We present a comprehensive insight into counting distributions from the perspective of the combinants extracted from them. In particular, we focus on cases where these combinants exhibit oscillatory behavior that can provide an invaluable new source of information about the dynamics of the process under study. We show that such behavior can be described only by specific combinations of compound distributions based on the Binomial Distribution and provide their analytical forms which can be used in further investigations and which can be helpful in the analysis of all other types of counting distributions.

Counting distributions from the perspective of combinants

A phenomenological model of particle production and hadronisation in high energy collisions is formulated using Dirac fields in Yukawa-like interaction and the resulting stochastic equation is solved numerically. Different initial conditions are used to compare particle- particle (ψ ψ) and particle-antiparticle (ψ* ψ) interactions. It is shown that in this simplified view, there is a clear difference between the final multiplicity distributions resulting from the two initial conditions. To model the restricted phase space (limited pseudorapidity) measurements in experiment, a “loss” function is also proposed to account for the undetected particles close to the beam line.

/pdf/on-multiparticle-production-in-very-high-energy-scattering-3awvcq92pz.pdf

On Multiparticle Production in Very High Energy Scattering

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.

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

The Bose-Einstein correlation (BEC) in forward region ($2.0<\eta<4.8$) measured at 7 TeV in the Large Hadron Collider (LHC) by the LHCb collaboration is analyzed using two conventional formulas of different types named CF$_{\rm I}$ and CF$_{\rm II}$. The first formula is well known and contains the degree of coherence ($\lambda$) and the exchange function $E_{\rm BE}^2$ from the BE statistics. The second formula is an extended formula (CF$_{\rm II}$) that contains the second degree of coherence $\lambda_2$ and the second exchange function $E_{\rm BE_2}^2$ in addition to CF$_{\rm I}$. To examine the physical meaning of the parameters estimated by CF$_{\rm II}$, we analyze the LHCb BEC data by using a stochastic approach of the three-negative binomial distribution and the three-generalized Glauber-Lachs formula. Our results reveal that the BEC at 7 TeV consisted of three activity intervals defined by the multiplicity $n$ ([8, 18], [19, 35], and [36, 96]) can be well explained by CF$_{\rm II}$.

Analysis of Bose-Einstein correlation at 7 TeV by LHCb collaboration based on stochastic approach

In this work we show that the proper analysis and interpretation of the experimental data on the multiplicity distributions of charged particles produced in jets measured in the ATLAS experiment at the LHC indicates their sub-Poissonian nature. We also show how, by using the recurrence relations and combinants of these distributions, one can obtain new and otherwise unavailable information contained in them, which may broaden our knowledge of the particle production mechanism. 

Sub-Poissonian multiplicity distributions in jets produced in hadron collisions

As shown recently, one can obtain additional information from the measured charged particle multiplicity distributions, $P(N)$, by investigating the so-called modified combinants, $C_j$, extracted from them. This information is encoded in the observed specific oscillatory behaviour of $C_j$, which phenomenologically can be described only by some combinations of compound distributions based on the Binomial Distribution. So far this idea has been checked in $pp$ and $e^+e^-$ processes (where observed oscillations are spectacularly strong). In this paper, we continue observation of multiparticle production from the modified combinants perspective by investigating dependencies of the observed oscillatory patterns on type of colliding particles, their energies and the phase space where they are observed. We also offer some tentative explanations based on different types of compound distributions and stochastic branching processes.

/pdf/a-look-at-multiparticle-production-via-modified-combinants-gv24wadjnk.pdf

A look at multiparticle production via modified combinants

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 $p\bar{p}$ 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.

Modified combinant analysis of the $e^+e^-$ multiplicity distributions.

As shown recently, one can obtain additional information from the measured charged particle multiplicity distributions, P(N), by investigating the so-called modified combinants, $$C_j$$, extracted from them. This information is encoded in the observed specific oscillatory behaviour of $$C_j$$, which phenomenologically can be described only by some combinations of compound distributions based on the Binomial Distribution. So far this idea has been checked in pp and $$e^+e^-$$ processes (where observed oscillations are spectacularly strong). In this paper we continue observation of multiparticle production from the modified combinants perspective by investigating dependencies of the observed oscillatory patterns on type of colliding particles, their energies and the phase space where they are observed. We also offer some tentative explanation based on different types of compound distributions and stochastic branching processes.

/pdf/a-look-at-multiparticle-production-via-modified-combinants-1ismdtsf5x.pdf

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A look at multiparticle production via modified combinants

Modified combinant analysis of the $e^+e^-$ multiplicity distributions.

A look at multiparticle production via modified combinants