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Register a new userAnalyses of multiplicity distributions of e^+e^- and e-p collisions by means of modified negative binomial distribution and Laguerre-type distribution: Interrelation of solutions in stochastic processes
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A pure birth stochastic process with several initial conditions is considered.We analyze multiplicity distributions of e^+e^- collisions and e-p collisions, usigthe Modified Negative Binomial Distribution (MNBD) and the Laguerre-type distribution. Several multiplicity distributions show the same minimum chi^2s values in analyses by means of two formulas: In these cases, we find that a parameter N contained in the MNBD becomes to be large. Taking large N limit in the MNBD, we find that the Laguerre-type distribution can be derived from it. Moreover, from the generalized MNBD we can also derive the generalized Glauber-Lachs formula. Finally stochastic properties of QCD and multiparticle dynamics are discussed.
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We analyze various data of multiplicity distributions by means of the Modified Negative Binomial Distribution (MNBD) and its KNO scaling function, since this MNBD explains the oscillating behavior of the cumulant moment observed in e^+e^- annihilations, h-h collisions and e-p collisions. In the present analyses, we find that the MNBD(discrete distributions) describes the data of charged particles in e^+e^- annihilations much better than the Negative Binomial Distribution (NBD). To investigate stochastic property of the MNBD, we derive the KNO scaling function from the discrete distribution by using a straightforward method and the Poisson transform. It is a new KNO function expressed by the Laguerre polynomials. In analyses of the data by using the KNO scaling function, we find that the MNBD describes the data better than the gamma function.Thus, it can be said that the MNBD is one of useful formulas as well as NBD.
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 continuation of our earlier work, in which we analysed the charged particle multiplicities in leptonic and hadronic interactions at different center of mass energies in full phase space as well as in restricted phase space with the shifted Gompertz distribution, a detailed analysis of the normalized and factorial moments is reported here. A two-component model in which probability distribution function is obtained from the superposition of two shifted Gompertz distributions introduced in our earlier work has also been used for the analysis. This is the first analysis of the moments with the shifted Gompertz distribution. Analysis has also been done to predict the moments of multiplicity distribution for the electron-positron collisions at c.m. energy of 500 GeV at a future Collider.
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.
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.
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