Model independent shape analysis of correlations in 1, 2 or 3 dimensions

A generic, model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT or GGLP), statistical, dynamical or other short-range correlation functions. The method is based on a data-motivated choice for the zero-th order approximation for the shape of the correlation function, and on a systematic determination of the correction terms with the help of complete orthonormal set of functions. The Edgeworth expansion is obtained for approximately Gaussian, the Laguerre expansion for approximately exponential correlation functions. Multi-dimensional expansions are also introduced and discussed.Comment: Latex, 15 pages, uses epsfig.sty elsart.sty, misprints correcte

The accuracy of merging approximation in generalized St. Petersburg games

Merging asymptotic expansions of arbitrary length are established for the distribution functions and for the probabilities of suitably centered and normalized cumulative winnings in a full sequence of generalized St. Petersburg games, extending the short expansions due to Cs\"org\H{o}, S., Merging asymptotic expansions in generalized St. Petersburg games, \textit{Acta Sci. Math. (Szeged)} \textbf{73} 297--331, 2007. These expansions are given in terms of suitably chosen members from the classes of subsequential semistable infinitely divisible asymptotic distribution functions and certain derivatives of these functions. The length of the expansion depends upon the tail parameter. Both uniform and nonuniform bounds are presented.Comment: 30 pages long version (to appear in Journal of Theoretical Probability); some corrected typo

Simple analytic solution of fireball hydrodynamics

A new family of simple analytic solutions of hydrodynamics is found for non-relativistic, rotationally symmetric fireballs assuming an ideal gas equation of state. The solution features linear flow profile and a non-trivial transverse temperature profile. The radial temperature gradient vanishes only in the collisionless gas limit. The Zimanyi-Bondorf-Garpman solution and the Buda-Lund parameterization of expanding hydrodynamical sources are recovered as special cases. The results are applied to predict new features of proton-proton correlations and spectra data at 1.93 AGeV Ni + Ni reactions.Comment: Latex, Revte

Bose-Einstein correlations for Levy stable source distributions

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 $0 < \alpha \le 2$, the peak has a stretched exponential shape. The Gaussian form corresponds then to the special case of $\alpha = 2$. 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.Comment: 30 pages, 1 figure, an important misprint in former eqs. (37-38) and other minor misprints are corrected, citations update

Squeezed K^+ K^- correlations in high energy heavy ion collisions

The hot and dense medium formed in high energy heavy ion collisions may modify some hadronic properties. In particular, if hadron masses are shifted in-medium, it was demonstrated that this could lead to back-to-back squeezed correlations (BBC) of particle-antiparticle pairs. Although well-established theoretically, the squeezed correlations have not yet been discovered experimentally. A method has been suggested for the empirical search of this effect, which was previously illustrated for phi-phi pairs. We apply here the formalism and the suggested method to the case of K^+ K^- pairs, since they may be easier to identify experimentally. The time distribution of the emission process plays a crucial role in the survival of the BBC's. We analyze the cases where the emission is supposed to occur suddenly or via a Lorentzian distribution, and compare with the case of a Levy distribution in time. Effects of squeezing on the correlation function of identical particles are also analyzed.Comment: 9 pages and 6 figures (figures 2 to 6 contain 4 plots each). Paragraph added to text, figures 2 to 6 revised for improving visualizatio

Many--Particle Correlations in Relativistic Nuclear Collisions

Many--particle correlations due to Bose-Einstein interference are studied in ultrarelativistic heavy--ion collisions. We calculate the higher order correlation functions from the 2--particle correlation function by assuming that the source is emitting particles incoherently. In particular parametrizations of and relations between longitudinal, sidewards, outwards and invariant radii and corresponding momenta are discussed. The results are especially useful in low statistics measurements of higher order correlation functions. We evaluate the three--pion correlation function recently measured by NA44 and predict the 2--pion--2--kaon correlation function. Finally, many particle Coulomb corrections are discussed.Comment: 5 corrected misprints, 14 pages, revtex, epsfig, 6 figures included, manuscript also available at http://www.nbi.dk/~vischer/publications.htm

Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics

In this paper we describe in full details a new family of recently found exact solutions of relativistic, perfect fluid dynamics. With an ansatz, which generalizes the well-known Hwa-Bjorken solution, we obtain a wide class of new exact, explicit and simple solutions, which have a remarkable advantage as compared to presently known exact and explicit solutions: they do not lack acceleration. They can be utilized for the description of the evolution of the matter created in high energy heavy ion collisions. Because these solutions are accelerating, they provide a more realistic picture than the well-known Hwa-Bjorken solution, and give more insight into the dynamics of the matter. We exploit this by giving an advanced simple estimation of the initial energy density of the produced matter in high energy collisions, which takes acceleration effects (i.e. the work done by the pressure and the modified change of the volume elements) into account. We also give an advanced estimation of the life-time of the reaction. Our new solutions can also be used to test numerical hydrodynamical codes reliably. In the end, we also give an exact, 1+1 dimensional, relativistic hydrodynamical solution, where the initial pressure and velocity profile is arbitrary, and we show that this general solution is stable for perturbations.Comment: 34 pages, 8 figures, detailed write-up of http://arxiv.org/abs/nucl-th/0605070

Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach

We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponent $\alpha$ estimated from the data. We treat $\alpha$ as an unknown parameter, but for theoretical simplicity we also consider the case that $\alpha$ is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions

Search for Squeezed-Pair Correlations at RHIC

Squeezed correlations of particle-antiparticle pairs, also called Back-to-Back Correlations, are predicted to appear if the hadron masses are modified in the hot and dense hadronic medium formed in high energy nucleus-nucleus collisions. Although well-established theoretically, the squeezed-particle correlations have not yet been searched for experimentally in high energy hadronic or heavy ion collisions, clearly requiring optimized forms to experimentally search for this effect. Within a non-relativistic treatment developed earlier we show that one promising way to search for the BBC signal is to look into the squeezed correlation function of pairs of phi-mesons at RHIC energies, plotted in terms of the average momentum of the pair, K12=(k1+k2)/2. This variable's modulus, 2|K12|, is the non-relativistic limit of the variable Q_bbc, introduced herewith. The squeezing effects on the HBT correlation function are also discussed.Comment: 4 pages, 2 figures. To be published in the Proceedings of Quark Matter 2008, Jaipur, Indi

An approximation to infinitely divisible laws

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41776/1/10474_2005_Article_BF01874676.pd