$ from SPS energies up to LHC energies. The SL model is demonstrated to describe the data with a strong non-exponential feature in a statistically acceptable manner. The energy dependence of the parameters of the model is determined and analyzed. The Lévy $α$ parameter of the model has an energy-independent value of 1.959 $\pm$ 0.002 following from the strong non-exponential behavior of the data. We strengthen the conclusion that the discrepancy between TOTEM and ATLAS elastic $pp$ differential cross section measurements arises only in the normalization and not in the shape of the distribution of the data as a function of $t$. We find that the slope parameter has different values for $pp$ and $p\bar p$ elastic scattering at LHC energies. This may be the effect of the odderon exchange or the jump in the energy dependence of the slope parameter in the energy interval 3 GeV $\lesssim \sqrt s \lesssim$ 4 GeV.
It is known that the Real Extended Bialas-Bzdak (ReBB) model describes the proton-proton ($pp$) and proton-antiproton ($p\bar p$) differential cross-section data in a statistically non-excludible way,\linebreak i.e., with a confidence level greater than or equal to 0.1\% in the center of mass energy range \linebreak 546 GeV $\leq\sqrt{s}\leq$ 8 TeV and in the squared four-momentum transfer range 0.37 GeV$^2$ $\leq -t\leq$ 1.2 GeV$^2$. Considering, instead of Gaussian, a more general Lévy $α$-stable shape for the parton distributions of the constituent quark and diquark inside the proton and for the relative separation between them, a generalized description of data is obtained, where the ReBB model corresponds to the $α=$ 2 special case. Extending the model to $α<$ 2, we conjecture that the validity of the model can be extended to a wider kinematic range, in particular, to lower values of the four-momentum transfer $-t$. We present the formal Lévy $α$-stable generalization of the Bialas-Bzdak model and show that a simplified version of this model can be successfully fitted, with $α<$ 2, to the non-exponential, low $-t$ differential cross-section data of elastic proton-proton scattering at $\sqrt{s} =$ 8 TeV.
Phi meson production is studied by the NA49 Collaboration in central Pb+Pb collisions at 20A, 30A, 40A, 80A and 158A GeV beam energy. The data are compared with measurements at lower and higher energies and to microscopic and thermal models. The energy dependence of yields and spectral distributions is compatible with the assumption that partonic degrees of freedom set in at low SPS energies.
The latest NA49 results on event-by-event transverse momentum fluctuations are presented for central Pb+Pb interactions over the whole SPS energy range (20A - 158A GeV). Two different methods are applied: evaluating the $Φ_{p_{T}}$ fluctuation measure and studying two-particle transverse momentum correlations. The obtained results are compared to predictions of the UrQMD model. The results on the energy dependence are compared to the NA49 data on the system size dependence. The NA61 (SHINE, NA49-future) strategy of searching of the QCD critical end-point is also discussed.
A model of particle production is developed based on a parallel with a theory of Bose-Einstein condensation and similarities with other critical phenomena such as critical opalescence. The role of a power law critical exponent tau and Levy index alpha are studied. Various features of this model are developed and compared with other commonly used models of particle production which are shown to differ by having different values for tau, alpha. While void scaling is a feature of this model, hierarchical structure is not a general property of it. The value of the exponent tau=2 is a transition point associated with void and hierarchical scaling features. An exponent gamma is introduced to describe enhanced fluctuations near a critical point. Experimentally determined properties of the void scaling function can be used to determine tau.
For particles emerging from a second order QCD phase transition, we show that a recently introduced shape parameter of the Bose-Einstein correlation function, the Levy index of stability equals to the correlation exponent - one of the critical exponents that characterize the behavior of the matter in the vicinity of the second order phase transition point. Hence the shape of the Bose-Einstein / HBT correlation functions, when measured as a function of bombarding energy and centrality in various heavy ion reactions, can be utilized to locate experimentally the second order phase transition and the critical end point of the first order phase transition line in QCD.
Bose-Einstein (or HBT) correlation functions are evaluated for the fractal structure of QCD jets. These correlation functions have a stretched exponential (or Levy-stable) form. The anomalous dimension of QCD determines the Levy index of stability, thus the running coupling constant of QCD becomes measurable with the help of two-particle Bose-Einstein correlation functions. These considerations are tested on NA22 and UA1 two-pion correlation data.
The peak of the two-particle Bose-Einstein correlation functions has a very interesting structure. It is often believed to have a multivariate Gaussian form. We show here that for the class of stable distributions, characterized by the index of stability $0 < α\le 2$, the peak has a stretched exponential shape. The Gaussian form corresponds then to the special case of $α= 2$. We give examples for the Bose-Einstein correlation functions for univariate as well as multivariate stable distributions, and check the model against two-particle correlation data.
The shape of Bose-Einstein (or HBT) correlation functions is determined for the case when particles are emitted from a stable source, obtained after convolutions of large number of elementary random processes. The two-particle correlation function is shown to have a {\it stretched exponential} shape, characterized by the Lévy index of stability $ 0 < α\le 2$ and the scale parameter $R$. The normal, Gaussian shape corresponds to a particular case, when $α= 2$ is selected. The asymmetry parameter of the stable source, $β$ is shown to be proportional to the angle, measured by the normalized three-particle cumulant correlations.
In QCD, the similarity of multiplicity distributions is violated i) by the running of the strong coupling constant alpha_s and ii) by the self-similar nature of parton cascades. It will be shown that the data collapsing behavior of P_n onto a unique scaling curve can be restored by performing the original scaling prescription (translation and dilatation) in the multiplicity moments' rank.
A generalization of the Polyakov-Koba-Nielsen-Olesen scaling law of the multiplicity distributions P(n,s) is developed. It states that a suitable change in the normalization point of P(n,s) compensated by a rescaling can restore data collapsing onto a universal curve if the original scaling rule is violated. We show that the iteratively executed transformation of P(n,s) can be viewed as varying the collision energy. The e+e- and p-pbar multiplicity data at top energies are found to exhibit a fixed point property of the iteration.
The H-function extension of the Negative Binomial Distribution is investigated for scaling exponents mu<0. Its analytic form is derived via a convolution property of the H-function. Applications are provided using multihadron and galaxy count data for P(n).
The recently introduced H-function extension of the Negative Binomial Distribution is investigated. The analytic form of P(n) is rederived by means of the Mellin transform. Applications of the HNBD are provided using experimental data for P(n) in e+e-, e+p, inelastic pp and non-diffractive p-pbar reactions.
A few remarks on hep-ph/9612213 are given.
An iterative procedure is developed with the aim of constructing homogeneity rules for the distribution P(rho,delta) of the particle density rho at resolution scale delta. A single iteration step consists of a change in the normalization point of P(rho,delta) followed by a rescaling. Similar transformation rule is introduced for density fluctuations contaminated by Poisson noise. Application of the iterative procedure is given for the Ginzburg-Landau description of phase-transition from the quark-gluon plasma and for random cascading models.
On the basis of a recently introduced generalization of the negative binomial distribution the influence of higher-order perturbative QCD effects on multiplicity fluctuations are studied for deep inelastic e^+p scattering at HERA energies. It is found that the multiplicity distributions measured by the H1 Collaboration indicate violation of infinite divisibility in agreement with pQCD calculations. Attention is called to future experimental analysis of combinants whose nontrivial sign-changing oscillations are predicted using the generalized negative binomial law.
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of the KNO scaling function derived in Polyakov's similarity hypothesis for strong interactions as well as in perturbative QCD. Various characteristics of the newly proposed distribution are investigated e.g. its generating function, factorial moments, factorial cumulants. Several limiting and special cases are discussed. A comparison is made to the multiplicity data available in e+e- annihilations at the Z0 peak.