618 research outputs found
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 , the peak has a stretched exponential
shape. The Gaussian form corresponds then to the special case of .
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
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
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
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
estimated from the data. We treat as an unknown parameter,
but for theoretical simplicity we also consider the case that 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
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