Event multiplicity, transverse momentum and energy dependence of charged particle production, and system thermodynamics in $pp$ collisions at the Large Hadron Collider
Rutuparna Rath, Arvind Khuntia, Raghunath Sahoo, Jean Cleymans
In the present work, we study the recent collision energy and multiplicity dependence of the charged particle transverse momentum spectra as measured by the ALICE collaboration in $pp$ collisions at $\sqrt{s}$ = 5.02 and 13 TeV using the non-extensive Tsallis distribution and the Boltzmann-Gibbs Blast Wave (BGBW) model. A thermodynamically consistent form of the Tsallis distribution is used to extract the kinetic freeze-out parameters from the transverse momentum spectra of charged particles at mid-rapidity. In addition, a comprehensive study of fitting range dependence of transverse momentum spectra on the freeze-out parameters is done using Tsallis statistics. The applicability of BGBW model is verified by fitting the transverse momentum spectra of the bulk part ($\sim 2.5~ {\rm GeV}/c$)for both 5.02 and 13 TeV energies and also in different multiplicity classes. The radial flow, $<β>$ is almost independent of collision energy and multiplicity whereas the behavior of kinetic freeze-out temperature significantly depends on multiplicity classes. It is found that the Tsallis distribution generally leads to a better description for the complete transverse momentum spectra whereas the BGBW model explains the bulk part of the system.
Hadronic resonances, having very short lifetime, like $\rm{K}^{*0}$, can act as useful probes to understand and estimate lifetime of hadronic phase in ultra-relativistic proton-proton, p--Pb and heavy-ion collisions. Resonances with relatively longer lifetime, like $ϕ$ meson, can serve as a tool to locate the QGP phase boundary. We estimate a lower limit of hadronic phase lifetime in Cu--Cu and Au--Au collisions at RHIC, and in pp, p--Pb and Pb--Pb collisions at different LHC collision energies. Also, we obtain the effective temperature of $ϕ$ meson using Boltzmann-Gibbs Blast-Wave function, w…
Heavy flavor measurements in high multiplicity proton-proton and proton-nucleus collisions at collider energies enable unique insights into their production and hadronization mechanism because experimental and theoretical uncertainties cancel in ratios of their cross-sections relative to minimum bias events. We explore such event engineering using the Color Glass Condensate (CGC) effective field theory to compute short distance charmonium cross-sections. The CGC is combined with heavy-quark fragmentation functions to compute $D$-meson cross-sections; for the $J/ψ$, hadronization is described e…
The collision system and multiplicity dependence of chemical freeze-out temperature ($T_{\rm ch}$) and strangeness saturation factor ($γ_{s}$) are obtained by studying the particle ratios at the Large Hadron Collider (LHC) energies. Here, we consider the new results in pp at 13 TeV, p+Pb at $\sqrt{s_{\rm NN}}$ = 5.02 TeV, Xe+Xe at $\sqrt{s_{\rm NN}}$ = 5.44 TeV and Pb+Pb at $\sqrt{s_{\rm NN}}$ = 5.02 TeV along with the earlier results in pp at $\sqrt{s}$ = 7 TeV and Pb+Pb at $\sqrt{s_{\rm NN}}$ = 2.76 TeV. A statistical thermal model is used to extract the chemical freeze-out parameters in dif…
The high-multiplicity pp collisions at the Large Hadron Collider energies with various heavy-ion-like signatures have warranted a deeper understanding of the underlying physics and particle production mechanisms. It is a common practice to use experimental data on the hadronic transverse momentum ($p_T$) spectra to extract thermodynamical properties of the system formed in heavy ion and high multiplicity pp collisions. The non-availability of event topology dependent experimental data for pp collisions at $\sqrt{s}$ = 13 TeV on the spectra of non-strange and strange hadrons constrains us to us…
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.
We discuss the physics of the ridge -- azimuthally collimated long range rapidity correlations -- in high multiplicity proton-proton and proton-nucleus collisions. We outline some of the theoretical discussions in the literature that address the systematics of these ridge correlations.
The collective behaviour of hadronic particles has been observed in high multiplicity proton-lead collisions at the Large Hadron Collider (LHC), as well as in deuteron-gold collisions at the Relativistic Heavy-Ion Collider (RHIC). In this work we present the first calculation, in the hydrodynamic framework, of thermal photon radiation from such small collision systems. Owing to their compact size, these systems can reach temperatures comparable to those in central nucleus-nucleus collisions. The thermal photons can thus shine over the prompt background, and increase the low $p_T$ direct photon…
The recent results in \sqrt{s}=2.76 TeV Pb+Pb collisions at the Large Hadron Collider (LHC) reported by the ALICE collaboration shows that the power-law energy-dependence of charged hadron multiplicity in Pb+Pb collisions is significantly different from p+p collisions. We show that this different energy-dependence can be explained by inclusion of a strong angular-ordering in the gluon-decay cascade within the Color-Glass-Condensate (or gluon saturation) approach. This effect is more important in nucleus-nucleus collisions where the saturation scale is larger than 1 GeV. Our prescription gives …
The present article reviews facts and problems concerning charge hadron production in high energy collisions. Main emphasis is laid on the qualitative and quantitative description of general characteristics and properties observed for charged hadrons produced in such high energy collisions. Various features of available experimental data e.g., the variations of charged hadron multiplicity and pseudo-rapidity density with the mass number of colliding nuclei, center-of-mass energies and the collision centrality obtained from heavy-ion collider experiments are interpreted in the context of variou…
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.
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…
In order to have a better understanding of the matter formed in ultra-relativistic collisions, we estimate the jet transport coefficient, $\hat q$, within the Color Sting Percolation Model (CSPM) for various multiplicity classes in proton-proton collisions and centrality classes in nucleus-nucleus collisions at the Large Hadron Collider energies. We study $\hat q$ as a function of final state charged-particle multiplicity and initial percolation temperature. Finally, we compare our obtained results with those calculated from the JET collaboration.
We provide quantitative predictions for the rapidity, centrality and energy dependencies of inclusive charged-hadron productions for the forthcoming LHC measurements in nucleus-nucleus collisions based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives very good descriptions of the first data from the LHC for the inclusive charged-hadron production in proton-proton collisions, the deep inelastic scattering at HERA at small Bjorken-x, and the hadron multiplicities in nucleus-nucleus collisions at RHIC.
Options for future $lepton-proton,lepton-nucleus,γ-proton,γ-nucleus$ and FEL$γ-nucleus$ colliders are discussed. In the spirit of this content, we consider TESLAxHERA, LEPxLHC, $μ$xTEVATRON, exRHIC, LinacxLHC, $\sqrt{s}=3TeV$ $μp$ and CLIC based colliders.
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%.
The multiplicity distribution of particles in relativistic gases is studied in terms of Tsallis' nonextensive statistics. For an entropic index q>1 the multiplicity distribution is wider than the Poisson distribution with the same average number of particles, being similar to the negative binomial distribution commonly used in phenomenological analysis of hadron production in high-energy collisions.
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.
In central Pb-Pb collisions at LHC the multiplicity of particles produced is so high that it should become feasible to examine the nature of transition from the deconfined quark-gluon state to the confined hadron state by methods that rely on the availability of high multiplicity events. We consider four classes of the transition process ranging from critical behavior to totally random behavior, depending on whether or not there is clustering of quarks and on whether or not there is contraction of dense clusters due to confinement. Fluctuations of bin multiplicities in each event are quantifie…
Transverse momentum distributions in ultra-relativistic heavy ion collisions carry considerable information about the dynamics of the hot system produced. Direct comparison with the same spectra from $p+p$ collisions has proven invaluable to identify novel features associated with the larger system, in particular, the "jet quenching" at high momentum and apparently much stronger collective flow dominating the spectral shape at low momentum. We point out possible hazards of ignoring conservation laws in the comparison of high- and low-multiplicity final states. We argue that the effects of ener…
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…
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.
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…
We construct the hadronic multiplicity distribution in terms of an elementary distribution (at given impact parameter) and the inelastic overlap function characterized by the observed BEL (Blacker-Edgier-Larger) behaviour. With suitable parametrizations for the elementary quantities, based on some geometrical arguments and the most recent data on e+e- annihilation, an excellent description of pp and p(bar)p inelastic multiplicity distributions at the highest energies is obtained.
Preliminary results on local multiplicity fluctuations in hadronic Z decays are presented. The data were obtained using the L3 detector at LEP. It is investigated to what extent Monte-Carlo models, which are tuned to reproduce global event-shape variables and single-particle inclusive distributions, can describe the local fluctuations measured by means of bunching parameters.
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.
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.
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…
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.
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.
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.
We develop the dynamical core-corona initialization framework as a phenomenological description of the formation of quark gluon plasma (QGP) fluids in high-energy nuclear collisions. Using this framework, we investigate the fraction of the fluidized energy to the total energy and strange hadron yield ratios as functions of multiplicity and scrutinize the multiplicity scaling of hadron yield ratios recently reported by the ALICE Collaboration. Our results strongly indicate that the QGP fluids are partly formed even at the averaged multiplicity for nonsingle diffractive p+p events.
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…
In this paper, we propose a parameterization which is based on a phenomenological model involving the wounded quarks interactions for explaining the average charged particle multiplicity $\ < n_{ch}\ >$, the central pseudo-rapidity density $\ < (dn/dη)_{η=0}\ >$ and complete rapidity dependence of $dn/dη$ in relativistic heavy-ion collider experiments. The model also interrelates nucleus-nucleus (A-A) collisions with p-A and p-p interactions. Our parameterization rests on simple assumptions regarding mean number of participating quarks and their average number of collisions. The results for $\…
Continuing previous work on forward-backward multiplicity correlation properties in proton-proton collisions in the framework of the weighted superposition model of two components (each one described by a negative binomial multiplicity distribution) with the addition of the leakage parameter which controls clan spreading from one hemisphere to the opposite one, we examine E735 data on the c.m. energy dependence of the total correlation strength and of the forward variance at fixed total multiplicity. A comparison with the Chou-Yang approach to the problem is presented and extrapolations of the…
It is shown that simple extension of the modified negative binomial distribution describes negatively charged particle multiplicity distributions in e+e- annihilation, measured in the whole phase space, as well as the modified negative binomial.
The transverse momentum ($p_{T}$) distribution of strange hadrons ($K_{S}^{0}$ and $Λ$) and multi-strange hadrons( $Ξ$ and $Ω$) measured in p$-$p, p$-$Pb, and Pb$-$Pb collisions at LHC energies have been studied for different multiplicity classes using Tsallis-Weibull (or q$-$Weibull)formalism. The distribution describes the measured $p_{T}$ spectra for all multiplicity (or centrality)classes. The multiplicity dependence of the extracted parameters are studied for the mentioned collisions systems. The $λ$ parameter was observed to increase systematically with the collision multiplicity and fol…
If gravity becomes strong at the TeV scale, we may have the chance to produce black holes at particle colliders. In this paper we study some experimental signatures of black hole production in TeV-gravity theories. In contrast with the usual lore, we show that the black hole energy loss in the bulk during the Hawking evaporation phase may be of the same order of the energy radiated into the brane. We investigate in detail the multiplicity of the decay products of black hole evaporation. We find that the number of particles produced during the evaporation phase is significantly lower than the a…
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.
COMPASS final results on multiplicities of charged hadrons and of identified pions and kaons produced in the deep inelastic muon scattering off an isoscalar target are presented and compared to HERMES results. Measurements are done in bins of x, y and z in a wide kinematic range. The hadron and pion data show a good agreement with (N)LO QCD expectations. The kaon data are long awaited for since they are needed to extract kaon fragmentation functions, a crucial ingredient in solving the strange quark polarisation puzzle. COMPASS results for kaons differ from the expectations of the old NLO DSS …
We present an analysis of data on light flavour hadron production as function of event multiplicity at LHC energies measured by the ALICE collaboration. The strangeness-canonical approach within the framework of the THERMUS statistical hadronisation model is used for a simultaneous description of pp, p-Pb, and Pb-Pb collisions. The rapidity window dependence of the strangeness correlation volume is addressed and a value of $Δy = 1.33 \pm 0.28$ is found. With the exception of the $ϕ$-meson, an excellent description of the experimental data is found.
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 showers of cosmic rays entering the Earth's atmosphere are main sources of information on cosmic rays and are also believed to provide information on elementary interactions at energies not accessible to accelerators. In this context we would like first to remind the role of inelasticity K and elementary cross section $σ$ and then argue that similar in importance are fluctuations of different observables. The later will be illustrated by multiplicity fluctuations in hadronic and nuclear collisions.
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.
The final state hadronic composition of proton-proton collisions at 7 TeV as a function of charged particle multiplicity density is studied. The thermal model is adjusted to match the experimental conditions in order to understand the effect of the experimental cuts on rapidity and multiplicity. This study indicates that the measured hadronic composition under a simultaneous cut on rapidity and multiplicity does not coincide with the fireball hadronic composition. Excluding proton to pion ratio, the adjusted model can explain the measured particle ratios. Therefore, the observed strangeness en…
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…
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…
The scaling behavior of factorial moments of the differences in multiplicities between well separated bins in heavy-ion collisions is proposed as a probe of quark-hadron phase transition. The method takes into account some of the physical features of nuclear collisions that cause some difficulty in the application of the usual method. It is shown in the Ginzburg-Landau theory that a numerical value $γ$ of the scaling exponent can be determined independent of the parameters in the problem. The universality of $γ$ characterizes quark-hadron phase transition, and can be tested directly by appropr…
In this paper we study the electroproduction of open heavy flavor $D$- and $B$-mesons in the kinematics of future $ep$ colliders, such as the Electron Ion Collider (EIC), the Large Hadron electron Collider (LHeC) and the Future Circular Collider (FCC-he). We study in detail the dependence of the cross-sections on multiplicity of co-produced hadrons, in view of its possible sensitivity to contributions from multipomeron contributions, and discuss different observables which might be used for its study. According to our theoretical expectations, in $ep$ collisions the multipomeron contributions …
We propose possible signatures of `exogamous' combinations between partons in the different W+ and W- hadron showers in e+e- -> W+W- events with purely hadronic final states. Within the space-time model for hadronic shower development that we have proposed previously, we find a possible difference of about 10 % between the mean hadronic multiplicity in such purely hadronic final states and twice the hadronic multiplicity in events in which one W decays hadronically and the other leptonically, i.e., <N_had(2W)> \ne 2 <N_{had}(W)>, associated with the formation of hadronic clusters by `exogamous…
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.
New facilities for particle and nuclear physics research, which will be available due to constructing the TESLA linear electron-positron collider tangentially to the HERA proton ring, are discussed.
We study the production of $J/ψ$ vector mesons as a function of charged hadron multiplicity in p+p and p+Pb collisions at LHC energies. We employ the color glass condensate framework, using running coupling Balitsky-Kovchegov evolved dipole amplitudes, to compute gluon and $c\bar{c}$-pair production. We use fragmentation functions to obtain charged hadrons, and explore two different hadronization schemes for the $J/ψ$: non-relativistic quantum chromodynamics and the improved color evaporation model. In our framework, event-by-event multiplicity fluctuations of both hadrons and $J/ψ$ are driven…
