Narrow Results

As shown recently, one can obtain additional information from the measured charged particle multiplicity distributions, $P(N)$, by extracting information from the modified combinants, $C_j$. This information is encoded in their specific oscillatory behavior, which can be described only by some combinations of compound distributions such as the Binomial Distribution. This idea has been applied to $pp$ and $p\bar{p}$ processes thus far. 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 Generalized Multiplicity Distribution (GMD) proposed some time ago.

We study the moments of multiplicty distribution and its relation to the Lee-Yang zeros of the generating function in electron-positron and hadron-hadron high energy collision. Our work shows that GMD moments can reproduce the oscillatory behaviour as shown in the experimental data and predicted by quantum chromodynamics at preasymptotic energy, while it can also be used to distinguish electron-positron (e⁺e^-) multiplicity data from hadron-hadron (pp and ) multiplicity. Furthermore, there seems to be a link between the development of shoulder structure in the multiplicity distribution and the development of ear structure in the Lee-Yang zeros. We predict that these structures is going to be very obvious at 14 TeV. We argue that the development of these structures indicates an ongoing transition from quark-dominated soft scattering events to gluon-dominated semihard scattering events.

We discuss various aspects of the multiparticle production processes at the LHC energy range with emphasis on the collective effects associated with appearance of the new scattering mode, which corresponds to the reflective scattering and its impact on multiparticle production processes.

The rapidity density and transverse momentum distributions of produced particles in multiple particle production are formulated assuming that the produced particles are emitted isotropically from several emitting centers. The energy distribution of produced particles in the rest frames of respective emitting centers is that of the Tsallis statistics. The distribution of emitting centers is flat with slanting cuts at both shoulders on the rapidity axis in the center of mass system. The formulation includes six adjustable parameters, among which four are energy dependent and more important and are determined so that the transverse momentum and the (pseudo-)rapidity density distributions fit to the data at various energies. The energy dependences of the four parameters, determined empirically, reproduce quite well the energy dependence of the average transverse momentum, that of the pseudo-rapidity density at η* = 0 and that of the charged multiplicity. The energy dependence of the inelasticity is either increasing or decreasing from the assumed value of K = 0.5 at , due to lack of experimental data at the most-forward rapidity region. The pseudo-rapidity density distribution at LHC energy expected by the present formulation is compared with those by the other models.

Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in phase space. They therefore serve as a reference point for more involved measurements. Distributions in phase space are usually investigated using the statistical approach, very successful in general but failing in cases of small colliding systems, small multiplicities, and at the edges of the allowed phase space, in which cases the underlying dynamical effects competing with the statistical distributions take over. We discuss an alternative approach, which applies to the whole phase space without detailed knowledge of dynamics. It is based on a modification of the usual statistics by generalizing it to a superstatistical form. We stress particularly the scaling and self-similar properties of such an approach manifesting themselves as the phenomena of the log-periodic oscillations and oscillations of temperature caused by sound waves in hadronic matter. Concerning the multiplicity distributions we discuss in detail the phenomenon of the oscillatory behavior of the modified combinants apparently observed in experimental data.

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.

We propose a model for multiple particle production of $pp$ and $\bar{p}p$ collisions at high energies. Most of the processes in the model are reasonable physically and/or with reasoning. A fire-ball of a gas, made of grains, is created in the collision and makes an adiabatic and approximately one-dimensional expansion along the collision axis. The fire-ball at the final state, when the grains are free in the fire-ball, is divided into several domains and the thermal equilibrium is realized in each of the domains with different temperatures. Each grain produces several hadrons at the final state. There are two processes of the grains without and with $p_T$ (transverse momentum), and the cross-section of the latter process increases with the incident energy. The grains in the domain at the final state obey the extended Maxwell distributions of the temperature $\mathrm{\Theta }$, and the hadrons in each grain do that of the temperature $T$. The values of the adjustable parameters are determined empirically in such a way as to reproduce the data of $p_T$ distributions and the rapidity density distributions at various incident energies. The model describes both distributions well at the incident energy of $\sqrt{s}=22.4$ to 7000GeV. The local equilibrium in each domain and the adiabatic expansion describe the flat plateau and the shrinkage of the forward region, respectively, of the rapidity density distribution. Another important conclusion is that a simple hydro-dynamical model does not describe the flat plateau of the rapidity density distribution of produced hadrons at high energies.

The model of multiple particle production in [A. Ohsawa, Int. J. Mod. Phys. A (2023) 2350166.] assumes a fire-ball of a gas, consisting of grains, with the adiabatic and one-dimensional expansion, local equilibrium at the final state and the extended Maxwell distribution for the energy distribution of the grains. There are small and large $p_T$ (transverse momentum) processes for grains. The grain produces several hadrons to be observed in the experiments at the final state. The model describes well the pseudo-rapidity density distributions and the $p_T$ distributions at various incident energies. In this paper it is shown that the model reproduces well the incident energy dependences of $〈p_T〉$ (the average $p_T$ of produced particles), $m_{ch}$ (the charged multiplicity) and ${\rho }_0$ (the pseudo-rapidity density at $\eta =0$). Furthermore it is shown that the inelasticity is almost energy-independent and $K=0.5$ in the energy region of $\sqrt{s}=10\sim 10^4$GeV, and that the Feynman scaling law is violated. The model indicates that the fire-ball satisfies the conditions for quark-gluon plasma, that the grains of the large $p_T$ process may be identified with jets, and that $p_T$’s of the grains in the large $p_T$ process are due to mutual collision of the grains during the one-dimensional expansion.

Self-affine multiplicity scaling is investigated in the framework of two-dimensional factorial moment methodology using the concept of the Hurst exponent (H) considering different bins of the phase space. We have investigated the fluctuation pattern of emitted pions in ²⁴Mg-AgBr interactions at 4.5 AGeV and this study reveals that the fluctuation is self-similar in some bins, whereas it is self-affine in other bins, that is, the multiplicity scaling is bin-dependent.

Nonstatistical fluctuations in the density distribution of shower tracks coming out of ³²S–Ag/Br interaction at an incident momentum of 200A GeV/c, have been characterized by using the intermittency and multifractality techniques. A sample of ³²S–Ag/Br nuclear emulsion events has been partitioned into three subsamples with respect to the shower track multiplicity in such a way that one can roughly estimate the average centrality for each subsample. Thereby, the centrality dependence of a set of relevant intermittency and multifractal issues has been investigated.

Significance of entropy, S, for explaining multiparticle production phenomenon in high energy nucleus–nucleus collisions is highlighted. For this, experimental data on 4.5A and 14.5A GeV/c ²⁸Si-nucleus interactions are analyzed. An attempt is also made to explain the phenomenon using HIJING simulated interactions. Entropy is calculated for different classes of interactions. The plots of against for different categories of interactions reveal scaling behavior.

Forward–backward (FB) charge correlations are investigated by analyzing experimental data on ¹⁶O–AgBr interactions at 14.5A, 60A and 200A GeV. Findings are compared with the predictions of Monte Carlo model, heavy-ion jet interaction generater (HIJING). The results reveal that the observed correlations are mainly of short-range type, which arise due to the decay of clusters and/or resonances produced in the central rapidity region. The range of FB correlations are observed to extend with increasing beam energy. However, there is no evidence for the presence of long-range correlations even at the highest incident energy considered.

A systematic study of rapidity dispersion parameter as a quantitative measure of clustering of particles has been carried out in the interactions of ¹⁶O, ²⁸Si and ³²S projectiles at 4.5 A GeV/c with heavy (AgBr) and light (CNO) groups of targets present in the nuclear emulsion. For all the interactions, the total ensemble of events has been divided into four overlapping multiplicity classes depending on the number of shower particles. For all the interactions and for each multiplicity class, the rapidity dispersion parameter values indicate the occurrence of clusterization during the multiparticle production at Dubna energy. The measured rapidity dispersion parameter values are found to decrease with the increase of average multiplicity for all the interactions. The dependence of rapidity dispersion parameter on the average multiplicity can be successfully described by a relation D(η) = a + b〈n_s〉 + c〈n_s〉². The experimental results have been compared with the results obtained from the analysis of Monte Carlo simulated (MC-RAND) events. MC-RAND events show weaker clusterization among the pions in comparison to the experimental data.

Presence of unusual azimuthal structures in the particle emission data obtained from the ²⁸Si–Ag/Br interaction at 14.5A GeV and from the ³²S–Ag/Br interaction at 200A GeV, are investigated in the framework of the Cherenkov gluon emission and/or Mach shock wave formation in nuclear/partonic medium. Nuclear photographic emulsion technique is used to collect the experimental data. The experiment is compared with the predictions of two simulations, namely (i) the Relativistic Quantum Molecular Dynamics (RQMD) and (ii) the Ultra-relativistic Quantum Molecular Dynamics (UrQMD). A charge reassignment algorithm is implemented over the outputs of the simulations to mimic the Bose–Einstein correlation (BEC) effect. Our analysis confirms presence of jet-like structures in both experiments beyond statistical noise. Such structures are more pronounced in the ³²S data than in the ²⁸Si data.

The transverse momentum spectra of hadrons produced in high energy collisions can be decomposed into two components: the exponential ("thermal") and the power ("hard") ones. Recently, the H1 Collaboration has discovered that the relative strength of these two components in Deep Inelastic Scattering (DIS) depends drastically upon the global structure of the event — namely, the exponential component is absent in the diffractive events characterized by a rapidity gap. We discuss the possible origin of this effect and speculate that it is linked to confinement. Specifically, we argue that the thermal component is due to the effective event horizon introduced by the confining string, in analogy to the Hawking–Unruh effect. In diffractive events, the t-channel exchange is color-singlet and there is no fragmenting string — so the thermal component is absent. The slope of the soft component of the hadron spectrum in this picture is determined by the saturation momentum that drives the deceleration in the color field, and thus the Hawking–Unruh temperature. We analyze the data on nondiffractive pp collisions and find that the slope of the thermal component of the hadron spectrum is indeed proportional to the saturation momentum.

Different aspects like multiplicity moments, $D_q$ moments and multiplicity fluctuations in terms of scaled variance of the shower particles has been carried out for central events of ${}^{16}\mathrm{\text{O}}-\mathrm{\text{AgBr}}$, ${}^{22}\mathrm{\text{Ne}}-\mathrm{\text{AgBr}}$ and ${}^{32}\mathrm{\text{S}}-\mathrm{\text{AgBr}}$ interactions at (4.1–4.5) AGeV/c. Comparison of our results with different experimental analysis of central collisions of emulsion data has been performed whenever available.

In this work, the interactions of ⁷Li nuclei with emulsion at 3 A GeV/c were studied. Multiplicity of the charged secondary particles as well as the charge of the outgoing projectile fragments were measured, while correlations among them are discussed. The values of the total charge of the noninteracting projectile nucleons and the average number of interacting projectile nucleons are estimated. The dependence of the secondary particles on the number of heavily-ionized tracks is analyzed. The results show that interactions of ⁷Li nuclei with emulsion nuclei exhibit a number of regularities, which had been noted in experiments with lighter nuclei. The absorption of relativistic particles, while increasing the degree of target destruction, is observed. The average multiplicities of the secondary charged particles depend on the impact parameter, as their values increase, while decreasing the impact parameter. The number of secondary charged particles in the heavy-ion interactions depends on the degree of disintegration of the target nuclei. This dependence is not observed in the case of the interaction of hadron with emulsion. The experimental data of the interaction of ⁷Li are systematically compared with the other interactions at different energies. The results agree with the corresponding results at nearly the same energy.

This paper deals with the target excitation dependence of the multifractal specific heat of pions produced in nucleus-nucleus collisions at 60 and 200 AGeV. Fluctuation pattern of pions is studied in two dimensions considering anisotropy of phase space. The parameter characterizing the anisotropy of phase space, Hurst exponent, is extracted by fitting one-dimensional factorial moment saturation curves. Values of intermittency exponent α_q and generalized dimension D_q are determined. The fluctuation pattern reveals multifractal behavior at all target excitations at both energies. The multifractal specific heat c is found to depend on target excitation and the dependence is found to be more pronounced at lower energy. The results are discussed in detail.

Another solution to the Kolmogorov backward partial differential equation for stationary branching is proposed leading to a new multiplicity relation. This relation is applied to CERN's ISR and SPS energies, in which excellent fits are obtained and compared to Chaudhuri,¹ Matinyan and Prokhorenko,² and Golyak.³ Further prediction to the highly-anticipated 14 TeV data for pp collision is also made.