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 we check the model against two-particle correlation data.
A brief summary of the basic properties of combinants is provided. Their behavior is analysed using the Opal multiplicity data for light quark jets in restricted rapidity bins. For |
Δy|≤1 the ...combinants do not exclude clustering effects with Poisson superposition. For |
Δy|≤2 this pattern of correlations is ruled out by the sign-changing oscillations of combinants, as well as other models which predict oscillations alternating in sign. The future experimental possibilities concerning combinants are discussed.
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 zeroth order approximation for the shape of the correlation function, and on a systematic determination of the correction terms with the help of complete orthonormal sets 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.
The running of the QCD coupling constant as well as multiplicative cascades of varying depth are found to give rise to data collapsing behavior of the multiplicity distributions after suitable ...location and scale change in the logarithm of multiplicity. Hence the onset of a log-KNO scaling law is predicted in high-energy collision processes. It is shown that the available multiplicity data in
e
+
e
− and
p
p
̄
collisions can be collapsed onto the same scaling curve.
The collapse of multiplicity distributions
P
n
onto a universal scaling curve arises when
P
n
is expressed as a function of the standardized multiplicity (
n−
c)/
λ with
c and
λ being location and ...scale parameters governed by leading particle effects and the growth of average multiplicity. It is demonstrated that self-similar multiplicative cascade processes such as QCD parton branching naturally lead to a novel type of scaling behavior of
P
n
which manifests itself in Mellin space through a location change controlled by the degree of multifractality and a scale change governed by the depth of the cascade. Applying the new scaling rule it is shown how to restore data collapsing behavior of
P
n
measured in
hh collisions at ISR and SPS energies.
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 proability 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,
ψ(
z)
α
z
α
exp(−
z
μ
). 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
Z
0 peak.
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
p
reactions.
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.
The H-function extension of the Negative Binomial Distribution is investigated for scaling exponents
μ<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
.
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