Research Article Charged-Particle Multiplicity Moments as Described by Shifted Gompertz Distribution in  +  - ,  , and  Collisions at High Energies Aayushi Singla and M. Kaur Physics Department, Panjab University, Chandigarh 160014, India Correspondence should be addressed to M. Kaur; manjit@pu.ac.in Received 8 March 2019; Revised 3 July 2019; Accepted 20 August 2019; Published 25 January 2020 Academic Editor: eocharis Kosmas Copyright © 2020 Aayushi Singla and M. Kaur. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e publication of this article was funded by SCOAP 3 . 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 using the shiſted Gompertz distribution, a detailed analysis of the normalized moments and normalized factorial moments is reported here. A two-component model in which a probability distribution function is obtained from the superposition of two shiſted Gompertz distributions, as introduced in our earlier work, has also been used for the analysis. is is the first analysis of the moments with the shiſted Gompertz distribution. Analysis has also been performed to predict the moments of multiplicity distribution for the  +  - collisions at √  = 500 GeV at a future collider. 1. Introduction In one of our recent papers, we introduced a statistical distribution, the shiſted Gompertz distribution to investigate the multiplicity distributions of charged particles produced in  +  - collisions at the LEP,   interactions at the SPS and  collisions at the LHC at different center of mass energies in full phase space as well as in restricted phase space [1]. A distribution of the larger of two independent random variables, the shiſted Gompertz distribution was introduced by Bemmaor [2] as a model of adoption of innovations. One of the parameters has an exponential distribution and the other has a Gumbel distribution, also known as log-Weibull distribution. e nonnegative fit parameters define the scale and shape of the distribution. Subsequently, the shiſted Gompertz distribution has been widely studied in various contexts [3–5]. In our earlier work [1] by studying the charged particle multiplicities, we showed that this distribution can be successfully used to study the statistical phenomena in high energy  +  - ,  , and  collisions at the LEP, SPS, and LHC colliders, respectively. A multiplicity distribution is represented by the proba- bilities of -particle events as well as by its moments or its generating function. e aim of the present work is to extend the analysis by calculating the higher moments of a multi- plicity distribution. Because the moments are calculated as derivatives of the generating function, the moment analysis is a powerful tool which helps to unfold the characteristics of multiplicity distribution. e multiparticle correlations can be studied through the normalized moments and nor- malized factorial moments of the distribution. e depend- ence of moments on energy can also reveal the KNO (Koba, Nielsen, and Olesen) scaling [6–8] conservation or violation. Several analyses of moments have been done at different energies, using different probability distribution functions and different types of particles [9–12]. e higher moments also can identify the correlations amongst produced particles. In Section 2, formulae for the probability distribution function (PDF) of the shiſted Gompertz distribution, normal- ized moments, and the normalized factorial moments used for the analysis are given. A two-component model has been used and modification of distributions carried out, in terms of these two components; one from soſt events and another from semi-hard events. Superposition of distributions from these two components, using appropriate weights is done to Hindawi Advances in High Energy Physics Volume 2020, Article ID 5192193, 24 pages https://doi.org/10.1155/2020/5192193