The method of scaling transformations permitting to carry out the reconstruction of cross sections of $γN$ and $γγ$ interactions on the basis of cross sections of nucleon-(anti)nucleon interactions is suggested. The photon--hadron scaling violation is a consequence of dependence of scaling transformation parameter $\bar n(s)$ on the energy. The universal function $\bar n(s)$ is interpreted as the multiplicity of photohadronization. This function is established by processing the data on $γp$ cross sections in the low energy region $\sqrt{s}< 20 \GeV$ and is extrapolated to the high energy region up to $\sqrt{s}\sim 200 \GeV$. The results of the reconstruction of $γN$ cross sections at high energies and of $γγ$ ones at all energies are in a remarkable agreement with available experimental data.
We discuss the possibility to suppress the nonperturbative effects if the very high multiplicity hadron final states are chosen. The theoretical uncertainties and possible experimental measurements are described.
We argue that recent NA49 results on multiparticle distributions and fluctuations, as a function of the number of participant nucleons, suggest that percolation plays an important role in particle production at high densities.
We argue that recent NA49 results on multiparticle distributions and fluctuations, as a function of the number of participant nucleons, suggest that percolation plays an important role in particle production at high densities.
We introduce the Weibull distribution as a simple parametrization of charged particle multiplicities in hadron-hadron collisions at all available energies, ranging from ISR energies to the most recent LHC energies. In statistics, the Weibull distribution has wide applicability in natural processes involving fragmentation processes. This gives a natural connection to the available state-of-the-art models for multi-particle production in hadron hadron collisions involving QCD parton fragmentation and hadronization.
The multiple production processes of secondary hadrons in proton-antiproton scattering are divided into three types. The first type is a shower of secondary hadrons produced from gluon string decay, the second type is a shower of secondary hadrons produced from two quark strings decay and the third is a shower produced from three quark strings decay. At the same time there are only two types for proton-proton scattering - shower from gluon string and shower from two quark strings. These showers do not correspond to pomeron showers originating from cuts of one, two, three, ... pomerons. Multipl…
Continuing previous work on forward-backward multiplicity correlation properties in proton-proton collisions in the framework of the weighted superposition model of two components (each one described by a negative binomial multiplicity distribution) with the addition of the leakage parameter which controls clan spreading from one hemisphere to the opposite one, we examine E735 data on the c.m. energy dependence of the total correlation strength and of the forward variance at fixed total multiplicity. A comparison with the Chou-Yang approach to the problem is presented and extrapolations of the…
It is shown that simple extension of the modified negative binomial distribution describes negatively charged particle multiplicity distributions in e+e- annihilation, measured in the whole phase space, as well as the modified negative binomial.
We describe recent applications of the MLLA evolution equations to the calculation of mean multiplicities in quark and gluon jets and the higher moments of hadron and sub-jet multiplicity distributions in $e^+e^-$-annihilation as function of c.m.s. energy $Q$ and resolution parameter $y_{cut}$. The transition from jets to hadrons with increasing jet resolution is considered.
The average charged hadron multiplicities induced by top quark decays are calculated in pQCD at LHC energies. Different modes of top production are considered. Proposed measurements can be used as an additional test of pQCD calculations independent on a fragmentation model.
It is shown that charged hadron multiplicity distributions in restricted (pseudo)rapidity intervals in e+e- annihilation and in e+p scattering at HERA are quite well described by the modified negative binomial distribution and its simple extension.
The paper contains a description of a first attempt to understand the extremely inelastic high energy hadron collisions, when the multiplicity of produced hadrons considerably exceeds its mean value. Problems with existing model predictions are discussed. The real-time finite-temperature $S$-matrix theory is built to have a possibility to find model-free predictions. This allows to include the statistical effects into consideration and build the phenomenology. The questions to experiment are formulated at the very end of the paper.
Recently exact numerical results from the evolution equation for parton multiplicities in QCD jets have been obtained. A comparison with various approximate results is presented. A good description is obtained not only of the jet multiplicities measured at LEP-1 but also of the hadron multiplicities for $cms$ energies above 1.6 GeV in \epem annihilation. The solution suggests that a final state hadron can be represented by a jet in the limit of small (nonperturbative) $k_\perp$ cut-off $Q_0$. In this description using as adjustable parameters only the QCD scale $Λ$ and the cut-off $Q_0$, the c…
Predictions of a thermodynamical model of hadron production for multiplicity distributions in $e^+e^-$ annihilations at LEP and PEP-PETRA centre of mass energies are shown. The production process is described as a two-step process in which primary hadrons emitted from the thermal source decay into final observable particles. The final charged tracks multiplicity distributions turn out to be of Negative Binomial type and are in quite good agreement with experimental observations. The average number of clans calculated from fitted Negative Binomial coincides with the average number of primary ha…
Oscillatory behavior of cumulant moments obtained from the experimental data in $pp$ collisions and $\bar{p}p$ collisions are analyzed by the modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Both distributions well describe the cumulant moments obtained from the data. This fact shows sharp contrast to the result in $e^+e^-$ collisions, which is described by the the MNBD much better than by the NBD.
Multiplicity distribution in small bins is studied within the Ginzburg-Landau description for first-order quark-hadron phase transition. Direct comparison of the distribution with a Poisson one (with the same average) is made. Dynamical factor $d_q$ for the distributionand ratio $D_q\equiv d_q/d_1$ are studied, and novel scaling behaviors between $D_q$ are found which can be used to detect the formation of quark-gluon plasma.
Multiple Reflection Expansion (MRE) formalism has been applied to hadron resonance gas (HRG) model to study the finite-size effect on thermodynamics of small systems of hadron gas at the chemical freeze-out temperature in high-multiplicity events of proton-proton (pp) colisions at the LHC. Comparison with larger systems of heavy-ion (AA) collisions helps in undersanding the usefulness of the effect on small systems. Thermodynamic properties of these systems at the chemical freeze-out, with and without system-size effect, are contrasted with those for infinite hadronic phase of strongly interac…
We analysed the identified hadron multiplicity predictions of the modified thermodynamical model of the multiparticle production processes with non-extensive statistic. The replacement of the standard Boltzmann exponential factor by the eventually much slower falling Tsallis one is suggested by the analysis of the transverse momentum distributions measured at high energies. The increase of high transverse momenta should accord with the abundance of heavy secondary particles, in particular multistrange barions. The introduction to the thermodynamical model of suppression factors similar to the …
Recently, the moments of multiplicity distributions in e+e- annihilation and the ratios H_q (cumulant over factorial moments K_q/F_q) have been determined both for the hadronic final state and for jets at variable resolution. These ratios show an oscillatory behaviour as function of q with strong dependence of the amplitude and length of oscillation on the jet resolution parameter y_{cut}. The recent explanation of this phenomenon based on perturbative QCD calculations is discussed.
The idea that the hard processes are dominate at the very high multiplicity (VHM) final states creation is considered. For this purpose quantitative realization of the Pomeron, DIS and large-angle annihilation (LAA) mechanism combinations are considered in the pQCD frame. The phase transition (condensation) in the soft pions system is described as the alternative to above mechanism. It is shown that in compared to QCD prediction last one predicts enhancement in the VHM distribution tail.
Measured multiplicity distributions of primary charged particles produced in the forward rapidity region of the $proton-proton$ ($pp$) collisions at the centre-of-mass energy, $\sqrt {s}$ = 7 TeV at the Large Hadron Collider (LHC) have been analyzed in terms of the Negative Binomial Distribution (NBD) function. Like the multiplicity distributions in the mid-rapidity region for the $pp$ collisions at $\sqrt {s}$ = 7 TeV, the distributions for the minimum bias events in the forward region also are better described with the superposition of two-NBDs, as proposed by a two-component model of partic…
The multiplicity distributions at high energy $e^+e^-$ annihilation are described well within the Two Stage Model in the region from 14 to 189 GeV. Energy dependence of parameters of this model gives the dynamic picture of the parton stage and the stage of hadronization. It is shown that oscillations in sign of the ratio of factorial cumulant moments over factorial moments of increasing order can be confirmed by this model.
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 recurrent relations and combinants of these distributions, one can obtain new information contained in them and otherwise unavailable, which may broaden our knowledge of the particle production mechanism.
If large-angle multigluon radiation gives significant contributions to parton showers in the LHC high-energy region, appropriate generalizations of parton branching methods are required for Monte Carlo simulations of exclusive high-multiplicity final states. We discuss the use in this context of transverse-momentum dependent kernels which factorize in the region of high energies. We give examples based on ep and p pbar multi-jet data, and point to possible developments for distributions associated with massive final states at the LHC.
QCD predictions for moments of multiplicity distributions are compared with experimental data on e+e- collisions and their two-NBD fits. Moments of the multiplicity distribution in a two-NBD model for 1.8 TeV pp collisions are considered. Three-NBD model predictions and fits for pp at LHC energies are also discussed. Analytic expressions for moments of hybrid NBD are derived and used to get insight into jet parameters and multicomponent structure of the processes. Interpretation of observed correlations is proposed.
We discuss the multiplicity distribution for highest accessible energies of $pp$- and $\bar pp$- interactions from the point of view of the multiparton collisions. The inelastic cross sections for the single, $σ_1$, and multiple (double and, presumably, triple, $σ_{2+3}$) parton collisions are extracted from the analysis of the experimental data on the multiplicity distribution up to the Tevatron energies. It follows that $σ_1$ becomes energy independent while $σ_{2+3}$ increases with $\sqrt{s}$ for $\sqrt{s}\ge$ 200 GeV. The observed growth of $<p_{\perp}>$ with multiplicity is attributed to …
We consider QCD based model of hadrons interaction in which gluons density in wave function of initial state is low in rapidity space and real hadrons are produced by decay of color field strings. Hadrons production processes in pp and p antip interactions differ on principle. There are three types of inelastic processes in p antip collision. The first type is production of secondary hadrons shower from decay of gluon string. The second type is shower produced from decay of two quark strings and the third one -- from decay of three quark strings. At the same time there are only two types of in…
Recursive solution for a general homogeneous in time pure birth branching process with simultaneous production of any number of particles and with continuous evolution parameter is given. Calculational algorithm based on the use of Koenigs function and functional Schroder equation is described. It is shown that multiplicity distributions in e+e- annihilation into hadrons for c.m. energies up to 189 GeV are well described by the modified negative binomial distribution, explained by simple pure birth branching process without multiple simultaneous particle production. The energy dependence of th…
Deviation of the multiplicity distribution $P_q$ in small bin from its Poisson counterpart $p_q$ is studied within the Ginzburg-Landau description for second-order quark-hadron phase transition. Dynamical factor $d_q\equiv P_q/p_q$ for the distribution and ratio $D_q\equiv d_q/d_1$ are defined, and novel scaling behaviors between $D_q$ are found which can be used to detect the formation of quark-gluon plasma. The study of $d_q$ and $D_q$ is also very interesting for other multiparticle production processes without phase transition.
We address the general features of event-by-event fluctuations of the multiplicity of gluons produced in the scattering of a dilute hadron off a large nucleus at high energy in the fragmentation region of the dilute hadron. We relate these fluctuations to the stochasticity of the number of quanta contained in the hadron at the time of the interaction. For simplicity, we address the ideal case in which the hadron is an onium, and investigate different kinematical regimes in rapidity and onium size. We show that at large rapidity, the multiplicity distribution exhibits an exponential tail in the…
In this paper we propose an approach which demonstrates the dependence of quarkoni production on the multiplicity of the accompanying hadrons. Our approach is based on the three gluons fusion mechanism, without assuming the multiplicity dependence of the saturation scale. We show, that we describe the experimental data, which has a dependence that is much steeper than the multiplicity of the hadrons.
In this paper, transverse momentum spectra of pi+, K+ and p measured at fix event-multiplicities and \sqrt s = 0.9, 2.76 and 7 TeV collision energies by the CMS Collabotaion are shown to fit the Tsallis-distribution. It is found that the power of the distribution shows a double-logarithmic dependence on the event-multiplicity N, while the T parameter depends linearly on N. A similar double-logarithmic dependence of the q parameter of pi0 spectra on the collision energy \sqrt{s} is found too. It is also shown that event-by-event fluctuations of the multiplicity N and the total E_T energy going …
The multiplicity per rapidity of the well-identified particles $π^{-}$, $π^{+}$, $k^{-}$, $k^{+}$, $\bar{p}$, $p$, and $p-\bar{p}$ measured in different high-energy experiments, at energies ranging from $6.3$ to $5500~$GeV, are successfully compared with the Cosmic Ray Monte Carlo (CRMC) event generator. For these rapidity distributions, we introduce a theoretical approach based on fluctuations and correlations (Carruthers) and another one based on statistical thermal assumptions (hadron resonance gas model). Both approaches are fitted to the two sets of results deduced from experiments and si…
Multi-hadron production in inelastic neutrino-nucleon interactions is investigated within the framework of the quark-gluon string model. The contributions of the planar (one-Reggeon exchange) and cylindrical (one-Pomeron exchange) graphs to different observables is computed using a Monte Carlo program for the generation of hadrons produced from the decay of colorless quark-antiquark strings. The suggested approach results in a satisfactory description of the experimental data on $ν(\barν) N\toμ^-(μ^+) h X$ reactions obtained recently at CERN by the NOMAD Collaboration. The data extends over a …
Using the coalescence model we compute the multiplicity of $Z_{cs} (3985)^-$ (treated as a compact tetraquark) at the end of the quark gluon plasma phase in heavy ion collisions. Then we study the time evolution of this state in the hot hadron gas phase. We calculate the thermal cross sections for the collisions of the $Z_{cs} (3985)^-$ with light mesons using effective Lagrangians and form factors derived from QCD sum rules for the vertices $Z_{cs}\bar{D}_{s }^* D $ and $Z_{cs} \bar{D}_{s} D^{*}$. We solve the kinetic equation and find how the $Z_{cs} (3985)^-$ multiplicity is affected by the…
Motivated by the relation existing between the gluon density in a hadron and the multiplicity of the particles measured in the final state of hadron-nucleus collisions, we study systematically the fluctuations of the gluon density in onia, which are the simplest dilute hadrons, of different sizes and at various rapidities. We argue that the small and the large-multiplicity tails of the gluon distributions present universal features, which should translate into properties of the multiplicity of the particles measured in the final state of high-energy proton-nucleus collisions, or of deep-inelas…
The average charged hadron multiplicity in the $e^+e^-$ events with the primary $t\bar{t}$-pair at the collision energy 500 GeV, as well as the average multiplicity of charged hadrons from the top quark are calculated in QCD to be $86.7 \pm 1.11$ and $41.0 \pm 0.54$, respectively.
Time evolution of a "little bang" created in heavy ion collisions can be divided into two phases, the pre-equilibrium and hydrodynamic. At what moment the evolution becomes hydrodynamic and is there any universality in the hydrodynamic flow? To answer these questions we briefly discuss various versions of hydrodynamics and their applicability conditions. In particular, we elaborate on the idea of "universal" (all-order resumed) hydrodynamics and propose a simple new model for it. The model is motivated by results obtained recently via the AdS/CFT correspondence. Finally, charged hadron multipl…
Moments play a crucial role in investigating the characteristics of charged particle multiplicities in high energy interactions. The success of any model which describes the multiplicity data can be understood well by studying the normalised and factorial moments of that distribution.~The Tsallis model is one of the most successful models which describes the multiplicity spectra, transverse momentum ($p_T$) spectra very precisely in high energy interactions.~In our previous work we have used the Tsallis $q$-statistics to describe the multiplicity distributions in leptonic and hadronic collisio…
The azimuthal collimation of di-hadrons with large rapidity separations in high multiplicity p+p collisions at the LHC is described in the Color Glass Condensate (CGC) effective theory [1] by N_c^2 suppressed multi-ladder QCD diagrams that are enhanced α_S^(-8) due to gluon saturation in hadron wavefunctions. We show that quantitative computations in the CGC framework are in good agreement with data from the CMS experiment on per trigger di-hadron yields and predict further systematics of these yields with varying trigger pT and charged hadron multiplicity. Radial flow generated by re-scatteri…
An unexpected result at the RHIC and the LHC is the observation that high-multiplicity hadronic events in heavy-ion and proton-proton collisions are distributed as two "ridges", approximately flat in rapidity and opposite in azimuthal angle. We propose that the origin of these events is due to the inelastic collisions of aligned gluonic flux tubes that underly the color confinement of the quarks in each proton. We predict that high-multiplicity hadronic ridges will also be produced in the high energy photon-photon collisions accessible at the LHC in ultra-peripheral proton-proton collisions or…
This paper investigates the configurational entropic content of hadron-nucleus collisions. Hadron multiplicities and Au nuclei are employed to compute the critical points of the configurational entropy as a function of the saturation scale in deep inelastic scatterings, in QCD. The results match phenomenological data to the precision of 0.39%.
Multiplicity fluctuations in rings around the jet axis and in off-axis cones have been measured by the DELPHI collaboration in $e^+e^-$ annihilations into hadrons at LEP energies. The measurements are compared with analytical perturbative QCD calculations for the corresponding multiparton system, using the concept of Local Parton Hadron Duality. Some qualitative features are confirmed by the data but substantial quantitative deviations are observed.
Multiplicity data up to 200 GeV in e+e- annihilation are described well by the two-stage model based on pQCD and suggested the phenomenological scheme of hadronization. This model confirms the fragmentation mechanism of hadronization (in vacuum). It allows to estimate mean multiplicity at 500 GeV and 1 TeV. Gluon dominance model is the modification of this model for the description of hadronic interactions. It was realised by an inclusion of gluons. It demonstrates very strong evidence of the recombination mechanism of hadronization. In this case, the mean multiplicity of hadrons formed from a…
Nuclear attenuation of the multi-hadron systems in the string model is considered. The improved two-scale model with set of parameters obtained recently for the single hadron attenuation is used for calculation of the multiplicity ratios of the one-, two- and three-hadron systems electroproduced on nuclear and deuterium targets. The comparison of the features of the one-, two- and three-hadron systems is performed. The predictions of the model for multiplicity ratios of multi-hadron systems as functions of different convenient variables are presented.
The improved two-scale model with symmetric Lund distribution function is used to perform the fit to the semi-inclusive deep-inelastic scattering (SIDIS) data on nuclear targets of HERMES experiment at DESY. The ratio of hadron multiplicity on nuclear target to the deuterium one is chosen as observable, as usually. Some peculiarities of the fit are discussed. The two-parameter's fit gives satisfactory agreement with the data. The results of the present and previous fits are compared.
Ratios of multiplicity moments, H_q (cumulant over factorial moments K_q/F_q), have been observed to show an oscillatory behaviour with respect to order, q. Recent studies of e^+e^- annihilations at LEP have shown, moreover, that the amplitude and oscillation length vary strongly with the jet resolution parameter y_{cut}. We study the predictions of the perturbative QCD parton cascade assuming low non-perturbative cut-off (Q_0\sim Λ_{QCD}\sim few 100 MeV) and derive the expectations as a function of the cms energy and jet resolution from threshold to very high energies. We consider numerical s…
The observed pronounced multiplicity dependence of correlation functions in hadron-hadron reactions and in particular of Bose-Einstein correlations provides information about underlying physics. We discuss in this contribution several interpretations, giving special attention to the string model for Bose-Einstein correlations of Andersson and Hofmann, as well as the core-halo picture of Csorgo, Lorstad and Zimanyi.
A two-component (soft + hard) model (TCM) of hadron production in yields and spectra derived from the charge-multiplicity dependence of 200 GeV p-p collisions at the relativistic heavy ion collider (RHIC) is extended to describe p-p spectrum data from the large hadron collider (LHC) up to 13 TeV. The LHC data include spectrum ratios that provide only partial information on the TCM. The LHC ratio method is applied to well-understood 200 GeV spectrum data to derive an algebraic link between spectrum ratios and the full TCM. Some aspects of the form of the hard component on transverse momentum ar…
In this paper we show that QCD at high energies leads to the multiplicity distribution $\frac{σ_n}{σ_{ \rm in}}\,\,=\,\,\frac{1}{N}\,\Lb \frac{N\,-\,1}{N}\Rb^{n - 1}$, (where $N$ denotes the average number of particles), and to entanglement entropy $S \,=\,\ln N$, confirming that the partonic stat at high energy is maximally entangled. However, the value of $N$ depends on the kinematics of the parton cascade. In particular, for DIS$N = xG(x,Q)$ , where $xG$ is the gluon structure function, whil for hadron-hadron collisions, $N \propto Q^2_S(Y)$, where $Q_s$ denotes the saturation scale. We che…
The dependence of the one dimensional Bose-Einstein correlation R_1D derived from proton-proton collisions is examined in terms of energy, hadron multiplicity and number of emerging hadronic jets. It is argued that the observed rise of R_1D with energy is the result of the increase of the average number of hadronic jets. It is further shown that by the relative straightforward measurements of R_1D and its chaoticity parameter $λ$ one should be able to estimate the average number of outgoing hadronic jets emitted over the entire final state phase space without the necessity to rely on a particu…
Study of high multiplicity events in proton-proton interactions is carried out at the U-70 accelerator (IHEP, Protvino). These events are extremely rare. Usually, Monte Carlo codes underestimate topological cross sections in this region. The gluon dominance model (GDM) was offered to describe them. It is based on QCD and a phenomenological scheme of a hadronization stage. This model indicates a recombination mechanism of hadronization and a gluon fission. Future program of the SVD Collaboration is aimed at studying a long-standing puzzle of excess soft photon yield and its connection with high…
In this paper we study the dependence of Bose-Einstein correlations on the multiplicity of an event. We found that events with large multiplicity, stem from the production of several parton showers, while the additional production of small multiplicity in the central rapidity region (central diffraction), gives a negligible contribution due to emission of soft gluons, that leads to the Sudakov suppression of the exclusive production of two gluon jets. Hence, the Bose-Einstein correlation is the main source of the azimuthal angle correlations which generates $v_n$ with odd and even $n$. We foun…
We study the system-size dependence of Knudsen number, a measure of degree of thermalization, for hadron resonance gas that follows the Lattice-QCD equation of state at zero chemical potential. A comparison between Knudsen numbers for the AuAu collisions at RHIC and the hadron gas of size similar to the size of high-multiplicity pp events at LHC, reassures the applicability of hydrodynamics in interpreting the features of particle production in high-multiplicity pp events.
In this paper we analyze in detail the production of strangeness in proton-proton collisions in the kinematics of large transverse momenta $p_{T}$ of produced hadrons. Using the color dipole framework, we estimated the production cross-sections for kaons, and demonstrated that the shapes of the $p_{T}$-dependence are in agreement with available experimental data. We also analyzed the self-normalized yields of strange hadrons as a function of multiplicity of co-produced hadrons, and found that the predictions are in agreement with the faster-than-linear growth seen in experimental data. Our des…
