Compelling evidence of oscillatory behaviour of hadronic multiplicities in the shifted Gompertz distribution

Study of charged particle multiplicity distribution in high energy interactions of particles helps in revealing the dynamics of particle production and the underlying statistical patterns, which these distributions follow. Several distributions derived from statistics have been employed to understand its behaviour. In one of our earlier papers, we introduced the shifted Gompertz distribution to investigate this variable and showed that the multiplicity distributions in a variety of processes at different energies can be very well described by this distribution. The fact that the shifted Gompertz distribution, which has been extensively used in diffusion theory, social networks and forecasting has been used for the first time in high energy physics collisions, remains interesting. In this paper we investigate the phenomenon of oscillatory behaviour of the counting statistics observed in the experimental data, resulting from different types of recurrence relations defining the probability distributions. We search for such oscillations in the multiplicity distributions well described by the shifted Gompertz distribution and compare our results with the analysis proposed by G. Wilk et al.