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Register a new userModified Weibull and Tsallis Distributions for multiplicities in $e^{+}e^{-}$ collisions at LEP2 energies
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Multiplicity distributions of charged particles produced in the $e^{+}e^{-}$ collisions at LEP2 energies ranging from 91 to 206 GeV in full phase space, are compared with predictions from Tsallis $q$-statistics and the recently proposed Weibull distribution functions.~The analysis uses data from two LEP experiments, L3 and OPAL.~It is shown that Tsallis $q$-statistics explains the data in a statistically acceptable manner in full phase space at all energies, while the Weibull distribution fails to explain the underlying properties of the data.~Modifications to the distributions proposed earlier, are applied to uncover manifold improvements in explaining the data characteristics.
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Multiplicity distributions of charged particles produced in the e^{+}e^{-} collisions at energies ranging from 14 to 91 GeV are studied using Tsallis q-statistics and the recently proposed Weibull distribution functions, in both restricted rapidity windows as well as in full phase space. It is shown that Tsallis $q$-statistics explains the data excellently in all rapidity ranges while the Weibull distribution fails to reproduce the data in full phase space. Modifications to the distributions are proposed to establish manifold improvements in the fitting of the data.
Charged hadron production in the $e^{+}e^{-}$ annihilations at 91 to 206 GeV in full phase space and in $overline{p}p$ collisions at 200 to 900~GeV collision energies are studied using non-extensive Tsallis and stochastic Weibull probability distributions.~The Tsallis distribution shows better description of the data than the Weibull distribution. The 2-jet modification of the statistical distribution is applied to describe $e^{+}e^{-}$ data.~The main features of these distributions can be described by a two-component model with soft, collective interactions at low transverse energy and hard, constituent interactions dominating at high transverse energy.~This modification is found to give much better description than a full-sample fit, and again Tsallis function is found to better describe the data than the Weibull one pointing at the non-extensive character of the multiparticle production process.
We present the exact O(alpha) correction to the process e+ e- -> f f-bar + gamma, f neq e, for ISR oplus FSR at and beyond LEP2 energies. We give explicit formulas for the completely differential cross section. As an important application, we compute the size of the respective sub-leading corrections of O(alpha L) to the f f-bar cross section, where L is the respective big logarithm in the renormalization group sense so that it is identifiable as L = ln |s|/m_e^2 when s is the squared e+e- cms energy. Comparisons are made with the available literature. We show explicitly that our results have the correct infrared limit, as a cross-check. Some comments are made about the implementation of our results in the framework of the Monte Carlo event generator KK MC.
As shown recently, one can obtain additional information from the measured multiplicity distributions, $P(N)$, by extracting the so-called modified combinants, $C_j$. This information is encoded in their specific oscillatory behavior, which can be described only by some combinations of compound distributions, the basic part of which is the Binomial Distribution. So far this idea was applied to $pp$ and $pbar{p}$ processes; in this note we show that an even stronger effect is observed in the $C_j$ deduced from $e^+e^-$ collisions. We present its possible explanation in terms of the so called Generalised Multiplicity Distribution (GMD) proposed some time ago.
In recent years the Tsallis statistics is gaining popularity in describing charged particle produc- tion and their properties, in particular pT spectra and the multiplicities in high energy particle collisions. Motivated by its success, an analysis of the LHC data of proton-proton collisions at ener- gies ranging from 0.9 TeV to 7 TeV in different rapidity windows for charged particle multiplicities has been done. A comparative analysis is performed in terms of the Tsallis distribution, the Gamma distribution and the shifted-Gamma distribution. An interesting observation on the inapplicability of these distributions at sqrt{s}=7 TeV in the lower rapidity windows is intriguing. The non-extensive nature of the Tsallis statistics is studied by determining the entropic index and its energy depen- dence. The analysis is extrapolated to predict the multiplicity distribution at sqrt{s}=14 TeV for one rapidity window, |y| < 1.5 with the Tsallis function.
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