Collectivity Signatures in High-Multiplicity pp Collisions from Hybrid Hydro+Tsallis Modeling of Pion Spectra
Abdul Wali Khan University Mardan（马尔丹阿卜杜勒瓦利汗大学）；Princess Nourah bint Abdulrahman University（公主努拉·宾特·阿卜杜勒拉赫曼大学）；Hubei University of Automotive Technology（湖北汽车工业学院）
Murad Badshah, Haifa I. Alrebdi, Muhammad Waqas, Hadiqa Qadir, Muhammad Ajaz
The transverse momentum (pT) distributions up to pT = 20 GeV/c for pions produced in the ten different multiplicity classes (MCs) of symmetric pp collisions at sqrt(s) = 7 TeV have been investigated. Two distinct models, the Tsallis-Pareto type function (model) and the combined BGBW model and Tsallis-Pareto type model have been employed to fit the pT distributions via the minimum chi-square method. The combined Hydro+Tsallis model is more reliably describing the pT spectra than the Tsallis-Pareto model. The Tsallis temperature (T), non-extensivity parameter (q), normalization constant (N0), Kinetic freeze-out temperature (T0), transverse flow velocity (betaT), and (mean pT) have been extracted through the fitting procedure via the employed models. The Tsallis-Pareto model gives T, q, N0 and mean pT while Hydro+Tsallis model gives T0, betaT, T, q, N0 and mean pT. Incorporating the values of the extracted T and q the thermodynamic quantities and response functions, including energy density (epsilon), particle density (n), entropy density (s), pressure (P), specific heat at constant volume (CV), squared speed of sound (cs2), mean free path (lambda), Knudsen number (Kn), isothermal compressibility (kappaT), and expansion coefficient (alpha) have been calculated at the freeze-out stage. It has been observed that T, betaT, mean pT, N0, epsilon, n, s, P, CV, cs2, and alpha increase with increasing(decreasing) the charged particles multiplicity density dNch/deta(MCs). While T0, q, lambda, Kn, and kappaT decrease with increasing(decreasing) dNch/deta(MCs). These systematic variations in the trends of parameters might suggest the gradual transition towards collectivity and thermal equilibration in the high multiplicity pp events, possibly signalling enhanced collective dynamics and partial thermalization in small collision systems.
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…
In this paper, we investigate the hydrodynamic collectivity in proton--proton (pp) collisions at 13 TeV, using iEBE-VISHNU hybrid model with HIJING initial conditions. With properly tuned parameters, our model simulations can remarkably describe all the measured 2-particle correlations, including integrated and differential elliptic flow coefficients for all charged and identified hadrons ($K_S^0$, $Λ$). However, our model calculations show positive 4-particle cumulant $c_{2}\{4\}$ in high multiplicity pp collisions, and can not reproduce the negative $c_{2}\{4\}$ measured in experiment. Furth…
We report on recent progress in understanding multiparticle correlations in small systems from the initial state. First, we consider a proof-of-principle parton model, which we use to demonstrate that many of the multiparticle correlations observed in light-heavy ion collisions, often ascribed to hydrodynamic collectivity, can be qualitatively reproduced in an initial state model. Then, we study the two-particle harmonics $v_2$ and $v_3$ for p/d/$^3$He+Au collisions at RHIC using the dilute-dense Color Glass Condensate Effective Field Theory framework. We show that this provides a viable alter…
Collectivity, as interpreted to mean flow of a dense medium in high-energy A-A collisions described by hydrodynamics, has been attributed to smaller collision systems -- p-A and even p-p collisions -- based on recent analysis of LHC data. However, alternative methods reveal that some data features attributed to flows are actually manifestations of minimum-bias (MB) jets. In this presentation I review the differential structure of single-particle $p_t$ spectra from SPS to LHC energies in the context of a two-component (soft + hard) model (TCM) of hadron production. I relate the spectrum hard co…
Recent observations of ridge-like structure in $p$-$p$ and $p$-$A$ angular correlations at the RHIC and LHC have been interpreted to imply collective motion in smaller collision systems. It is argued that if correlation structures accepted as manifestations of flow in $A$-$A$ collisions appear in smaller systems collectivity (flow) must extend to the smaller systems. But the argument could be reversed to conclude that such structures appearing in $A$-$A$ collisions may not imply hydrodynamic flow. I present spectrum, correlation and fluctuation data from RHIC $p$-$p$ and Au-Au collisions and $…
An extension of the rope hadronization model, which has previously provided good descriptions of hadrochemistry in high multiplicity pp collisions, is presented. The extension includes a dynamically generated transverse pressure, produced by the excess energy from overlapping strings. We find that this model can qualitatively reproduce soft features of Quark Gluon Plasma in small systems, such as higher $\langle p_\perp \rangle$ for heavier particles and long range azimuthal correlations forming a ridge. The effects are similar to those obtained from a hydrodynamic expansion, but without assum…
The interferometric radii in the system formed in ultra-relativistic proton-lead collisions are investigated in a framework based on event-by-event 3+1 dimensional viscous hydrodynamics. We argue that the most central p-Pb collisions undergoing collective expansion behave similarly to the peripheral nucleus-nucleus collisions. The interferometric observables can serve as signatures of the formation of an extended fireball.
Measurements of multi-particle correlations in the collisions of small systems such as $p+p$, $p/d/^3He+A$ show striking similarity to the observations in heavy ion collisions. A number of observables measured in the high multiplicity events of these systems resemble features that are attributed to collectivity driven by hydrodynamics. However alternative explanations based on initial state dynamics are able to describe many characteristic features of these measurements. In this brief review we highlight some of the recent developments and outstanding issues in this direction.
The bulk motion of nuclear matter at the ultra-high temperatures created in heavy-ion collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider is well described in terms of nearly inviscid hydrodynamics, thereby establishing this system of quarks and gluons as the most perfect fluid in nature. A revolution in the field is underway, spearheaded by the discovery of similar collective, fluid-like phenomena in much smaller systems including p+p, p+A, d+Au, and $^3$He$+$Au collisions. We review these exciting new observations and their implications.
We study the multiplicity and rapidity dependence of thermal and prompt photon production in p+Pb collisions at 5.02 TeV, using a (3+1)D viscous hydrodynamic framework. Direct photon anisotropic flow coefficients $v^γ_{2,3}$ and nuclear modification factor $R^γ_\mathrm{pPb}(p_T)$ are presented in both the p-going (backward) and the Pb-going (forward) directions. The interplay between initial state cold nuclear effect and final state thermal enhancement at different rapidity regions is discussed. The proposed rapidity dependent thermal photon enhancement and direct photon anisotropic flow obser…
Qualitative features of multiparticle correlations in light-heavy ion ($p+A$) collisions at RHIC and LHC are reproduced in a simple initial state model of partons in the projectile coherently scattering off localized domains of color charge in the heavy nuclear target. These include i) the ordering of the magnitudes of the azimuthal angle $n$th Fourier harmonics of two-particle correlations $v_n\{2\}$, ii) the energy and transverse momentum dependence of the four-particle Fourier harmonic $v_2\{4\}$, and iii) the energy dependence of four-particle symmetric cumulants measuring correlations bet…
The production of $J/ψ$ mesons in heavy-ion collisions at the Large Hadron Collider is believed to be dominated by the recombination of charm and anti-charm quarks in a hot QCD medium. However, measurements of the elliptic flow ($v_2$) of $J/ψ$ mesons in these reactions are not well described by existing calculations of $J/ψ$ recombination for transverse momenta $p_T\geq$4 GeV. Here, we revisit these calculations in two main aspects. By employing the resonance recombination model, we implement distribution functions of charm quarks transported through the quark-gluon plasma using state-of-the-…
Nonextensive statistics has attracted attention as a description of particle spectra in nuclear collisions at QCD energies. First, we construct the equation of state by incorporating Tsallis statistics based on the hadron resonance gas and parton gas models. Thermodynamic conditions are found to impose constraints on the $q$-parameter of Tsallis distribution. Next, we apply the equation of state to the relativistic hydrodynamic modeling of nuclear collisions. The Cooper-Frye prescription is consistently modified. Numerical demonstrations indicate that the model may describe charged particle sp…
Collective flow of the final-state hadrons observed in ultrarelativistic heavy-ion collisions or even in smaller systems formed in high-multiplicity pp and p/d/$^3$He-nucleus collisions is one of the most important diagnostic tools to probe the initial state of the system and to shed light on the properties of the short-lived, strongly-interacting many-body state formed in these collisions. Limited, in the initial years, to the study of mainly the directed and elliptic flows -- the first two Fourier harmonics of the single-particle azimuthal distribution -- this field has evolved in recent yea…
Identical-particle (pion and kaon) femtoscopy in Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV with Therminator2 modeled with (3+1)D viscous hydrodynamics
Indian Institute of Technology Bombay（印度理工学院孟买分校）；University of Tsukuba（筑波大学）
利用 (3+1)D 粘性流体动力学和 THERMINATOR 2 代码研究 Pb-Pb 碰撞中介子和 K 介子的费米简缩，发现半径随对偶动量增加而减小，表明强集体性。
We have implemented the Tsallis q-statistics in the Weibull model of particle production known as the q-Weibull distribution to describe the transverse-momentum (pT ) distribution of the charged hadrons at mid-rapidity measured at RHIC and LHC energies. The model describes the data remarkably well for the entire pT range measured in nucleus-nucleus and nucleon-nucleon collisions. The proposed distribution is based on the non-extensive Tsallis q-statistics which replaces the usual thermal equilibrium assumption of hydrodynamical models. The parameters of the distribution can be related to the v…
In a recent analysis of high-statistics $p_t$ spectra from 5 and 13 TeV $p$-$p$ collisions a two-component (soft+hard) model (TCM) of hadron production near midrapidity, based on fixed model functions independent of collision multiplicity $n_{ch}$ or event selection criteria, was employed as a reference to determine data biases induced by the selection criteria. As in previous studies the fixed TCM accurately isolated jet-related and nonjet contributions to spectra. It was observed that two selection criteria (V0M and SPD), based on different pseudorapidity $η$ acceptances, bias the spectrum h…
Relativistic p+A collisions may produce droplets of quark gluon plasma (QGP) that quickly develop a toroidal vortex structure similar to that of an expanding smoke ring. We present viscous relativistic hydrodynamic calculations of ultra-central p+A collisions and develop an experimental observable to probe the structure, correlating the polarization and momentum of hyperons emitted from the collision. The effect is robust against changes in the definition of vorticity used to calculate the polarization. Experiments at RHIC and LHC may test the existence and strength of the vortex toroids, brin…
Purported signatures of collective dynamics in small systems like proton-proton (pp) or proton-nucleus (p-A) collisions still lack unambiguous understanding. Despite the qualitative and/or quantitative agreement of the data to hydrodynamic models, it has remained unclear whether the harmonic flows in small systems relate to the common physical picture of hydrodynamic collectivity driven by the initial geometry. In the present work, we aim to address this issue by invoking a novel concept of Event Shape Engineering (ESE), which has been leveraged to get some control of the initial geometry in h…
The scenario of a collective expansion of matter created in proton-proton (p-p) collisions at the CERN Large Hadron Collider (LHC) is discussed. Assuming a small transverse size and a formation time of 0.1fm/c of the source we observe the build up of a substantial transverse flow in relativistic hydrodynamic simulations. In order to demonstrate the collectivity in p-p collisions we propose to look at the multiplicity dependence of the elliptic flow coefficient. If high multiplicity events originate from azimuthally asymmetric events containing two flux tubes, an observable signal above the sta…
Nuclear Modification Factor in Pb-Pb and p-Pb collisions at $\sqrt{s_{NN}}$=5.02 TeV at LHC energies using Boltzmann Transport Equation with Tsallis Blast Wave Description
The high-multiplicity events of pPb collisions at $\sqrt s_{NN}$ = 5.02 TeV at the LHC exhibit unforeseen collective behaviour. One of the possible explanations to the collectivity could be the formation of thermalized partonic matter, like the one formed in relativistic nucleus-nucleus collisions and is described by the hydrodynamic models. This article presents a study on the centrality dependent long-range 2 < $|Δη|$ < 4 two-particle azimuthal correlations of D-mesons and charged particles in pPb collisions at $\sqrt s_{NN}$ = 5.02 TeV. The study has been conducted on the events, generated …
The study of multiparticle correlations and collectivity in the hot and dense matter created in collisions of heavy-ions as well as those of smaller systems such as proton--heavy-ion collisions has progressed to the point where detailed knowledge of the three-dimensional structure of the proton is needed to confront experimental data. We discuss results from a simple proof-of-principle initial state parton model which reproduces many features of the data on proton--heavy-ion collisions that are often ascribed to hydrodynamic flow. We outline how this model can be further improved with particul…
Recently the inclusive transverse momentum distributions of primary charged particles were measured for different centralities in $Pb+Pb$ collisions. A strong suppression of the nuclear modification factor in central collisions around $p_T \sim 6-7$ GeV/c was seen. As a possible explanation, the hydrodynamic description of the collision process was tentatively proposed. However, such effect, (albeit much weaker) also exists in the ratio of data/fits, both in nuclear $Pb+Pb$ collisions, and in the elementary $p+p$ data in the same range of transverse momenta for which such an explanation is dou…
System size and event shape dependence of particle-identified balance functions in proton-proton collisions at $\sqrt{s} = 13$ TeV using PYTHIA 8 and EPOS models
INFN–Sezione di Roma（意大利国家核物理研究所罗马分所）；INFN–Sezione di Bologna（意大利国家核物理研究所博洛尼亚分所）
