788 research outputs found
Stable Bose-Einstein correlations
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 L\'evy index of stability and the
scale parameter . The normal, Gaussian shape corresponds to a particular
case, when is selected. The asymmetry parameter of the stable
source, is shown to be proportional to the angle, measured by the
normalized three-particle cumulant correlations.Comment: 7 pages, no figures, invited talk of T. Csorgo at the 2nd Warsaw
Meeting on Particle Correlations and Resonances in HIC, see
http://hirg.if.pw.edu.pl/en/meeting/oct2003/talks/csorgo/Csorgo.pp
Bose-Einstein or HBT correlation signature of a second order QCD phase transition
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.Comment: 8 pages, talk given by T. Csorgo at the Workshop on Particle
Correlations and Femtoscopy 2005, Kromeriz, Czech Republic, August 200
Bose-Einstein or HBT correlations and the anomalous dimension of 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.Comment: 8 pages, 5 figures, presented by T. Csorgo at the XXXIV International
Symposium on Multiparticle Dynamics, Sonoma County, California, USA, July
2004, to appear in Acta Physica Polonica
The Influence of High Multiplicities at RHIC on the Gamov Factor
The corrections for two-pion correlations due to electromagnetic final-state
interactions at high secondary multiplicities are investigated. The analysis is
performed by solving the Schr\"odinger equation with a potential which is
dictated by the multi-particle environment. Two different post-freeze-out
scenarios are examined. First, for a uniformly spread environment of secondary
particles, a screened Coulomb potential is exploited. It is shown that the
presence of a static and uniform post-freeze-out medium results in a noticeable
deviation from the standard Gamov factor. However, after going to a more
realistic model of an expanding pion system, this conclusion changes
drastically. We argue that the density of the secondary pions n_\pi(t,R), where
R is a distance from the fireball, is bounded from above by n_\pi(t,R)\le
const/R^2 for all times t. Then, a two-particle scalar potential which is found
as a solution of the Maxwell equation for non-uniform medium replaces the
screened one. Even this upper limit does not result in an essential deviation
from the Gamov correction.Comment: 11 pages, 7 figures, minor text corrections are mad
Some forgotten features of the Bose Einstein Correlations
Notwithstanding the visible maturity of the subject of Bose-Einstein
Correlations (BEC), as witnessed nowadays, we would like to bring to ones
attention two points, which apparently did not received attention they deserve:
the problem of the choice of the form of correlation function when
effects of partial coherence of the hadronizing source are to be included and
the feasibility to model effects of Bose-Einstein statistics, in particular the
BEC, by direct numerical simulations.Comment: Talk delivered by G.Wilk at the International Workshop {\it
Relativistic Nuclear Physics: from Nuclotron to LHC energies}, Kiev, June
18-22, 2007, Ukraine; misprints correcte
Bose-Einstein Correlations of Pion Wavepackets
A wavepacket model for a system of free pions, which takes into account the
full permutation symmetry of the wavefunction and which is suitable for any
phase space parametrization is developed. The properties of the resulting mixed
ensembles and the two-particle correlation function are discussed. A physical
interpretation of the chaoticity lambda as localizat of the pions in the source
is presented.
Two techniques to generate test-particles, which satisfy the probability
densities of the wavepacket state, are studied:
1. A Monte Carlo procedure in momentum space based on the standard Metropolis
technique.
2. A molecular dynamic procedure using Bohm's quantum theory of motion.
In order to reduce the numerical complexity, the separation of the
wavefunction into momentum space clusters is discussed. In this context th
influence of an unauthorized factorization of the state, i. e. the omissio of
interference terms, is investigated. It is shown that the correlation radius
remains almost uneffected, but the chaoticity parameter decreases
substantially. A similar effect is observed in systems with high multiplic
where the omission of higher order corrections in the analysis of two-part
correlations causes a reduction of the chaoticity and the radius.
The approximative treatment of the Coulomb interaction between pions and
source is investigated. The results suggest that Coulomb effects on the co
radii are not symmetric for pion pairs of different charges. For negative the
radius, integrated over the whole momentum spectrum, increases substan while
for positive pions the radius remains almost unchanged.Comment: 15 pages, 8 figures, 0.8 Mb, uses ljour2-macro, Submitted to Z. Phys.
A (1997
Multi-boson effects and the normalization of the two-pion correlation function
The two-pion correlation function can be defined as a ratio of either the
measured momentum distributions or the normalized momentum space probabilities.
We show that the first alternative avoids certain ambiguities since then the
normalization of the two-pion correlator contains important information on the
multiplicity distribution of the event ensemble which is lost in the second
alternative. We illustrate this explicitly for specific classes of event
ensembles.Comment: 6 pages, three figures,submit to PR
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