The generating functional is suggested for multiparticle generation processes. In mean field approximation of high density QCD two equations for new generating functional are derived: linear functional equation for an arbitrary initial condition and non-linear one for a specific initial condition. The non-linear equation has the form of Kovchegov-Levin equation for diffraction production and gives its generalization on the processes with fixed multiplicities of produced particles.
I discuss various QCD tests for multiparticle production, such as multiplicities, dead-cone effect and inclusive spectra. The common feature of all these predictions is the crucial importance of coherence effect to be taken into account.
We compare QCD predictions with experimental data on inclusive multiparticle observables whereby we discuss various realizations of the idea of parton hadron duality which is related to a soft confinement mechanism. Special emphasis is given on effects from the running $α_s$, the soft gluon interference, scaling properties and the role of the limiting scale $Q_0$ in cascade evolution.
The multiparton density matrices of the QCD gluon cascade are investigated. The generating functional and master equation for momentum space multiparton density in the double logarithmic approximation (DLA) are proposed.
We consider the dynamics of high energy multiparticle production and discuss how the space-time picture of inelastic interaction may reveal itself in identical particles Bose-Einstein correlations.
I discuss recent developments in the QCD cascade formalism. I focus on the importance of and uncertainties in higher order corrections to the Modified Leading Log approximation for final-state radiation. I also talk about the CCFM and LDC evolution equations for initial-state radiation in DIS.
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 perturbative quantum chromodynamics (QCD) is quite successful in the description of main features of multiparticle production processes. Ten most appealing characteristics are described in this brief review talk and compared with QCD predictions. The general perturbative QCD approach is demonstrated and its problems are discussed. It is shown that the analytical calculations at the parton level with the low-momentum cut-off reproduce experimental data on the hadronic final state surprisingly accurately even though the perturbative expansion parameter is not very small. Moreover, the pertur…
Gluon dominance model is proposed to study multiparticle production. This model describes multiplicyty distributions in $e^+e^-$, $p\bar p$ annihilation and $pp$ interactions.
We study the impact of a hidden sector beyond the Standard Model, e.g. a Hidden Valley model, on factorial moments and cumulants of multiplicity distributions in multiparticle production with a special emphasis on the prospects for LHC results.
The evolution properties of propagating particles produced at high energies in a randomly distributed environment are studied. The finite size of the phase space of the multiparticle production region as well as the chaoticity can be derived.
Processes with multiparticle final states in weakly coupled theories, both with and without instantons, cannot be studied perturbatively at most interesting energies and multiplicities. Semiclassical approaches to the calculation of their cross sections are reviewed.
After inserting the heavy quark mass dependence into QCD partonic evolution equations, we determine the mean charged hadron multiplicity and second multiplicity correlators of jets produced in high energy collisions. We thereby extend the so-called dead cone effect to the phenomenology of multiparticle production in QCD jets and find that the average multiplicity of heavy-quark initiated jets decreases significantly as compared to the massless case, even taking into account the weak decay products of the leading primary quark. We emphasize the relevance of our study as a complementary check of…
We review the perturbative approach to multiparticle production in hard collision processes. It is investigated to what extent parton level analytical calculations at low momentum cut-off can reproduce experimental data on the hadronic final state. Systematic results are available for various observables with the next-to-leading logarithmic accuracy (the so-called modified leading logarithmic approximation - MLLA). We introduce the analytical formalism and then discuss recent applications concerning multiplicities, inclusive spectra, correlations and angular flows in multi-jet events. In vario…
This paper contains a review of the main results of a search of regularities in collective variables properties in multiparticle dynamics, regularities which can be considered as manifestations of the original simplicity suggested by QCD. The method is based on a continuous dialog between experiment and theory. The paper follows the development of this research line, from its beginnings in the seventies to the current state of the art, discussing how it produced both sound interpretations of the most relevant experimental facts and intriguing perspectives for new physics signals in the TeV ene…
The production of gluons in a jet is considered in limited phase space, either with a cut in transverse momentum with respect to the jet axis $k_\perp<k_\perp^{cut}$ or with a cut in absolute momentum $|\vec{k} | <k^{cut}$. It is shown in the perturbative QCD calculations that in the soft limit $k_\perp^{cut} \to 0$ the multiplicity distribution becomes Poissonian, whereas for $k^{cut} \to 0$ the distribution remains non-Poissonian. The Poissonian limit is a consequence of the soft gluon coherence in the genuine multiparticle correlations. We also investigate how incoherent hadronization proce…
The QCD evolution equations in Modified Leading Log Approximation for the factorial moments of the multiplicity distribution in quark and gluon jets are numerically solved with initial conditions at threshold by fully taking into account the energy conservation law. After applying Local Parton Hadron Duality as hadronization prescription, a consistent quantitative description of available experimental data for factorial cumulants and factorial moments of arbitrary order and for their ratio both in quark and gluon jets and in $e^+e^-$ annihilation is achieved.
Recently suggested method of measuring Renyi entropies of multiparticle systems produced in high-energy collisions is presented in the form of a "do-list", explaining explicitely how to perform the measurement and suggesting improvements in the treatment of the data.
We use perturbation theory to estimate the energy scale beyond which multiparticle final states become a dominant feature of high energy weak interactions. Using estimates from a weak parton model and comparing two, three and four body final states we deduce that multiparticle states become important at energy scales in the range 10**7 - 10**9 GeV.
In this review we discuss the analytical perturbative approach, based on perturbative QCD and Local Parton Hadron Duality (LPHD), and its application to multiparticle production in jets in the semisoft region. Analytical formulae are presented for various observables within the accuracy of the Modified Leading Logarithmic Approximation (MLLA), i.e. with terms of relative order $\sqrt{α_s}$ taken into account systematically, and in some cases with even higher accuracy. These predictions are confronted with existing experimental data. Many details of the perturbative approach to multiple hadropr…
The obtained $π^{-}$ and charged multiplicity distribution parameters of Gluon Dominance Model explain the experimental data in nucleus-nucleus, p nucleus, pd, pp, p antip and $π^{-}$(p,n) interactions. We have undertaken an attempt to give description in different processes of multiparticle production by means of a unifed approach based on quark-gluon picture using the phenomenological hadronization. We have obtained agreement of GDM with experimental data in a very wide energy range.
We review the assumptions and domain of applicability of Landau's Hydrodynamical Model. By considering two models of particle production, pair production from strong electric fields and particle production in the linear sigma model, we demonstrate that many of Landau's ideas are verified in explicit field theory calculations.
We show that the effects of quantum interference can be implemented in Monte-Carlo generators by modelling the generalized Wigner functions. A specific prescription for an appropriate modification of the weights of events produced by standard generators is proposed.
Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on the total cross sections. The connection with classical field equations in $D$ dimensions is established. Previous results on multiparticle amplitudes are easily reproduced.
Theoretical and experimental studies of high multiplicity events are analyzed. Some interesting phenomena can be revealed at high multiplicities. Preliminary results of project "Thermalization" are reported.
Bose-Einstein correlations are being exploited to obtain information about the structure of the sources of hadrons in multiple particle production processes. In this paper the principles of this approach are described and some of the controversies about their implementation are discussed.
We discuss role of absorbtion and antishadowing in particle production. Antishadowing, which leads to domination of elastic scattering at high energies, appears to be consistent with growth of mean multiplicity in hadronic collisions. Moreover, we demonstrate possibility to reproduce power-like energy behavior of the mean multiplicity in the model with antishadowing and discuss physical implications of such behavior for the hadron structure.
We discuss the role of absorbtion and antishadowing in particle production. We reproduce power-like energy behavior of the mean multiplicity in the model with antishadowing and discuss physical implications of such behavior for the hadron structure.
The effects of interpreting classical phase space distributions as Wigner functions, which is common in models of multiparticle production, are discussed. The temperature for the classical description is always higher than that for its Wigner function interpretation. A rough estimate shows that the corresponding correction is proportional to R^(-2), where R is the radius of the interaction region, and that it is negligible for heavy ion scattering, but at the few percent level for e^+e^- annihilations.
QCD equations for generating functionals are solved at coinciding momenta of particles. As a result, the relations for $q$-particle correlation functions at equal momenta are obtained. They are directly connected to previously derived results about the factorial and cumulant moments of multiplicity distributions. It is predicted that the correlations at coinciding points decrease, first, as a function of the rank $q$, and then start oscillating when represented in a form of the ratio of cumulant to factorial correlations. In particular, the cumulant function of the fifth rank should become neg…
In all multiparticle processes the concept of sources directly emitting finally observed secondaries (mostly pions) plays crucial role. Here we shall present them from yet another point of view in which elementary sources composing all processes (from e+e- annihilation, via pp up to AA interactions) remain both totally 'chaotic' and Poissonian at the same time.
Among the many topics related to soft QCD in which Bo Andersson gave an important contribution to experiments, this report selects a few for which the final word has not yet been pronounced.
A model-independent lower bound on the entropy S of the multiparticle system produced in high energy collisions, provided by the Renyi entropy H_2, is shown to be very effective. Estimates show that the ratio H_2/S remains close to one half for all realistic values of the parameters.
We discuss correlations in the hadron production in the $pp$-collision with emphasize on the ridge-like structure origin in the two-particle correlation function. We suggest that this structure can appear due to a rotating nature of the transient state of matter generated in the intermidiate stage of proton collison.
Multiparticle production in (2+1) dimensions is investigated. We show that in a small region around the threshold the perturbation theory becomes unapplicable due to infrared divergencies in a class of Feynman graphs with rescattering in final state. We develop a technique based on renormalization group for summing up leading logarithms and apply it to the $ϕ^4$ models with and without symmetry breaking and to the $O(N)$ $ϕ^4$ theory.
Most signatures of new physics in colliders have been studied so far on the transverse plane with respect to the beam direction. In this work however we study the impact of a hidden sector beyond the Standard Model (SM) on inclusive (pseudo)rapidity correlations and moments of the multiplicity distributions, with special emphasis in the LHC results.
We introduce an eikonal Monte Carlo model (running in conjunction with HERWIG) for simulating multiparticle production in hadron-hadron interactions. We compare our simulated data to the CDF Tevatron measurement of the underlying event activity in hard inelastic proton-antiproton scattering at sqrt(s)=1.8 TeV. By fixing the only free parameter in our model, the total hadron-hadron cross section, we find that our model describes the data better than either the HERWIG Underlying Event model or the Hard Multiparton model.
Properties of multiparticle final states produced in the central rapidity region of small-x deep inelastic scattering (DIS) are discussed. It is pointed out that these properties contain important information on the nature of the Pomeron - used for the description of total cross section and diffractive production in DIS. It is shown that models based on universality of the Pomeron predict charged particle multiplicities in small-x DIS which are in good agreement with recent HERA results.
We present and discuss results on multiplicity and angular distributions of shower particles produced in silicon-nucleus collisions at 4.5 A GeV/c. These results are compared with those obtained for different values of impact parameter. Shower width distribution has also been investigated .
The theory of strong interactions, quantum chromodynamics (QCD), is quite successful in the prediction and description of main features of multiparticle production processes at high energies. The general perturbative QCD approach to these processes (mainly to e+e- -annihilation) is briefly formulated and its problems are discussed. It is shown that the analytical calculations at the parton level with the low-momentum cut-off reproduce experimental data on the hadronic final state in multiparticle production processes at high energies surprisingly accurately even though the perturbative expansi…
The properties of QCD vacuum and the confinement of quarks and gluons certainly influence the multiparticle production processes. Some phenomenological attempts of the consideration of related collective effects and the possibilities of their experimental detection are briefly discussed in this review. We consider in particular the correlation characteristics of pion systems, statistical and hydrodynamical analogies, the problem of phase transition from a quark-gluon plasma to a multipion state and the possible modifications of the evolution of the quark-gluon jets. The presentation is somewha…
The gluon dominance model offers a description of multiparticle production in e^+e- - annihilation and proton-proton collisions. The multiplicity distributions in e^+e^- annihilation are well described. The energy dependence of model parameters gives the dynamic parton stage and hadronisation picture. It is shown that this model has confirmed oscillations in sign of the ratio of factorial cumulant moments over factorial moments of the increasing order. The collective behavior of secondary particles in $pp$-interactions at 70 GeV/c is studied in the project "Thermalization". An active role of g…
We review theoretical and experimental advances in the application of the perturbative QCD approach to the description of particle distributions in jets in the (semi) soft region with particular emphasis on HERA physics.
The study of the singularities and zeros of the generating functions of multiplicity distributions is advocated. Some hints from well known probability distributions and experimental data are given. The statistical mechanics analogies provoke to look for a signature of phase transitions. The program of further experimental studies of the singularities is formulated.
The origin of the erraticity behaviour observed recently in the experiment is studied in some detail. The negative-binomial distribution is used to fit the experimental multiplicity distribution. It is shown that, with the multiplicity distribution taken into account, the experimentally observed erraticity behaviour can be well reproduced using a flat probability distribution. The dependence of erraticity behaviour on the width of multiplicity distribution is studied.
We report results of our ongoing nonperturbative numerical study of a classical effective theory describing low-x partons in the central region of a heavy-ion collision. In particular, we give estimates of the initial transverse energies and multiplicities for a wide range of collision regimes, including those at RHIC and at LHC.
It is shown that the multiplicity distribution associated to self-shadowing events satisfies an universal equation in terms of the minimum bias distribution. The number of elementary collisions, basic in the structure of any multiple scattering, is reduced if a collective effect like percolation of strings takes place. The main consequences of the percolation are briefly discussed.
Using the theory talks at ISMD2010 as a guidance, I present a personal review of our current understanding of multiparticle interactions in QCD. For more clarity, I separately consider hard, semi-hard, and soft interactions, and I devote most of the space to those phenomena for which progress has been recently made from first principles. Also, priority is given to processes which are directly relevant for QCD studies at the LHC, notably to forward particle production and ultrarelativistic heavy ion collisions.
We consider the phenomenological consequences of the assumption that the baryons are the systems of three quarks and string junction. The process of baryon number transfer due to string junction propagation in rapidity space is considered in detail. At high energies it leads to a significant effect in the net baryon production in $hN$ and $hA$ collisions at mid-rapidities and in the incident meson fragmentation region. The results of numerical calculations in the framework of the Quark--Gluon String Model are in reasonable agreement with the data.
The experimental results on the falling down of scaled factorial moments in azimuthal variable $ϕ$ is studied in some detail. It is shown that this phenomenon may be referred to the influence of transverse momentum conservation. The existing experimental data from DELPHI, EMU08, NA22 and UA1 are successfully explained. Various methods are proposed to partly eliminate this influence and rule out the 'falling down' of factorial moments.
In order to analyze data on joint charged-particle/photon distributions from an experimental search (T-864, MiniMax) for disoriented chiral condensate (DCC) at the Fermilab Tevatron collider, we have identified robust observables, ratios of normalized bivariate factorial moments, with many desirable properties. These include insensitivity to many efficiency corrections and the details of the modeling of the primary pion production, and sensitivity to the production of DCC, as opposed to the generic, binomial-distribution partition of pions into charged and neutral species. The relevant formali…
In this paper we address two problems in the BFKL Pomeron calculus in zero transverse dimensions: the summation of the Pomeron loops and the calculation of the processes of multiparticle generation. We introduce a new generating functional for these processes and obtain the evolution equation for it. We argue that in the kinematic range given by $ 1 \ll \ln(1/\as^2) \ll \as Y \ll \frac{1}{\as}$, we can reduce the Pomeron calculus to exchange of non-interacting Pomerons with the renormalized amplitude of their interaction with the target. Therefore, the summation of the Pomeron loops can be per…
We propose a semiclassical approach to calculate multiparticle cross sections in scalar theories, which have been strongly argued to have the exponential form $\exp(λ^{-1}F(λn,ε))$ in the regime $λ\to0$, $λn$, $ε=$ fixed, where $λ$ is the scalar coupling, $n$ is the number of produced particles, and $ε$ is the kinetic energy per final particle. The formalism is based on singular solutions to the field equation, which satisfy certain boundary and extremizing conditions. At low multiplicities and small kinetic energies per final particle we reproduce in the framework of this formalism the main p…
Multiple interaction models satisfying $s$-channel unitarity predict that, in contrast to inelastic processes, factorization is violated in diffractive processes. The size of this effect can be characterized in terms of the rapidity gap survival probability. The possibility of its measurement at HERA is pointed out. Furthermore a method to measure photon diffraction dissociation at LEP2 and planned linear colliders is discussed and cross section predictions are given.
We present an effective field theory of multiparticle correlations based on analogy with Ginzburg-Landau theory of superconductivity. With the assumption that the field represents particle density fluctuations, and in the case of gaussian-type effective action we find that there are no higer-order correlations, in agreement with the recent observations in high energy heavy-ion collisions. We predict that three-dimensional two-particle correlations have Yukawa form. We also present our results for the two-dimensional and one-dimensional two-particle correlations (i.e. cumulants) as projections …
The gluon dominance model presents a description of multiparticle production in proton-proton collisions and proton-antiproton annihilation. The collective behavior of secondary particles in $pp$-interactions at 70 GeV/c and higher is studied in the project {\bf "Thermalization"}. The obtained neutral and charged multiplicity distribution parameters explain some RHIC-data. The gluon dominance model is modified by the inclusion of intermediate quark topology for the multiplicity distribution description in the pure $p\bar p$-annihilation at few tens GeV/c and explains behavior of the second cor…
Recently equations for the generating functional in the perturbative quantum chromodynamics (QCD) have been extended by including the non-perturbative dissipation in QCD jets. The resulting equations have been solved rigorously and new family of scaling solutions, the so-called delta - scaling, generalizing the well-known Kubo-Nielsen-Olesen scaling law for hadron multiplicity distributions have been found. The relevance of delta - scaling is discussed in the Landau - Ginzburg theory of phase transitions. Preliminary application of these ideas to the p{\bar p} data of the UA5 Collaboration is …
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 …
We review hitherto attempts to look at the multiparticle production processes from the Information Theory point of view (both in its extensive and nonextensive versions).
