One of the greatest uncertainties in heavy-ion collisions is the description of the initial state. Different models predict a wide range of initial energy density distributions based on their underlying assumptions. Final flow harmonics are sensitive to these differences in the initial state due to the nearly linear mapping between eccentricities and anisotropic flow harmonics. The Trento code uses a model-agnostic approach by phenomenologically parameterizing the initial state and constraining those parameters from a Bayesian analysis. There the multiplicity fluctuations were determined by a one parameter $Γ$ distribution. However, initial-state models arising from the Color-Glass Condensate (CGC) framework lead to an initial energy density which is outside the functional form considered in Trento and its later Bayesian analyses because they rely on log-normal multiplicity fluctuations. We compare $T_{A}T_{B}$ scaling (CGC-like) to $\sqrt{T_{A}T_{B}}$ scaling (preferred from a Trento Bayesian analysis) and find that the $T_A T_B$ form together with log-normal fluctuations is a reasonable candidate to describe the multiplicity fluctuations but leads to larger eccentricities, which would affect the extraction of viscosity in small systems.
The initial state is one of the greatest uncertainties in heavy-ion collisions. A model-agnostic approach is taken in the phenomenological Trento framework which constrains parameters using Bayesian analysis. However, the color-glass condensate (CGC) effective theory predicts initial energy densities that lie outside the recent Bayesian analyses due, in part, to the assumption in Trento of event-by-event multiplicity fluctuations following a $Γ$ distribution. We compare the Trento-preferred $\sqrt{T_{A}T_{B}}$ scaling to CGC-like $T_{A}T_{B}$ scaling coupled with log-normal fluctuations in $Au…
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 $Δ$-scaling method has been applied to ultra-relativistic p+p, C+C and Pb+Pb collision data simulated using a high energy Monte Carlo package, LUCIAE 3.0. The $Δ$-scaling is found to be valid for some physical variables, such as charged particle multiplicity, strange particle multiplicity and number of binary nucleon-nucleon collisions from these simulated nucleus-nucleus collisions over an extended energy ranging from $E_{lab}$ = 20 to 200 A GeV. In addition we derived information entropy from the multiplicity distribution as a function of beam energy for these collisions.
We investigate the relative importance of initial and final state effects on azimuthal correlations of gluons in low and high multiplicity p+Pb collisions. To achieve this, we couple Yang-Mills dynamics of pre-equilibrium gluon fields (IP-GLASMA) to a perturbative QCD based parton cascade for the final state evolution (BAMPS) on an event-by-event basis. We find that signatures of both the initial state correlations and final state interactions are seen in azimuthal correlation observables, such as $v_2\left\lbrace2PC\right\rbrace(p_T)$, their strength depending on the event multiplicity and tr…
We provide a simple derivation for particle production in heavy-ion collisions that is proportional to the rate of entropy production. We find that the particle production depends only on the power of the centre-of-mass collision energy $\sqrt{s_{\rm NN}}$ and the effective phase-space/volume (e.g. geometry of the collision approximated by the number of nucleons participating in the collision $N_{\rm part}$). We show that at low-energies the pseudo-rapidity density of particles per participating nucleon pair scales linearly with $\sqrt{s_{\rm NN}}$ while at high-energies with $\sqrt{s_{\rm NN}…
Oliinychenko, Bugaev and Sorin [arXiv:1204.0103 [hep-ph]] considered the role of conservation laws in discussing possible weaknesses of thermal models which are utilized in describing the hadron multiplicities measured in central nucleus-nucleus collisions. They argued to analyse the criteria for chemical freeze-out and to conclude that none of them were robust. Based on this, they suggested a new chemical freeze-out criterion. They assigned to the entropy per hadron the ad hoc value 7.18 and supposed to remain unchanged over the whole range of the baryo-chemical potentials. Due to unawareness…
We use experimentally measured identified particle spectra and Hanbury Brown-Twiss radii to determine the entropy per unit rapidity $dS/dy$ produced in $\sqrt{s} = 7$ TeV pp and $\sqrt{s_{\rm NN}} = 2.76$ TeV Pb-Pb collisions. We find that $dS/dy = 11335 \pm 1188$ in 0-10% Pb-Pb, $dS/dy = 135.7 \pm 17.9$ in high-multiplicity pp, and $dS/dy = 37.8 \pm 3.7$ in minimum bias pp collisions and compare the corresponding entropy per charged particle $(dS/dy)/(dN_{\rm ch}/dy)$ to predictions of statistical models. Finally, we use the QCD kinetic theory pre-equilibrium and viscous hydrodynamics to mode…
We study the influence and interplay of initial state and final state effects in the dynamics of small systems, focusing on azimuthal correlations at different multiplicities. To this end we introduce a new model, matching the classical Yang-Mills dynamics of pre-equilibrium gluon fields (IP-GLASMA) to a perturbative QCD based parton cascade for the final state evolution (BAMPS) on an event-by-event basis. Depending on multiplicity of the event, we see transverse momentum dependent signatures of the initial, but also the final state in azimuthal correlation observables, such as $v_2\left\lbrac…
Measurements indicate that the centrality dependence of the direct photon multiplicity scales approximately with the number of binary nucleon collisions. Importantly, these same measurements suggest that this scaling does not depend on the cutoff used to define the photon multiplicity. In this work we provide a theoretical perspective on these observations. We emphasize the importance of stronger experimental constraints, in particular for the cutoff independence of the centrality scaling. We highlight the importance of revisiting theoretical studies of jet-medium photons and of medium-modifie…
The fluctuation-dissipation relation tells that dissipation always accompanies with thermal fluctuations. Relativistic fluctuating hydrodynamics is used to study the effects of the thermal fluctuations in the hydrodynamic expansion of the quark-gluon plasma created in the high-energy nuclear collisions. We show that the thermal noise obeys the steady-state fluctuation theorem when (i) the time scales of the evolution of thermodynamic quantities are sufficiently longer than the relaxation time, and (ii) the thermal fluctuations of temperature are sufficiently small. The steady-state fluctuation…
The centrality dependence of the charged multiplicity, transverse energy, and elliptic flow coefficient is studied in a hydrodynamic model, using a variety of different initializations which model the initial energy or entropy production process as a hard or soft process, respectively. While the charged multiplicity depends strongly on the chosen initialization, the p_t-integrated elliptic flow for charged particles as a function of charged particle multiplicity and the p_t-differential elliptic flow for charged particles in minimum bias events turn out to be almost independent of the initial …
In order to understand the detailed dynamics of systems produced in $pp$ collisions, it is essential to know about the Equation of State (EoS) and various thermodynamic properties. In this work, we study the shear viscosity to entropy density ratio, isothermal compressibility and speed of sound of the system by considering a differential freeze-out scenario. We have used a thermodynamically consistent Tsallis non-extensive statistics to have a better explanation for the dynamics of $pp$ collision systems. While the shear viscosity to entropy density ratio provides information about the measure…
Entropy, dimensions and other multifractal characteristics of multiplicity distributions of relativistic charged hadrons produced in ion-ion collisions at SPS energies are investigated. The analysis of the experimental data is carried out in terms of phase space bin-size dependence of multiplicity distributions following the Takagi's approach. Yet another method is also followed to study the multifractality which, is not related to the bin-width and (or) the detector resolution, rather involves multiplicity distribution of charged particles in full phase space in terms of information entropy a…
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.
Multiplicity distributions of charged particles and their event-by-event fluctuations have been compiled for relativistic heavy-ion collisions from the available experimental data at Brookhaven National Laboratory and CERN and also by the use of an event generator. Multiplicity fluctuations are sensitive to QCD phase transition and to the presence of critical point in the QCD phase diagram. In addition, multiplicity fluctuations provide baselines for other event-by-event measurements. Multiplicity fluctuation expressed in terms of the scaled variance of the multiplicity distribution is an inte…
To have a better understanding of the matter formed in ultra-relativistic collisions, using the Color String Percolation Model (CSPM), we have estimated initial energy density, mean free path, squared speed of sound, shear viscosity to entropy density ratio ($η/s$), bulk viscosity to entropy density ratio and bulk modulus for $pp$, $p$-Pb, Xe-Xe and Pb-Pb collisions at the Large Hadron Collider (LHC). These observables are studied as a function of final state charged particle multiplicity density and initial state percolation temperature. The results from this work are compared with the result…
We study the effects of the equation of state on the nuclear suppression of heavy flavours in quark gluon plasma and estimate the initial entropy density of the system produced at the highest RHIC energy. For this purpose we have used the experimental data on the charged particle multiplicity and the nuclear suppression of single electron spectra originating from the semi-leptonic decays of open charm and beauty mesons. We have used inputs from lattice QCD to minimize the model dependence of the results. We obtain the value of the initial entropy density which varies from 20 to 59 /fm$^3$ depe…
Event-by-event fluctuations and correlations between particles produced in relativistic nuclear collisions are studied. The fluctuations in positive, negative, total and net charge are closely related through correlations. In the event of a phase transitions to a quark-gluon plasma, fluctuations in total and net charge can be enhanced and reduced respectively which, however, is very sensitive to the acceptance and centrality. If the colliding system experiences strong density fluctuations due, e.g., to droplet formation in a first-order phase transition, all fluctuations can be enhanced substa…
Fragmentation of Nuclear Remnants in Electron-Nucleus Collisions at High Energy as a Nonextensive Process
Shanxi University（山西大学）；Beijing Vocational College of Agriculture（北京农业职业学院）；Physical-Technical Institute of Uzbekistan Academy of Sciences（乌兹别克斯坦科学院物理技术研究所）；National University of Science and Technology MISIS (NUST MISIS)（俄罗斯国立科技大学MISIS）
Scattering processes often inevitably include the production of infrared states, which are highly correlated with the hard scattering event, and decohere the hard states. This can be described using the entropy of the hard reduced density matrix, which is obtained from tracing over infrared states. We determine this entropy for an asymptotically-free gauge theory by separating the Hilbert space into hard and infrared states, and calculate it in a leading-logarithmic approximation for jets. We find that the entropy increases when the resolution scales defining the hard radiation are lowered, th…
We examine entropy production in relativistic U+U collisions on the basis of a Color Glass Condensate (CGC) type picture as implemented in the Kharzeev-Levin-Nardi model (KLN). In this framework, we find that the peak entropy density produced in tip-on-tip U+U collisions is about 30% greater than that seen in central Au+Au collisions. Although the resulting difference in the produced charged particle multiplicity between tip-on-tip and side-on-side collisions is smaller than that predicted by previous Glauber model estimates, it is still large enough to allow for experimental discrimination be…
Israel-Stewart's causal theory of dissipative hydrodynamics, with the ADS/CFT lower limit of shear viscosity to entropy ratio ($η/s$=0.08), give consistent description of a number of experimental observables in Au+Au collisions at RHIC (c.m. energy $\sqrt{s}$=200 GeV) \cite{Chaudhuri:2008sj}. Assuming that in Pb+Pb collisions at LHC (c.m. energy $\sqrt{s}$=5.5 TeV), except for the initial temperature, other parameters of the fluid remain unchanged, we have predicted for the centrality dependence of multiplicity, mean $p_T$, $p_T$-spectra, elliptic flow. The central temperature of the fluid is …
We discuss the importance of initial state and early time effects with regard to the theoretical understanding of long range azimuthal correlations observed in high-multiplicity $p+p$ and $p+A$ collisions.
The study of fluctuations of particle multiplicities in relativistic heavy-ion reactions has drawn much attention in recent years, because they have been proposed as a probe for underlying dynamics and possible formation of quark-gluon plasma. Thus, it is of uttermost importance to describe the baseline of statistical fluctuations in the hadron gas phase in a correct way. We have performed a comprehensive study of multiplicity distributions in the full ideal hadron-resonance gas in different ensembles, namely grand-canonical, canonical and microcanonical, using two different methods: asymptoti…
The new state of matter produced at Relativistic Heavy Ion Collider reveals a strongly coupled quark-gluon plasma with an extremely small shear viscosity to entropy density ratio eta/s. We calculate the eta/s of an equilibrated hadron matter characterized by a relativistic hadron resonance gas with a Hagedorn mass spectrum that grows exponentially with the hadron mass. We find with increase in temperature of the system the eta/s value decreases due to rapid increase in the multiplicity of massive resonances. In the vicinity of the critical temperature for deconfinement transition, the minimum …
Mechanisms for particle production at intermediate pT in nuclear collisions at RHIC are discussed, emphasizing the differences in associated jet-like correlations between color-neutral and colored production. An alternative production mechanism involving both recombination and fragmentation is suggested, which might simultaneously lead to an enhancement of baryons and to jet-like correlations. To gain more insight into the relative importance of different mechanisms a study of constrained distributions of associated multiplicity is proposed. In a simple model it is shown that these multiplicit…
Using numerical results from ideal and viscous relativistic hydrodynamic simulations with three different equations of state, for Au+Au and Cu+Cu collisions at different centralities and initial energy densities, we explore the dependence of the eccentricity-scaled elliptic flow, v_2/epsilon, and the produced entropy fraction, Delta S/S_0, on the final charged hadron multiplicity density dN_ch/dy per unit transverse overlap area S, (1/S)(dN_ch/dy). The viscous hydrodynamic simulations are performed with two different versions of the Israel-Stewart kinetic evolution equations, and in each case …
