# Selected Experimental Results from Heavy-Ion Collisions at LHC

Authors: Ranbir Singh; Lokesh Kumar; Pawan Kumar Netrakanti; Bedangadas Mohanty
Journal: Advances in High Energy Physics
 (2013)

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## Abstract

We review a subset of experimental results from the heavy-ion collisions at the Large Hadron Collider (LHC) facility at CERN. Excellent consistency is observed across all the experiments at the LHC (at center of mass energysNN=2.76 TeV) for the measurements such as charged particle multiplicity density, azimuthal anisotropy coefficients, and nuclear modification factor of charged hadrons. Comparison to similar measurements from the Relativistic Heavy Ion Collider (RHIC) at lower energy (sNN=200 GeV) suggests that the system formed at LHC has a higher energy density and larger system size and lives for a longer time. These measurements are compared to model calculations to obtain physical insights on the properties of matter created at the RHIC and LHC.


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## Body

## 1. Introduction

The main goal of the high energy heavy-ion collisions is to study the phase structure of the quantum chromodynamic (QCD) phase diagram [1–3]. One of the most interesting aspects of these collisions is the possibility of forming a phase of deconfined quarks and gluons, a system that is believed to have existed in a few microseconds-old universe. First principle QCD calculations suggest that it is possible to have such a state of matter if the temperatures attained can be of the order of the QCD scale (~200 MeV) [4–6]. In laboratory, such temperatures could be attained by colliding heavy ions at relativistic energies. Furthermore, in very high energy collisions of heavy ions at the LHC and RHIC, the lifetime of the deconfined phase may be long enough to allow for the detailed study of the fundamental constituents (quarks and gluons) of the visible matter.The results from heavy-ion collisions at RHIC have clearly demonstrated the formation of a deconfined system of quarks and gluons inAu+Au collisions at sNN=200 GeV [7–11]. The produced system exhibits copious production of strange hadrons, shows substantial collectivity developed in the partonic phase, and exhibits suppression in high transverse momentum (pT) hadron production relative to p+p collisions and small fluidity as reflected by a small value of viscosity to entropy density ratio (η/s). A factor of 14 increase in sNN for Pb+Pb collisions at LHC is expected to unravel the temperature dependence of various observables and to extend the kinematic reach in rapidity and pT of previous measurements at RHIC. On the other hand, the beam energy scan program at RHIC is expected to provide additional details of the QCD phase diagram not accessible at the LHC [12].In this review paper, we discuss a subset of results that have come out from LHCPb+Pb collisions at sNN=2.76 TeV. We have divided the discussion into three sections. In the second section, we discuss the consistency of various measurements among the three LHC experiments that have heavy-ion programs: ALICE, ATLAS, and CMS. Section 2.1 discusses the results on the charged particle multiplicity. Section 2.2 discusses the results on azimuthal anisotropy, and Section 2.3 discusses the results on the nuclear modification factor.In the third section, we make a comparative study between similar observables measured at lower energy collisions at RHIC and those from LHC. In doing this, we highlight the additional information that heavy-ion collisions at LHC bring compared to RHIC. In Section3.1, we discuss the bulk properties at freeze-out that include results on multiplicity, average transverse mass and Bjorken energy density, volume and decoupling time, kinetic freeze-out temperature and average flow velocity, and fluctuations. Section 3.2 is devoted on the results to azimuthal anisotropy, where we discuss the energy dependence of pT integrated v2, dependence of various azimuthal anisotropy coefficients on pT, and flow fluctuations. In Section 3.3, we discuss results for nuclear modification factor.In the fourth section, we present a comparison of various model calculations to the corresponding measurements at LHC. We concentrate mainly on the results for charged particle multiplicity density andK/π ratio in Section 4.1, azimuthal anisotropy in Section 4.2, and nuclear modification factor in Section 4.3.Finally, we summarize our observations in the last section of the paper.


## 2. Consistency of Results among LHC Experiments

### 2.1. Charged Particle Multiplicity

One of the first measurements to come out of the heavy-ion collision program at LHC is the charged particle multiplicity per unit pseudorapidity inPb+Pb collisions at sNN=2.76 TeV. Figure 1 shows the centrality (reflected by the number of participating nucleons, Npart, obtained from a Glauber model calculation [13]) dependence of dNch/dη at midrapidity for Pb+Pb collisions at sNN=2.76 TeV from ALICE [14], CMS [15], and ATLAS [16] experiments. The error bars reflect statistical uncertainties. The ATLAS measurements of dNch/dη|η=0 are obtained over |η|<0.5 using a minimum bias trigger with a central solenoid magnet off data set. The charged particles are reconstructed using two different algorithms using the information from pixel detectors covering |η|< 2.0. The Npart values are obtained by comparing the summed transverse energy in the forward calorimeter over a pseudorapidity range 3.2<|η|<4.9 to a Glauber model simulation. The CMS results for dNch/dη|η=0 are from the barrel section of the pixel tracker covering |η|< 2.5. The minimum bias trigger data set was in the magnetic field off configuration so as to improve the acceptance of low pT particles. The centrality determinations as in the case of ATLAS experiment are done using information from hadron forward calorimeter (2.9<|η|<5.2) and Glauber model simulations. The ALICE measurement uses a minimum bias data set from the silicon pixel detector (|η|<2.0). The centrality selection is carried out using signals from VZERO detectors (2 arrays of 32 scintillator tiles) covering the regions 2.8<η<5.1 and -3.7<η<-1.7, along with the corresponding Glauber modeling of the data.Figure 1
(Color online) Average charged particle multiplicity per unit pseudorapidity (dNch/dη) at midrapidity per participating nucleon (〈Npart〉) pair plotted as a function of 〈Npart〉 for Pb+Pb collisions at sNN = 2.76 TeV. The measurements are shown from ALICE [14], CMS [15], and ATLAS [16] experiments.In spite of the difference in operating conditions and measurement techniques, thedNch/dη versus Npart results for Pb+Pb collisions at sNN = 2.76 TeV show a remarkable consistency across the three experiments. The results show that the charged particle multiplicity per unit pseudorapidity per nucleon pair increases from peripheral to central collisions. This gradual increase in dNch/dη per participating nucleon pair indicates that in central head-on collisions, where the number of participating nucleons is more, the charged particle production is different compared to that in peripheral collisions.


### 2.2. Azimuthal Anisotropy

Azimuthal anisotropy has been studied in great detail in heavy-ion collision experiments. It can provide information about initial stages of heavy-ion collisions. Figure2 (top panels) shows the azimuthal anisotropy of produced charged particles (vn=〈cos(n(ϕ-Ψn))〉) as a function of pT for 30–40% Pb+Pb collisions at sNN=2.76 TeV from the three different experiments: ATLAS, ALICE, and CMS. Here, ϕ is the azimuthal angle of the produced particles, and Ψn is the nth order reaction plane angle measured in the experiments. The left panel in the figure corresponds to v2, the middle panel corresponds to v3, and the right panel corresponds to v4, respectively. Bottom panels show the ratio of the experimental data to a polynomial fit to the ALICE data.Figure 2
(Color online)vn versus pT at midrapidity for 30–40% Pb+Pb collisions at sNN=2.76 TeV. The results are shown from different LHC experiments: CMS [17–20], ATLAS [21–24], and ALICE [25]. The bottom panels show the ratio of the experimental data to a polynomial fit to the ALICE data.In the CMS experiment [17–20], the v2 measurements use the information from the silicon tracker in the region |η|<2.5 with a track momentum resolution of 1% at pT = 100 GeV/c kept within a magnetic field of 3.8 Tesla. The event plane angle (Ψ2) is obtained using the information on the energy deposited in the hadron forward calorimeter. A minimum η gap of 3 units is kept between the particles used for obtaining Ψ2 and v2. This ensures suppression of nonflow correlations which could arise, for example, from dijets. The event plane resolution obtained using three subevents technique varies from 0.55 to 0.84, depending on the collision centrality. The ATLAS experiment [21–24] measured vn using the inner detectors in the |η|<2.5, kept inside a 2 Tesla field of superconducting solenoid magnet. The event planes are obtained using forward calorimeter information, with a resolution varying from 0.2 to 0.85, depending on collision centrality. The ALICE experiment [25] measured vn using charged tracks reconstructed from the Time Projection Chamber (|η|<0.8); the event plane was obtained using information from VZERO detectors kept at a large rapidity gap from the TPC. The momentum resolution of the tracks is better than 5%.A very nice agreement forv2, v3, and v4 versus pT is found between all the experiments to a level of within 10% for most of the pT ranges presented. The results show an increase of v2, v3, and v4 values with pT for the low pT and a decrease  for pT above ~3 GeV/c. The hydrodynamical evolution of the system affects most of the low pT particles and hence the increasing vn at low pT.


### 2.3. Nuclear Modification Factor

One of the established signatures of the QGP at top RHIC energy is the suppression of high transverse momentum (pT) particles in heavy-ion collisions compared to corresponding data from the binary collisions scaled p+p collisions. It has been interpreted in terms of energy loss of partons in QGP. This phenomenon is referred to as the jet quenching in a dense partonic matter. The corresponding measurement is called the nuclear modification factor (RAA).Figure3 shows the nuclear modification factor for inclusive charged hadrons measured at midrapidity in LHC experiments for Pb+Pb collisions at sNN = 2.76 TeV. The nuclear modification factor is defined as RAA=(dNAA/dηd2pT)/(TABdσNN/dηd2pT). Here, the overlap integral TAB=Nbinary/σinelasticpp with Nbinary being the number of binary collisions commonly estimated from Glauber model calculation and dσNN/dηd2pT is the cross section of charged hadron production in p+p collisions at s = 2.76 TeV.Figure 3
(Color online) Nuclear modification factorRAA of charged hadrons measured by ALICE [26] and CMS [27] experiments at midrapidity for 0–5% most central Pb-Pb collisions at sNN = 2.76 TeV. The boxes around the data denote pT-dependent systematic uncertainties. The systematic uncertainties on the normalization are shown as boxes at RAA = 1.The ALICE experiment [26] uses the inner tracking system (ITS) and the time projection chamber (TPC) for vertex finding and tracking in a minimum bias data set. The CMS experiment [27] reconstructs charged particles based on hits in the silicon pixel and strip detectors. In order to extend the statistical reach of the pT spectra in the highly prescaled minimum bias data recorded in 2011, it uses unprescaled single-jet triggers. Both experiments take the value of σinelasticpp=64±5 mb. The result shows that the charged particle production at high pT in LHC is suppressed in heavy-ion collisions relative to nucleon-nucleon collisions. The suppression value reaches to a minimum at pT 6-7 GeV/c and then gradually increases to attain an almost constant value at ~40 GeV/c. This can be understood in terms of energy loss mechanism differences in intermediate and higher pT regions. The rise in the RAA above pT 6-7 GeV/c may imply the dominance of the constant fractional energy loss which is the consequence of flattening of the unquenched nucleon-nucleon spectrum. An excellent agreement for RAA versus pT for charged hadrons in 0–5% central Pb+Pb collisions at sNN=2.76 TeV is observed between the two experiments.Having discussed the consistency of these first measurements inPb+Pb collisions among different experiments, the major detectors used, acceptances, and ways to determine centrality and event plane, we now discuss the comparison between measurements at RHIC and LHC heavy-ion collisions.


## 2.1. Charged Particle Multiplicity

One of the first measurements to come out of the heavy-ion collision program at LHC is the charged particle multiplicity per unit pseudorapidity inPb+Pb collisions at sNN=2.76 TeV. Figure 1 shows the centrality (reflected by the number of participating nucleons, Npart, obtained from a Glauber model calculation [13]) dependence of dNch/dη at midrapidity for Pb+Pb collisions at sNN=2.76 TeV from ALICE [14], CMS [15], and ATLAS [16] experiments. The error bars reflect statistical uncertainties. The ATLAS measurements of dNch/dη|η=0 are obtained over |η|<0.5 using a minimum bias trigger with a central solenoid magnet off data set. The charged particles are reconstructed using two different algorithms using the information from pixel detectors covering |η|< 2.0. The Npart values are obtained by comparing the summed transverse energy in the forward calorimeter over a pseudorapidity range 3.2<|η|<4.9 to a Glauber model simulation. The CMS results for dNch/dη|η=0 are from the barrel section of the pixel tracker covering |η|< 2.5. The minimum bias trigger data set was in the magnetic field off configuration so as to improve the acceptance of low pT particles. The centrality determinations as in the case of ATLAS experiment are done using information from hadron forward calorimeter (2.9<|η|<5.2) and Glauber model simulations. The ALICE measurement uses a minimum bias data set from the silicon pixel detector (|η|<2.0). The centrality selection is carried out using signals from VZERO detectors (2 arrays of 32 scintillator tiles) covering the regions 2.8<η<5.1 and -3.7<η<-1.7, along with the corresponding Glauber modeling of the data.Figure 1
(Color online) Average charged particle multiplicity per unit pseudorapidity (dNch/dη) at midrapidity per participating nucleon (〈Npart〉) pair plotted as a function of 〈Npart〉 for Pb+Pb collisions at sNN = 2.76 TeV. The measurements are shown from ALICE [14], CMS [15], and ATLAS [16] experiments.In spite of the difference in operating conditions and measurement techniques, thedNch/dη versus Npart results for Pb+Pb collisions at sNN = 2.76 TeV show a remarkable consistency across the three experiments. The results show that the charged particle multiplicity per unit pseudorapidity per nucleon pair increases from peripheral to central collisions. This gradual increase in dNch/dη per participating nucleon pair indicates that in central head-on collisions, where the number of participating nucleons is more, the charged particle production is different compared to that in peripheral collisions.


## 2.2. Azimuthal Anisotropy

Azimuthal anisotropy has been studied in great detail in heavy-ion collision experiments. It can provide information about initial stages of heavy-ion collisions. Figure2 (top panels) shows the azimuthal anisotropy of produced charged particles (vn=〈cos(n(ϕ-Ψn))〉) as a function of pT for 30–40% Pb+Pb collisions at sNN=2.76 TeV from the three different experiments: ATLAS, ALICE, and CMS. Here, ϕ is the azimuthal angle of the produced particles, and Ψn is the nth order reaction plane angle measured in the experiments. The left panel in the figure corresponds to v2, the middle panel corresponds to v3, and the right panel corresponds to v4, respectively. Bottom panels show the ratio of the experimental data to a polynomial fit to the ALICE data.Figure 2
(Color online)vn versus pT at midrapidity for 30–40% Pb+Pb collisions at sNN=2.76 TeV. The results are shown from different LHC experiments: CMS [17–20], ATLAS [21–24], and ALICE [25]. The bottom panels show the ratio of the experimental data to a polynomial fit to the ALICE data.In the CMS experiment [17–20], the v2 measurements use the information from the silicon tracker in the region |η|<2.5 with a track momentum resolution of 1% at pT = 100 GeV/c kept within a magnetic field of 3.8 Tesla. The event plane angle (Ψ2) is obtained using the information on the energy deposited in the hadron forward calorimeter. A minimum η gap of 3 units is kept between the particles used for obtaining Ψ2 and v2. This ensures suppression of nonflow correlations which could arise, for example, from dijets. The event plane resolution obtained using three subevents technique varies from 0.55 to 0.84, depending on the collision centrality. The ATLAS experiment [21–24] measured vn using the inner detectors in the |η|<2.5, kept inside a 2 Tesla field of superconducting solenoid magnet. The event planes are obtained using forward calorimeter information, with a resolution varying from 0.2 to 0.85, depending on collision centrality. The ALICE experiment [25] measured vn using charged tracks reconstructed from the Time Projection Chamber (|η|<0.8); the event plane was obtained using information from VZERO detectors kept at a large rapidity gap from the TPC. The momentum resolution of the tracks is better than 5%.A very nice agreement forv2, v3, and v4 versus pT is found between all the experiments to a level of within 10% for most of the pT ranges presented. The results show an increase of v2, v3, and v4 values with pT for the low pT and a decrease  for pT above ~3 GeV/c. The hydrodynamical evolution of the system affects most of the low pT particles and hence the increasing vn at low pT.


## 2.3. Nuclear Modification Factor

One of the established signatures of the QGP at top RHIC energy is the suppression of high transverse momentum (pT) particles in heavy-ion collisions compared to corresponding data from the binary collisions scaled p+p collisions. It has been interpreted in terms of energy loss of partons in QGP. This phenomenon is referred to as the jet quenching in a dense partonic matter. The corresponding measurement is called the nuclear modification factor (RAA).Figure3 shows the nuclear modification factor for inclusive charged hadrons measured at midrapidity in LHC experiments for Pb+Pb collisions at sNN = 2.76 TeV. The nuclear modification factor is defined as RAA=(dNAA/dηd2pT)/(TABdσNN/dηd2pT). Here, the overlap integral TAB=Nbinary/σinelasticpp with Nbinary being the number of binary collisions commonly estimated from Glauber model calculation and dσNN/dηd2pT is the cross section of charged hadron production in p+p collisions at s = 2.76 TeV.Figure 3
(Color online) Nuclear modification factorRAA of charged hadrons measured by ALICE [26] and CMS [27] experiments at midrapidity for 0–5% most central Pb-Pb collisions at sNN = 2.76 TeV. The boxes around the data denote pT-dependent systematic uncertainties. The systematic uncertainties on the normalization are shown as boxes at RAA = 1.The ALICE experiment [26] uses the inner tracking system (ITS) and the time projection chamber (TPC) for vertex finding and tracking in a minimum bias data set. The CMS experiment [27] reconstructs charged particles based on hits in the silicon pixel and strip detectors. In order to extend the statistical reach of the pT spectra in the highly prescaled minimum bias data recorded in 2011, it uses unprescaled single-jet triggers. Both experiments take the value of σinelasticpp=64±5 mb. The result shows that the charged particle production at high pT in LHC is suppressed in heavy-ion collisions relative to nucleon-nucleon collisions. The suppression value reaches to a minimum at pT 6-7 GeV/c and then gradually increases to attain an almost constant value at ~40 GeV/c. This can be understood in terms of energy loss mechanism differences in intermediate and higher pT regions. The rise in the RAA above pT 6-7 GeV/c may imply the dominance of the constant fractional energy loss which is the consequence of flattening of the unquenched nucleon-nucleon spectrum. An excellent agreement for RAA versus pT for charged hadrons in 0–5% central Pb+Pb collisions at sNN=2.76 TeV is observed between the two experiments.Having discussed the consistency of these first measurements inPb+Pb collisions among different experiments, the major detectors used, acceptances, and ways to determine centrality and event plane, we now discuss the comparison between measurements at RHIC and LHC heavy-ion collisions.


## 3. Comparison of LHC and RHIC Results

In the first subsection, we discuss the energy dependence of basic measurements made in heavy-ion collisions. These includedNch/dη, 〈mT〉 (mT=pT2+m2; here, m represents mass of hadron), Bjorken energy density (ϵBj), life time of the hadronic phase (τf), system volume at the freeze-out, kinetic and chemical freeze-out conditions, and finally, the fluctuations in net-charge distributions. In the next subsection, we discuss the energy dependence of pT integrated v2, vn versus pT, and flow fluctuations at RHIC and LHC. In the final subsection, we compare the nuclear modification factor for hadrons produced in heavy-ion collisions at RHIC and LHC.


### 3.1. Bulk Properties at Freeze-Out

#### 3.1.1. Multiplicity

Figure4(a) shows the charged particle multiplicity density at midrapidity (dNch/dη) per participating nucleon pair produced in central heavy-ion collisions versus sNN. We observe that the charged particle production increases by a factor 2 as the energy increases from RHIC to LHC. The energy dependence seems to rule out a logarithmic dependence of particle production with sNN and supports a power law type of dependence on sNN. The red solid curve seems to describe the full energy range. More detailed discussions on the energy dependence of these measurements can be found in [28].(Color online) (a)dNch/dη per participating nucleon pair at midrapidity in central heavy-ion collisions as a function of sNN. (b) Comparison of dNch/dη per participating nucleon at midrapidity in central heavy-ion collisions [15, 16, 29–37] to corresponding results from p+p(p-) [38–47] and p(d) + A collisions [29, 48, 49].
(a)
(b)Figure4(b) shows the excess of dNch/dη/〈Npart〉 in A+A collisions [15, 16, 29–37] over corresponding yields in p+p(p-) [38–47] and p(d)+A collisions [29, 48, 49]. This observation also seen at RHIC persists at LHC but is proportionately larger at the higher energy collisions at the LHC. A power law fit to the p+p collision charged particle multiplicity density leads to a dependence ~s0.11, while those for A+A collisions go as ~s0.15. There is no scaling observed in the charged particle multiplicity density per participating nucleon, when compared between elementary collisions like p+p and heavy-ion collisions. This is a clear indication that A+A collisions at RHIC and LHC are not a simple superposition of several p+p collisions, whereas the p+A collisions scale with the p+p collisions.


#### 3.1.2. Average Transverse Mass and Bjorken Energy Density

Figure5(a) shows the 〈mT〉 values for pions in central heavy-ion collisions as a function of sNN. The 〈mT〉 value increases with sNN at lower AGS energies [50, 51], stays independent of sNN for the SPS energies [52, 53], and then tends to rise further with increasing sNN at the higher beam energies of LHC. About 25% increase in 〈mT〉 is observed from RHIC [41, 54] to LHC [55]. For a thermodynamic system, 〈mT〉 can be an approximate representation of the temperature of the system, and dN/dy∝ln(sNN) may represent its entropy [56]. In such a scenario, the observations could reflect the characteristic signature of a phase transition, as proposed by Van Hove [57]. Then, the constant value of 〈mT〉 versus sNN has one possible interpretation in terms of formation of a mixed phase of a QGP and hadrons during the evolution of the heavy-ion system. The energy domains accessed at RHIC and LHC will then correspond to partonic phase, while those at AGS would reflect hadronic phase. However, there could be several other effects to which 〈mT〉 is sensitive, which also need to be understood for proper interpretation of the data [56].(a)〈mT〉 for charged pions in central heavy-ion collisions at midrapidity for AGS [50, 51], SPS [52, 53], RHIC [41, 54], and LHC [55] energies. The errors shown are the quadrature sum of statistical and systematic uncertainties. (b) The product of Bjorken energy density, ϵBj [58], and the formation time (τ) in central heavy-ion collisions at midrapidity as a function of sNN [59–64].
(a)
(b)Figure5(b) shows the product of the estimated Bjorken energy density (ϵBj=(1/(A⊥τ))dET/dy; A⊥ [58] is the transverse overlap area of the nuclei, and ET is the transverse energy) and formation time (τ) as a function of sNN [59–64]. The product of energy density and the formation time at LHC seem to be a factor of 3 larger compared to those attained at RHIC. If we assume the same value of τ0  (=1 fm/c) for LHC and RHIC, the Bjorken energy density is about a factor of 3 larger at the LHC compared to that at RHIC in central collisions.


#### 3.1.3. Volume and Decoupling Time

The top panel of Figure6 shows the energy dependence of the product of the three radii (Rout, Rside, and Rlong) obtained from pion HBT or Bose-Einstein correlation analysis. Here, the “out” corresponds to the axis pointing along the pair transverse momentum, the  “side” to the axis perpendicular to it in the transverse plane, and the “long” corresponds to the axis along the beam (Bertsch-Pratt convention [65, 66]). The product of the radii is connected to the volume of the homogeneity region at the last interaction. The product of the three radii shows a linear dependence on the charged-particle pseudorapidity density. The data indicates that the volume of homogeneity region is two times larger at the LHC than at RHIC.(a) Product of the three pion HBT radii atkT (average transverse momenta of two pions) =0.3 GeV/c for central heavy-ion collisions at AGS [68], SPS [69, 70], RHIC [71, 72], and LHC [73] energies. (b) The decoupling time extracted from Rlong(kT) for central heavy-ion collisions at midrapidity at AGS, SPS, RHIC, and LHC energies as a function of (dNch/dη)1/3.
(a)
(b)Furthermore, within a hydrodynamic picture, the decoupling time for hadrons (τf) at midrapidity can be estimated from the magnitude of radii Rlong as follows: Rlong2 = τf2TK2(mT/T)/mTK1(mT/T), with mT=mπ2+kT2, where mπ is the mass of the pion, T is the kinetic freeze-out temperature, and K1 and K2 are the integer-order modified Bessel functions [67]. For the estimation of τf, the average value of the kinetic freeze-out temperature T is taken to be 120 MeV from AGS to LHC energies. However, the energy dependence of kinetic freeze-out temperature, as discussed in the next subsection, would provide a more accurate description of the τf values. The extracted τf values for central heavy-ion collisions at midrapidity at AGS [68], SPS [69, 70], RHIC [71, 72], and LHC [73] energies are shown as a function of cube root of dNch/dη in the bottom panel of Figure 6. We observe that τf scales linearly with (dNch/dη)1/3 and is about 10 fm/c at LHC energies. This value is about 40% larger than at RHIC. It may be noted that the above expression ignores transverse expansion of the system and finite chemical potential for pions. Also there are uncertainties associated with freeze-out temperature that could lead to variations in the extracted τf values.


#### 3.1.4. Freeze-Out Temperature and Radial Flow Velocity

The hadron yields and spectra reflect the properties of the bulk matter at chemical and kinetic freeze-out, respectively. Generally, the point at which the inelastic collisions cease is called the chemical freeze-out, and the point where even the elastic collisions stop is called the kinetic freeze-out.The transverse momentum distribution of different particles contains two components: one random and the other collective. The random component can be identified with the temperature of the system at kinetic freeze-out (Tkin). The collective component, which could arise from the matter density gradient from the center to the boundary of the fireball created in high energy nuclear collisions, is called collective flow in transverse direction (〈β〉). Using the assumption that the system attains thermal equilibrium, the blast wave formulation can be used to extract Tkin and 〈β〉. These two quantities are shown in Figure 7 versus sNN [41, 55, 74–77]. For beam energies at AGS and above, one observes a decrease in Tkin with sNN. This indicates that the higher the beam energy is, the longer interactions are among the constituents of the expanding system and the lower the temperature. From RHIC top energy to LHC, there seems to be, however, a saturation in the value of Tkin. In contrast to the temperature, the collective flow increases with the increase in beam energy, rapidly, reaching a value close to 0.6 times the speed of light at the LHC energy.Kinetic freeze-out temperature (a) and radial flow velocity (b) in central heavy-ion collisions as a function of collision energy [41, 55, 74–77].
(a)
(b)Figure8 shows the chemical freeze-out temperature (Tch) versus the baryon chemical potential (μB) in central heavy-ion collisions [41, 55, 78–85]. These quantities are obtained by fitting the particle yields to a statistical model assuming thermal equilibrium within the framework of a Grand Canonical ensemble. There are two values of temperature quoted for LHC energies. A Tch value of about 164 MeV and fixed μB value of 1 MeV seem to reproduce the multistrange ratios (involving Ξ and Ω) quite well but were observed to miss the data for p/π and Λ/π. On the other hand, the statistical thermal model prediction with Tch=152 MeV and fixed μB=1MeV fits the measured p/π and Λ/π ratios better but misses the ratios involving multistrange hadrons [86]. This issue is not yet resolved, being possibly related to hadronic final state interactions [87]. The curve corresponds to generalization of the energy dependence of Tch-μB using statistical thermal model calculations [78, 79]. The model works within the framework of a Grand Canonical ensemble and takes as input the produced particle yields from experiments to extract the freeze-out parameters such as Tch and μB.Figure 8
(Color online) Chemical freeze-out temperature versus baryon chemical potential in central heavy-ion collisions [41, 55, 78–85]. The curve corresponds to model calculations from [78, 79].


#### 3.1.5. Fluctuations

One of the proposed signatures to search for the phase transition from hadronic to partonic medium is to study the net-charge fluctuations in heavy-ion collisions. The partonic phase has constituents with fractional charges, while the hadronic phase has constituents with integral units of charge; hence, the measure of the fluctuations in the net-charge particle production is expected to be different in these two cases. Specifically, net-charge fluctuations are expected to be smaller if the system underwent a phase transition. However, it is important to address how these fluctuations may or may not survive the evolution of the system in the heavy-ion collisions. An experimental measure of net-charge fluctuations is defined asν(+-,dyn)=(〈N+(N+-1)〉/〈N+2〉)+(〈N-(N--1)〉/〈N-2〉)-2(〈N-N+〉/〈N-〉〈N+〉), where 〈N-〉 and 〈N+〉 are average negative and positive charged particle multiplicity, respectively [88].Figure9 shows the product of ν(+-,dyn) and 〈Nch〉 (average number of charged particles) as a function of sNN [89–91]. We find that this observable fluctuation rapidly decreases with sNN and approaches expectation for a simple QGP-like scenario [92] as we move from RHIC to LHC energies. Given that several other observables already indicate that a hot and dense medium of color charges has been formed at RHIC and LHC, the net-charge fluctuation result may indicate that the observable ν(+-,dyn) is not sensitive enough to QGP physics or the process of hadronization washes out the QGP signal for this observable. It may be also noted that the model’s results do not incorporate the acceptance effects and do not consider any dynamic evolution of the system like, for example, the dilution of the signals in the hadronization process.Figure 9
(Color online) Energy dependence of net-charge fluctuations about midrapidity in central heavy-ion collisions at SPS [89], RHIC [90], and LHC [91] energies. Also shown are the expectations from a hadron resonance gas model and for a simple QGP picture [92].


### 3.2. Azimuthal Anisotropy

#### 3.2.1. Energy Dependence ofpT Integrated v2

Figure10 shows the pT integrated v2 close to midrapidity of charged particles for collision centralities around 20–30% as a function of center of mass energy. We observe that there is an increase in magnitude of v2 by about 30% from top RHIC energy (sNN = 200 GeV) to LHC energy (sNN=2.76 TeV). This needs to be viewed within the context of a similar magnitude of increase in 〈pT〉 of pions from RHIC to LHC energies. The increase of v2 beyond beam energy of 10 GeV is logarithmic in sNN. This is expected to be determined by the pressure gradient-driven expansion of the almond-shape fireball produced in the initial stages of a noncentral heavy-ion collision [93] while for v2 measured at lower beam energies, the dependences observed are due to interplay of passing time of spectators and time scale of expansion of the system. A preference for an inplane emission versus out-of-plane (“squeeze-out”) pattern of particles as a function of beam energy is observed. The experimental data used are from FOPI [94, 95], EOS, E895 [96], E877 [97], CERES [98], NA49 [99], STAR [100], PHOBOS [101], PHENIX [102], ALICE [25], ATLAS [103], and CMS [17–20] experiments. Charged particles are used for LHC, RHIC, CERES, and E877 experiments, pion data is used from NA49 experiment, protons’ results are from EOS and E895 experiments, and FOPI results are for all particles with Z=1.Figure 10
(Color online) Transverse momentum integratedv2 close to midrapidity for charged (Z=1) particles for collision centralities around 20–30% as a function of center of mass energy.


#### 3.2.2. Azimuthal Anisotropy Coefficients versus Transverse Momentum

Figure11(a) shows the comparison of v2(pT), v3(pT), and v4(pT) for 30–40% collision centrality at RHIC (PHENIX experiment [104]) and LHC (ALICE [105]) at midrapidity in Au+Au and Pb+Pb collisions, respectively. The bottom panel of this figure shows the ratio of LHC and RHIC results to a polynomial fit to the LHC data. The vn(pT) measurement techniques are similar at RHIC and LHC energies. One observes that at lower pT (<2 GeV/c), the v2(pT) and v3(pT) are about 10–20% smaller at RHIC compared to the corresponding LHC results. However, at higher pT, the results are quite similar. The v4(pT) seems higher at RHIC compared to that at LHC.(Color online) (a) Comparison ofvn(pT) at midrapidity for 30–40% collision centrality at RHIC (Au+Au collisions at sNN=200 GeV from PHENIX experiment [104]) and at LHC (Pb+Pb collisions at sNN = 2.76 TeV from ALICE experiment [105]). (b) show the ratio of vn at LHC and RHIC. (b) v2 versus pT and v2/nq versus pT/nq for pions and protons at midrapidity for 10–20% collision centrality from Au+Au collisions at sNN=200 GeV (PHENIX experiment [106]) and Pb+Pb collisions at sNN=2.76 TeV (ALICE experiment [107]).
(a)
(b)One of the most striking observations to come out from RHIC is the number of constituent quark (nq) scaling of v2(pT) for identified hadrons. The basis of such a scaling is the splitting of v2(pT) between baryons and mesons at intermediate pT (2–6 GeV/c). This is shown in the bottom panels of Figure 11(b). Such a splitting between baryon and meson v2(pT) is also observed at intermediate pT at LHC energies (seen in the top panels of Figure 11(b)). However, the degree to which nq scaling holds could be different at RHIC [106] and LHC [107] energies. The nq scaling is much more closely followed at RHIC compared to LHC. It may be noted that there are several factors which could dilute such scaling, which include energy dependence of radial flow, an admixture of higher Fock states, and consideration of a realistic momentum distribution of quarks inside a hadron [108, 109]. The observation of the baryon-meson splitting is commonly interpreted as due to substantial amount of collectivity being generated in the deconfined phase. Another important feature is that at both RHIC and LHC energies, a clear hydrodynamic feature of mass dependence of v2(pT) is observed at low pT (<2 GeV/c).Figure12 shows the charged hadron v2(pT) for 30–40% collision centrality in Au+Au collisions at sNN = 200 GeV and Pb+Pb collisions at sNN=2.76 TeV for |η|<1 [17–20]. This figure demonstrates the kinematic reach for higher energy collisions at LHC relative to RHIC. LHC data allows us to study the v2(pT) in the pT range never measured before in heavy-ion collisions. The v2(pT)~0 for pT>40 GeV/c might suggest that those particles must have been emitted very early in the interactions when the collective effects had not set in. These high transverse momentum data are useful to understand the effects of the initial geometry or path-length dependence of various properties associated with parton modification inside the hot QCD medium. In addition, it also provides significantly improved precision measurement of v2 for 12<pT<20 GeV/c.Figure 12
(Color online) Comparison ofv2(pT) at midrapidity for 30–40% collision centrality at RHIC (Au+Au collisions at sNN = 200 GeV from STAR experiment) and at LHC (Pb+Pb collisions at sNN=2.76 TeV from CMS experiment [17–20]). The shaded band about CMS data point are systematic errors and vertical lines represent statistical errors.


#### 3.2.3. Flow Fluctuations

Fluctuations in azimuthal anisotropy coefficientv2 have gained quite an attention in recent times. In particular, the measurement of event-by-event v2 fluctuations can pose new constraints on the models of the initial state of the collision and their subsequent hydrodynamic evolution. In extracting event-by-event v2 fluctuations, one needs to separate nonflow effects, and so far, there is no direct method to decouple v2 fluctuations and nonflow effects in a model independent from the experimental measurements. However, several techniques exist where the nonflow effects can be minimized; for example, flow and non-flow contributions can be possibly separated to a great extent with a detailed study of two particle correlation function in Δϕ and its dependence on η and Δη. Here, we discuss another technique to extract and compare the v2 fluctuations at RHIC and LHC. We assume that the difference between v2{2} (two-particle cumulant) and v2{4} (four-particle cumulant) is dominated by v2 fluctuations, and nonflow effect is negligible for v2{4}. Then, the ratio Rv(2-4)=(v2{2}2-v2{4}2)/(v2{2}2+v2{4}2) can be considered as an estimate for v2 fluctuations in the data. Figure 13 shows the Rv(2-4) as a function of collision centrality and 〈dNch/dη〉 for RHIC [110] and LHC [107] energies. The centrality dependence of Rv(2-4) at RHIC or LHC as seen in Figure 13 could be an interplay of residual nonflow effects which increases for central collisions and multiplicity fluctuations which dominate smaller systems. It is striking to see that Rv(2-4) when presented as a function of % cross section is similar at RHIC and LHC, suggesting it reflects features associated with initial state of the collisions, for example, the event-by-event fluctuations in the eccentricity of the system. But when presented as a function of dNch/dη, it tends to suggest a different behavior for most central collisions at RHIC.(Color online) The ratioRv(2-4)=(v2{2}2-v2{4}2)/(v2{2}2+v2{4}2), an estimate of v2 fluctuations plotted as a function of collision centrality (a) and 〈dNch/dη〉 (b) for RHIC (STAR experiment: Au+Au collisions at sNN=200 GeV [110]) and LHC (ALICE: Pb+Pb collisions at sNN=2.76 TeV [107]) at midrapidity. The bands reflect the systematic errors.
(a)
(b)Recently, a great interest has been generated on extracting initial condition and flow fluctuation information from the measurement of the probability distribution ofvn at LHC. The probability density of vn can be expressed as a Gaussian function in transverse plane [111] as p(vn)=(1/2πδvn2)e-(vn-vnRP)2/(2δvn2) or as one dimensional Bessel-Gaussian function [112, 113] as p(vn)=(vn/δvn2)e-(((vn)2+(vnRP)2)/2δvn2)I0(vnRPvn/δvn2), where I0 is the modified Bessel function of the first kind and δvn is the fluctuation in vn, with δvn≈σvn for δvn≪vnRP (vn measured with respect to reaction plane).Figure14 shows the v2RP and δv2 values extracted from the v2 distributions as a function of 〈Npart〉 by fitting to the above probability functions [114]. They are compared with values of 〈v2〉 and σv2 obtained directly from the v2 distributions. The v2RP value is always smaller than the value for 〈v2〉, and it decreases to zero in the 0–2% centrality interval. The value of δv2 is close to σv2, except in the most central collisions. This leads to a value of δv2/v2RP larger than σv2/〈v2〉 over the full centrality range as shown in Figure 14(c). The value of δv2/v2RP decreases with 〈Npart〉 and reaches a minimum at 〈Npart〉≈200 but then increases for more central collisions. Thus, the event-by-event v2 distribution brings additional insight for the understanding of v2 fluctuations.(Color online) The dependence ofv2RP and 〈v2〉 (a), δv2 and σv2 (b), and δv2/v2RP and σv2/〈v2〉 (c) on 〈Npart〉 [114]. The shaded boxes indicate the systematic uncertainties.
(a)
(b)
(c)


### 3.3. Nuclear Modification Factor

Figure15 shows the RAA of various particles produced in heavy-ion collisions at RHIC and LHC. In Figure 15(a), we observe that the shape of the RAA versus pT of charged hadrons at RHIC and LHC [26, 27] is very similar for the common pT range of measurements. The values RAA at RHIC are higher compared to those at LHC energies up to pT<8 GeV/c. The higher kinematic reach of LHC in pT allows us to see the full pT evolution of RAA in high energy heavy-ion collisions. All these measurements suggest that the energy loss of partons in the medium formed in heavy-ion collisions at LHC energies is perhaps larger compared to that at RHIC. In Figure 15(b), we observe that the nuclear modification factors for d+Au collisions at sNN=200 GeV [115] and p+Pb collisions at sNN=5.02 TeV [116] are greater than unity for the pT>2 GeV/c. The values for RHIC are slightly larger compared to those for LHC. A value greater than unity for the nuclear modification factor in p(d)+A collisions is generally interpreted as due to Cronin effect [117, 118]. However, several other physics effects could influence the magnitude of the nuclear modification factor in p(d)+A collisions such as nuclear shadowing and gluon saturation effects. But the results that the nuclear modification factors in p(d)+A collisions are not below unity strengthen the argument (from experimental point of view) that a hot and dense medium of color charges is formed in A+A collisions at RHIC and LHC. In Figure 15(c), we show the RAA of particles that do not participate in strong interactions, and some of them are most likely formed in the very early stages of the collisions. These particles (photon [119, 120], W± [121], and Z [122] bosons) have an RAA~ 1, indicating that the RAA<1, observed for charged hadrons in A+A collisions, is due to the strong interactions in a dense medium consisting of color charges.(Color online) (a) Nuclear modification factorRAA of charged hadrons measured by ALICE [26] and CMS [27] experiments at midrapidity for 0–5% most central Pb+Pb collisions at sNN=2.76 TeV. For comparison, shown are the RAA of charged hadrons at midrapidity for 0–5% most central collisions measured by STAR [115] and RAA of π0 at midrapidity for 0–10% most central collisions measured by PHENIX [173] for Au+Au collisions at sNN=200 GeV. (b) Comparison of nuclear modification factor for charged hadrons versus pT at midrapidity for minimum bias collisions in d+Au collisions at sNN=200 GeV [115] and p+Pb collisions at sNN=5.02 TeV [116]. (c) The nuclear modification factor versus pT for isolated photons in central nucleus-nucleus collisions at sNN=200 GeV [119] and 2.76 TeV [120]. Also shown are the pT integrated RAA of W± [121] and Z bosons [122] at corresponding mT at LHC energies. Open and shaded boxes represents the systematic uncertainties in the experimental measurements and normalization uncertainties, respectively.
(a)
(b)
(c)


## 3.1. Bulk Properties at Freeze-Out

### 3.1.1. Multiplicity

Figure4(a) shows the charged particle multiplicity density at midrapidity (dNch/dη) per participating nucleon pair produced in central heavy-ion collisions versus sNN. We observe that the charged particle production increases by a factor 2 as the energy increases from RHIC to LHC. The energy dependence seems to rule out a logarithmic dependence of particle production with sNN and supports a power law type of dependence on sNN. The red solid curve seems to describe the full energy range. More detailed discussions on the energy dependence of these measurements can be found in [28].(Color online) (a)dNch/dη per participating nucleon pair at midrapidity in central heavy-ion collisions as a function of sNN. (b) Comparison of dNch/dη per participating nucleon at midrapidity in central heavy-ion collisions [15, 16, 29–37] to corresponding results from p+p(p-) [38–47] and p(d) + A collisions [29, 48, 49].
(a)
(b)Figure4(b) shows the excess of dNch/dη/〈Npart〉 in A+A collisions [15, 16, 29–37] over corresponding yields in p+p(p-) [38–47] and p(d)+A collisions [29, 48, 49]. This observation also seen at RHIC persists at LHC but is proportionately larger at the higher energy collisions at the LHC. A power law fit to the p+p collision charged particle multiplicity density leads to a dependence ~s0.11, while those for A+A collisions go as ~s0.15. There is no scaling observed in the charged particle multiplicity density per participating nucleon, when compared between elementary collisions like p+p and heavy-ion collisions. This is a clear indication that A+A collisions at RHIC and LHC are not a simple superposition of several p+p collisions, whereas the p+A collisions scale with the p+p collisions.


### 3.1.2. Average Transverse Mass and Bjorken Energy Density

Figure5(a) shows the 〈mT〉 values for pions in central heavy-ion collisions as a function of sNN. The 〈mT〉 value increases with sNN at lower AGS energies [50, 51], stays independent of sNN for the SPS energies [52, 53], and then tends to rise further with increasing sNN at the higher beam energies of LHC. About 25% increase in 〈mT〉 is observed from RHIC [41, 54] to LHC [55]. For a thermodynamic system, 〈mT〉 can be an approximate representation of the temperature of the system, and dN/dy∝ln(sNN) may represent its entropy [56]. In such a scenario, the observations could reflect the characteristic signature of a phase transition, as proposed by Van Hove [57]. Then, the constant value of 〈mT〉 versus sNN has one possible interpretation in terms of formation of a mixed phase of a QGP and hadrons during the evolution of the heavy-ion system. The energy domains accessed at RHIC and LHC will then correspond to partonic phase, while those at AGS would reflect hadronic phase. However, there could be several other effects to which 〈mT〉 is sensitive, which also need to be understood for proper interpretation of the data [56].(a)〈mT〉 for charged pions in central heavy-ion collisions at midrapidity for AGS [50, 51], SPS [52, 53], RHIC [41, 54], and LHC [55] energies. The errors shown are the quadrature sum of statistical and systematic uncertainties. (b) The product of Bjorken energy density, ϵBj [58], and the formation time (τ) in central heavy-ion collisions at midrapidity as a function of sNN [59–64].
(a)
(b)Figure5(b) shows the product of the estimated Bjorken energy density (ϵBj=(1/(A⊥τ))dET/dy; A⊥ [58] is the transverse overlap area of the nuclei, and ET is the transverse energy) and formation time (τ) as a function of sNN [59–64]. The product of energy density and the formation time at LHC seem to be a factor of 3 larger compared to those attained at RHIC. If we assume the same value of τ0  (=1 fm/c) for LHC and RHIC, the Bjorken energy density is about a factor of 3 larger at the LHC compared to that at RHIC in central collisions.


### 3.1.3. Volume and Decoupling Time

The top panel of Figure6 shows the energy dependence of the product of the three radii (Rout, Rside, and Rlong) obtained from pion HBT or Bose-Einstein correlation analysis. Here, the “out” corresponds to the axis pointing along the pair transverse momentum, the  “side” to the axis perpendicular to it in the transverse plane, and the “long” corresponds to the axis along the beam (Bertsch-Pratt convention [65, 66]). The product of the radii is connected to the volume of the homogeneity region at the last interaction. The product of the three radii shows a linear dependence on the charged-particle pseudorapidity density. The data indicates that the volume of homogeneity region is two times larger at the LHC than at RHIC.(a) Product of the three pion HBT radii atkT (average transverse momenta of two pions) =0.3 GeV/c for central heavy-ion collisions at AGS [68], SPS [69, 70], RHIC [71, 72], and LHC [73] energies. (b) The decoupling time extracted from Rlong(kT) for central heavy-ion collisions at midrapidity at AGS, SPS, RHIC, and LHC energies as a function of (dNch/dη)1/3.
(a)
(b)Furthermore, within a hydrodynamic picture, the decoupling time for hadrons (τf) at midrapidity can be estimated from the magnitude of radii Rlong as follows: Rlong2 = τf2TK2(mT/T)/mTK1(mT/T), with mT=mπ2+kT2, where mπ is the mass of the pion, T is the kinetic freeze-out temperature, and K1 and K2 are the integer-order modified Bessel functions [67]. For the estimation of τf, the average value of the kinetic freeze-out temperature T is taken to be 120 MeV from AGS to LHC energies. However, the energy dependence of kinetic freeze-out temperature, as discussed in the next subsection, would provide a more accurate description of the τf values. The extracted τf values for central heavy-ion collisions at midrapidity at AGS [68], SPS [69, 70], RHIC [71, 72], and LHC [73] energies are shown as a function of cube root of dNch/dη in the bottom panel of Figure 6. We observe that τf scales linearly with (dNch/dη)1/3 and is about 10 fm/c at LHC energies. This value is about 40% larger than at RHIC. It may be noted that the above expression ignores transverse expansion of the system and finite chemical potential for pions. Also there are uncertainties associated with freeze-out temperature that could lead to variations in the extracted τf values.


### 3.1.4. Freeze-Out Temperature and Radial Flow Velocity

The hadron yields and spectra reflect the properties of the bulk matter at chemical and kinetic freeze-out, respectively. Generally, the point at which the inelastic collisions cease is called the chemical freeze-out, and the point where even the elastic collisions stop is called the kinetic freeze-out.The transverse momentum distribution of different particles contains two components: one random and the other collective. The random component can be identified with the temperature of the system at kinetic freeze-out (Tkin). The collective component, which could arise from the matter density gradient from the center to the boundary of the fireball created in high energy nuclear collisions, is called collective flow in transverse direction (〈β〉). Using the assumption that the system attains thermal equilibrium, the blast wave formulation can be used to extract Tkin and 〈β〉. These two quantities are shown in Figure 7 versus sNN [41, 55, 74–77]. For beam energies at AGS and above, one observes a decrease in Tkin with sNN. This indicates that the higher the beam energy is, the longer interactions are among the constituents of the expanding system and the lower the temperature. From RHIC top energy to LHC, there seems to be, however, a saturation in the value of Tkin. In contrast to the temperature, the collective flow increases with the increase in beam energy, rapidly, reaching a value close to 0.6 times the speed of light at the LHC energy.Kinetic freeze-out temperature (a) and radial flow velocity (b) in central heavy-ion collisions as a function of collision energy [41, 55, 74–77].
(a)
(b)Figure8 shows the chemical freeze-out temperature (Tch) versus the baryon chemical potential (μB) in central heavy-ion collisions [41, 55, 78–85]. These quantities are obtained by fitting the particle yields to a statistical model assuming thermal equilibrium within the framework of a Grand Canonical ensemble. There are two values of temperature quoted for LHC energies. A Tch value of about 164 MeV and fixed μB value of 1 MeV seem to reproduce the multistrange ratios (involving Ξ and Ω) quite well but were observed to miss the data for p/π and Λ/π. On the other hand, the statistical thermal model prediction with Tch=152 MeV and fixed μB=1MeV fits the measured p/π and Λ/π ratios better but misses the ratios involving multistrange hadrons [86]. This issue is not yet resolved, being possibly related to hadronic final state interactions [87]. The curve corresponds to generalization of the energy dependence of Tch-μB using statistical thermal model calculations [78, 79]. The model works within the framework of a Grand Canonical ensemble and takes as input the produced particle yields from experiments to extract the freeze-out parameters such as Tch and μB.Figure 8
(Color online) Chemical freeze-out temperature versus baryon chemical potential in central heavy-ion collisions [41, 55, 78–85]. The curve corresponds to model calculations from [78, 79].


### 3.1.5. Fluctuations

One of the proposed signatures to search for the phase transition from hadronic to partonic medium is to study the net-charge fluctuations in heavy-ion collisions. The partonic phase has constituents with fractional charges, while the hadronic phase has constituents with integral units of charge; hence, the measure of the fluctuations in the net-charge particle production is expected to be different in these two cases. Specifically, net-charge fluctuations are expected to be smaller if the system underwent a phase transition. However, it is important to address how these fluctuations may or may not survive the evolution of the system in the heavy-ion collisions. An experimental measure of net-charge fluctuations is defined asν(+-,dyn)=(〈N+(N+-1)〉/〈N+2〉)+(〈N-(N--1)〉/〈N-2〉)-2(〈N-N+〉/〈N-〉〈N+〉), where 〈N-〉 and 〈N+〉 are average negative and positive charged particle multiplicity, respectively [88].Figure9 shows the product of ν(+-,dyn) and 〈Nch〉 (average number of charged particles) as a function of sNN [89–91]. We find that this observable fluctuation rapidly decreases with sNN and approaches expectation for a simple QGP-like scenario [92] as we move from RHIC to LHC energies. Given that several other observables already indicate that a hot and dense medium of color charges has been formed at RHIC and LHC, the net-charge fluctuation result may indicate that the observable ν(+-,dyn) is not sensitive enough to QGP physics or the process of hadronization washes out the QGP signal for this observable. It may be also noted that the model’s results do not incorporate the acceptance effects and do not consider any dynamic evolution of the system like, for example, the dilution of the signals in the hadronization process.Figure 9
(Color online) Energy dependence of net-charge fluctuations about midrapidity in central heavy-ion collisions at SPS [89], RHIC [90], and LHC [91] energies. Also shown are the expectations from a hadron resonance gas model and for a simple QGP picture [92].


## 3.1.1. Multiplicity

Figure4(a) shows the charged particle multiplicity density at midrapidity (dNch/dη) per participating nucleon pair produced in central heavy-ion collisions versus sNN. We observe that the charged particle production increases by a factor 2 as the energy increases from RHIC to LHC. The energy dependence seems to rule out a logarithmic dependence of particle production with sNN and supports a power law type of dependence on sNN. The red solid curve seems to describe the full energy range. More detailed discussions on the energy dependence of these measurements can be found in [28].(Color online) (a)dNch/dη per participating nucleon pair at midrapidity in central heavy-ion collisions as a function of sNN. (b) Comparison of dNch/dη per participating nucleon at midrapidity in central heavy-ion collisions [15, 16, 29–37] to corresponding results from p+p(p-) [38–47] and p(d) + A collisions [29, 48, 49].
(a)
(b)Figure4(b) shows the excess of dNch/dη/〈Npart〉 in A+A collisions [15, 16, 29–37] over corresponding yields in p+p(p-) [38–47] and p(d)+A collisions [29, 48, 49]. This observation also seen at RHIC persists at LHC but is proportionately larger at the higher energy collisions at the LHC. A power law fit to the p+p collision charged particle multiplicity density leads to a dependence ~s0.11, while those for A+A collisions go as ~s0.15. There is no scaling observed in the charged particle multiplicity density per participating nucleon, when compared between elementary collisions like p+p and heavy-ion collisions. This is a clear indication that A+A collisions at RHIC and LHC are not a simple superposition of several p+p collisions, whereas the p+A collisions scale with the p+p collisions.


## 3.1.2. Average Transverse Mass and Bjorken Energy Density

Figure5(a) shows the 〈mT〉 values for pions in central heavy-ion collisions as a function of sNN. The 〈mT〉 value increases with sNN at lower AGS energies [50, 51], stays independent of sNN for the SPS energies [52, 53], and then tends to rise further with increasing sNN at the higher beam energies of LHC. About 25% increase in 〈mT〉 is observed from RHIC [41, 54] to LHC [55]. For a thermodynamic system, 〈mT〉 can be an approximate representation of the temperature of the system, and dN/dy∝ln(sNN) may represent its entropy [56]. In such a scenario, the observations could reflect the characteristic signature of a phase transition, as proposed by Van Hove [57]. Then, the constant value of 〈mT〉 versus sNN has one possible interpretation in terms of formation of a mixed phase of a QGP and hadrons during the evolution of the heavy-ion system. The energy domains accessed at RHIC and LHC will then correspond to partonic phase, while those at AGS would reflect hadronic phase. However, there could be several other effects to which 〈mT〉 is sensitive, which also need to be understood for proper interpretation of the data [56].(a)〈mT〉 for charged pions in central heavy-ion collisions at midrapidity for AGS [50, 51], SPS [52, 53], RHIC [41, 54], and LHC [55] energies. The errors shown are the quadrature sum of statistical and systematic uncertainties. (b) The product of Bjorken energy density, ϵBj [58], and the formation time (τ) in central heavy-ion collisions at midrapidity as a function of sNN [59–64].
(a)
(b)Figure5(b) shows the product of the estimated Bjorken energy density (ϵBj=(1/(A⊥τ))dET/dy; A⊥ [58] is the transverse overlap area of the nuclei, and ET is the transverse energy) and formation time (τ) as a function of sNN [59–64]. The product of energy density and the formation time at LHC seem to be a factor of 3 larger compared to those attained at RHIC. If we assume the same value of τ0  (=1 fm/c) for LHC and RHIC, the Bjorken energy density is about a factor of 3 larger at the LHC compared to that at RHIC in central collisions.


## 3.1.3. Volume and Decoupling Time

The top panel of Figure6 shows the energy dependence of the product of the three radii (Rout, Rside, and Rlong) obtained from pion HBT or Bose-Einstein correlation analysis. Here, the “out” corresponds to the axis pointing along the pair transverse momentum, the  “side” to the axis perpendicular to it in the transverse plane, and the “long” corresponds to the axis along the beam (Bertsch-Pratt convention [65, 66]). The product of the radii is connected to the volume of the homogeneity region at the last interaction. The product of the three radii shows a linear dependence on the charged-particle pseudorapidity density. The data indicates that the volume of homogeneity region is two times larger at the LHC than at RHIC.(a) Product of the three pion HBT radii atkT (average transverse momenta of two pions) =0.3 GeV/c for central heavy-ion collisions at AGS [68], SPS [69, 70], RHIC [71, 72], and LHC [73] energies. (b) The decoupling time extracted from Rlong(kT) for central heavy-ion collisions at midrapidity at AGS, SPS, RHIC, and LHC energies as a function of (dNch/dη)1/3.
(a)
(b)Furthermore, within a hydrodynamic picture, the decoupling time for hadrons (τf) at midrapidity can be estimated from the magnitude of radii Rlong as follows: Rlong2 = τf2TK2(mT/T)/mTK1(mT/T), with mT=mπ2+kT2, where mπ is the mass of the pion, T is the kinetic freeze-out temperature, and K1 and K2 are the integer-order modified Bessel functions [67]. For the estimation of τf, the average value of the kinetic freeze-out temperature T is taken to be 120 MeV from AGS to LHC energies. However, the energy dependence of kinetic freeze-out temperature, as discussed in the next subsection, would provide a more accurate description of the τf values. The extracted τf values for central heavy-ion collisions at midrapidity at AGS [68], SPS [69, 70], RHIC [71, 72], and LHC [73] energies are shown as a function of cube root of dNch/dη in the bottom panel of Figure 6. We observe that τf scales linearly with (dNch/dη)1/3 and is about 10 fm/c at LHC energies. This value is about 40% larger than at RHIC. It may be noted that the above expression ignores transverse expansion of the system and finite chemical potential for pions. Also there are uncertainties associated with freeze-out temperature that could lead to variations in the extracted τf values.


## 3.1.4. Freeze-Out Temperature and Radial Flow Velocity

The hadron yields and spectra reflect the properties of the bulk matter at chemical and kinetic freeze-out, respectively. Generally, the point at which the inelastic collisions cease is called the chemical freeze-out, and the point where even the elastic collisions stop is called the kinetic freeze-out.The transverse momentum distribution of different particles contains two components: one random and the other collective. The random component can be identified with the temperature of the system at kinetic freeze-out (Tkin). The collective component, which could arise from the matter density gradient from the center to the boundary of the fireball created in high energy nuclear collisions, is called collective flow in transverse direction (〈β〉). Using the assumption that the system attains thermal equilibrium, the blast wave formulation can be used to extract Tkin and 〈β〉. These two quantities are shown in Figure 7 versus sNN [41, 55, 74–77]. For beam energies at AGS and above, one observes a decrease in Tkin with sNN. This indicates that the higher the beam energy is, the longer interactions are among the constituents of the expanding system and the lower the temperature. From RHIC top energy to LHC, there seems to be, however, a saturation in the value of Tkin. In contrast to the temperature, the collective flow increases with the increase in beam energy, rapidly, reaching a value close to 0.6 times the speed of light at the LHC energy.Kinetic freeze-out temperature (a) and radial flow velocity (b) in central heavy-ion collisions as a function of collision energy [41, 55, 74–77].
(a)
(b)Figure8 shows the chemical freeze-out temperature (Tch) versus the baryon chemical potential (μB) in central heavy-ion collisions [41, 55, 78–85]. These quantities are obtained by fitting the particle yields to a statistical model assuming thermal equilibrium within the framework of a Grand Canonical ensemble. There are two values of temperature quoted for LHC energies. A Tch value of about 164 MeV and fixed μB value of 1 MeV seem to reproduce the multistrange ratios (involving Ξ and Ω) quite well but were observed to miss the data for p/π and Λ/π. On the other hand, the statistical thermal model prediction with Tch=152 MeV and fixed μB=1MeV fits the measured p/π and Λ/π ratios better but misses the ratios involving multistrange hadrons [86]. This issue is not yet resolved, being possibly related to hadronic final state interactions [87]. The curve corresponds to generalization of the energy dependence of Tch-μB using statistical thermal model calculations [78, 79]. The model works within the framework of a Grand Canonical ensemble and takes as input the produced particle yields from experiments to extract the freeze-out parameters such as Tch and μB.Figure 8
(Color online) Chemical freeze-out temperature versus baryon chemical potential in central heavy-ion collisions [41, 55, 78–85]. The curve corresponds to model calculations from [78, 79].


## 3.1.5. Fluctuations

One of the proposed signatures to search for the phase transition from hadronic to partonic medium is to study the net-charge fluctuations in heavy-ion collisions. The partonic phase has constituents with fractional charges, while the hadronic phase has constituents with integral units of charge; hence, the measure of the fluctuations in the net-charge particle production is expected to be different in these two cases. Specifically, net-charge fluctuations are expected to be smaller if the system underwent a phase transition. However, it is important to address how these fluctuations may or may not survive the evolution of the system in the heavy-ion collisions. An experimental measure of net-charge fluctuations is defined asν(+-,dyn)=(〈N+(N+-1)〉/〈N+2〉)+(〈N-(N--1)〉/〈N-2〉)-2(〈N-N+〉/〈N-〉〈N+〉), where 〈N-〉 and 〈N+〉 are average negative and positive charged particle multiplicity, respectively [88].Figure9 shows the product of ν(+-,dyn) and 〈Nch〉 (average number of charged particles) as a function of sNN [89–91]. We find that this observable fluctuation rapidly decreases with sNN and approaches expectation for a simple QGP-like scenario [92] as we move from RHIC to LHC energies. Given that several other observables already indicate that a hot and dense medium of color charges has been formed at RHIC and LHC, the net-charge fluctuation result may indicate that the observable ν(+-,dyn) is not sensitive enough to QGP physics or the process of hadronization washes out the QGP signal for this observable. It may be also noted that the model’s results do not incorporate the acceptance effects and do not consider any dynamic evolution of the system like, for example, the dilution of the signals in the hadronization process.Figure 9
(Color online) Energy dependence of net-charge fluctuations about midrapidity in central heavy-ion collisions at SPS [89], RHIC [90], and LHC [91] energies. Also shown are the expectations from a hadron resonance gas model and for a simple QGP picture [92].


## 3.2. Azimuthal Anisotropy

### 3.2.1. Energy Dependence ofpT Integrated v2

Figure10 shows the pT integrated v2 close to midrapidity of charged particles for collision centralities around 20–30% as a function of center of mass energy. We observe that there is an increase in magnitude of v2 by about 30% from top RHIC energy (sNN = 200 GeV) to LHC energy (sNN=2.76 TeV). This needs to be viewed within the context of a similar magnitude of increase in 〈pT〉 of pions from RHIC to LHC energies. The increase of v2 beyond beam energy of 10 GeV is logarithmic in sNN. This is expected to be determined by the pressure gradient-driven expansion of the almond-shape fireball produced in the initial stages of a noncentral heavy-ion collision [93] while for v2 measured at lower beam energies, the dependences observed are due to interplay of passing time of spectators and time scale of expansion of the system. A preference for an inplane emission versus out-of-plane (“squeeze-out”) pattern of particles as a function of beam energy is observed. The experimental data used are from FOPI [94, 95], EOS, E895 [96], E877 [97], CERES [98], NA49 [99], STAR [100], PHOBOS [101], PHENIX [102], ALICE [25], ATLAS [103], and CMS [17–20] experiments. Charged particles are used for LHC, RHIC, CERES, and E877 experiments, pion data is used from NA49 experiment, protons’ results are from EOS and E895 experiments, and FOPI results are for all particles with Z=1.Figure 10
(Color online) Transverse momentum integratedv2 close to midrapidity for charged (Z=1) particles for collision centralities around 20–30% as a function of center of mass energy.


### 3.2.2. Azimuthal Anisotropy Coefficients versus Transverse Momentum

Figure11(a) shows the comparison of v2(pT), v3(pT), and v4(pT) for 30–40% collision centrality at RHIC (PHENIX experiment [104]) and LHC (ALICE [105]) at midrapidity in Au+Au and Pb+Pb collisions, respectively. The bottom panel of this figure shows the ratio of LHC and RHIC results to a polynomial fit to the LHC data. The vn(pT) measurement techniques are similar at RHIC and LHC energies. One observes that at lower pT (<2 GeV/c), the v2(pT) and v3(pT) are about 10–20% smaller at RHIC compared to the corresponding LHC results. However, at higher pT, the results are quite similar. The v4(pT) seems higher at RHIC compared to that at LHC.(Color online) (a) Comparison ofvn(pT) at midrapidity for 30–40% collision centrality at RHIC (Au+Au collisions at sNN=200 GeV from PHENIX experiment [104]) and at LHC (Pb+Pb collisions at sNN = 2.76 TeV from ALICE experiment [105]). (b) show the ratio of vn at LHC and RHIC. (b) v2 versus pT and v2/nq versus pT/nq for pions and protons at midrapidity for 10–20% collision centrality from Au+Au collisions at sNN=200 GeV (PHENIX experiment [106]) and Pb+Pb collisions at sNN=2.76 TeV (ALICE experiment [107]).
(a)
(b)One of the most striking observations to come out from RHIC is the number of constituent quark (nq) scaling of v2(pT) for identified hadrons. The basis of such a scaling is the splitting of v2(pT) between baryons and mesons at intermediate pT (2–6 GeV/c). This is shown in the bottom panels of Figure 11(b). Such a splitting between baryon and meson v2(pT) is also observed at intermediate pT at LHC energies (seen in the top panels of Figure 11(b)). However, the degree to which nq scaling holds could be different at RHIC [106] and LHC [107] energies. The nq scaling is much more closely followed at RHIC compared to LHC. It may be noted that there are several factors which could dilute such scaling, which include energy dependence of radial flow, an admixture of higher Fock states, and consideration of a realistic momentum distribution of quarks inside a hadron [108, 109]. The observation of the baryon-meson splitting is commonly interpreted as due to substantial amount of collectivity being generated in the deconfined phase. Another important feature is that at both RHIC and LHC energies, a clear hydrodynamic feature of mass dependence of v2(pT) is observed at low pT (<2 GeV/c).Figure12 shows the charged hadron v2(pT) for 30–40% collision centrality in Au+Au collisions at sNN = 200 GeV and Pb+Pb collisions at sNN=2.76 TeV for |η|<1 [17–20]. This figure demonstrates the kinematic reach for higher energy collisions at LHC relative to RHIC. LHC data allows us to study the v2(pT) in the pT range never measured before in heavy-ion collisions. The v2(pT)~0 for pT>40 GeV/c might suggest that those particles must have been emitted very early in the interactions when the collective effects had not set in. These high transverse momentum data are useful to understand the effects of the initial geometry or path-length dependence of various properties associated with parton modification inside the hot QCD medium. In addition, it also provides significantly improved precision measurement of v2 for 12<pT<20 GeV/c.Figure 12
(Color online) Comparison ofv2(pT) at midrapidity for 30–40% collision centrality at RHIC (Au+Au collisions at sNN = 200 GeV from STAR experiment) and at LHC (Pb+Pb collisions at sNN=2.76 TeV from CMS experiment [17–20]). The shaded band about CMS data point are systematic errors and vertical lines represent statistical errors.


### 3.2.3. Flow Fluctuations

Fluctuations in azimuthal anisotropy coefficientv2 have gained quite an attention in recent times. In particular, the measurement of event-by-event v2 fluctuations can pose new constraints on the models of the initial state of the collision and their subsequent hydrodynamic evolution. In extracting event-by-event v2 fluctuations, one needs to separate nonflow effects, and so far, there is no direct method to decouple v2 fluctuations and nonflow effects in a model independent from the experimental measurements. However, several techniques exist where the nonflow effects can be minimized; for example, flow and non-flow contributions can be possibly separated to a great extent with a detailed study of two particle correlation function in Δϕ and its dependence on η and Δη. Here, we discuss another technique to extract and compare the v2 fluctuations at RHIC and LHC. We assume that the difference between v2{2} (two-particle cumulant) and v2{4} (four-particle cumulant) is dominated by v2 fluctuations, and nonflow effect is negligible for v2{4}. Then, the ratio Rv(2-4)=(v2{2}2-v2{4}2)/(v2{2}2+v2{4}2) can be considered as an estimate for v2 fluctuations in the data. Figure 13 shows the Rv(2-4) as a function of collision centrality and 〈dNch/dη〉 for RHIC [110] and LHC [107] energies. The centrality dependence of Rv(2-4) at RHIC or LHC as seen in Figure 13 could be an interplay of residual nonflow effects which increases for central collisions and multiplicity fluctuations which dominate smaller systems. It is striking to see that Rv(2-4) when presented as a function of % cross section is similar at RHIC and LHC, suggesting it reflects features associated with initial state of the collisions, for example, the event-by-event fluctuations in the eccentricity of the system. But when presented as a function of dNch/dη, it tends to suggest a different behavior for most central collisions at RHIC.(Color online) The ratioRv(2-4)=(v2{2}2-v2{4}2)/(v2{2}2+v2{4}2), an estimate of v2 fluctuations plotted as a function of collision centrality (a) and 〈dNch/dη〉 (b) for RHIC (STAR experiment: Au+Au collisions at sNN=200 GeV [110]) and LHC (ALICE: Pb+Pb collisions at sNN=2.76 TeV [107]) at midrapidity. The bands reflect the systematic errors.
(a)
(b)Recently, a great interest has been generated on extracting initial condition and flow fluctuation information from the measurement of the probability distribution ofvn at LHC. The probability density of vn can be expressed as a Gaussian function in transverse plane [111] as p(vn)=(1/2πδvn2)e-(vn-vnRP)2/(2δvn2) or as one dimensional Bessel-Gaussian function [112, 113] as p(vn)=(vn/δvn2)e-(((vn)2+(vnRP)2)/2δvn2)I0(vnRPvn/δvn2), where I0 is the modified Bessel function of the first kind and δvn is the fluctuation in vn, with δvn≈σvn for δvn≪vnRP (vn measured with respect to reaction plane).Figure14 shows the v2RP and δv2 values extracted from the v2 distributions as a function of 〈Npart〉 by fitting to the above probability functions [114]. They are compared with values of 〈v2〉 and σv2 obtained directly from the v2 distributions. The v2RP value is always smaller than the value for 〈v2〉, and it decreases to zero in the 0–2% centrality interval. The value of δv2 is close to σv2, except in the most central collisions. This leads to a value of δv2/v2RP larger than σv2/〈v2〉 over the full centrality range as shown in Figure 14(c). The value of δv2/v2RP decreases with 〈Npart〉 and reaches a minimum at 〈Npart〉≈200 but then increases for more central collisions. Thus, the event-by-event v2 distribution brings additional insight for the understanding of v2 fluctuations.(Color online) The dependence ofv2RP and 〈v2〉 (a), δv2 and σv2 (b), and δv2/v2RP and σv2/〈v2〉 (c) on 〈Npart〉 [114]. The shaded boxes indicate the systematic uncertainties.
(a)
(b)
(c)


## 3.2.1. Energy Dependence ofpT Integrated v2

Figure10 shows the pT integrated v2 close to midrapidity of charged particles for collision centralities around 20–30% as a function of center of mass energy. We observe that there is an increase in magnitude of v2 by about 30% from top RHIC energy (sNN = 200 GeV) to LHC energy (sNN=2.76 TeV). This needs to be viewed within the context of a similar magnitude of increase in 〈pT〉 of pions from RHIC to LHC energies. The increase of v2 beyond beam energy of 10 GeV is logarithmic in sNN. This is expected to be determined by the pressure gradient-driven expansion of the almond-shape fireball produced in the initial stages of a noncentral heavy-ion collision [93] while for v2 measured at lower beam energies, the dependences observed are due to interplay of passing time of spectators and time scale of expansion of the system. A preference for an inplane emission versus out-of-plane (“squeeze-out”) pattern of particles as a function of beam energy is observed. The experimental data used are from FOPI [94, 95], EOS, E895 [96], E877 [97], CERES [98], NA49 [99], STAR [100], PHOBOS [101], PHENIX [102], ALICE [25], ATLAS [103], and CMS [17–20] experiments. Charged particles are used for LHC, RHIC, CERES, and E877 experiments, pion data is used from NA49 experiment, protons’ results are from EOS and E895 experiments, and FOPI results are for all particles with Z=1.Figure 10
(Color online) Transverse momentum integratedv2 close to midrapidity for charged (Z=1) particles for collision centralities around 20–30% as a function of center of mass energy.


## 3.2.2. Azimuthal Anisotropy Coefficients versus Transverse Momentum

Figure11(a) shows the comparison of v2(pT), v3(pT), and v4(pT) for 30–40% collision centrality at RHIC (PHENIX experiment [104]) and LHC (ALICE [105]) at midrapidity in Au+Au and Pb+Pb collisions, respectively. The bottom panel of this figure shows the ratio of LHC and RHIC results to a polynomial fit to the LHC data. The vn(pT) measurement techniques are similar at RHIC and LHC energies. One observes that at lower pT (<2 GeV/c), the v2(pT) and v3(pT) are about 10–20% smaller at RHIC compared to the corresponding LHC results. However, at higher pT, the results are quite similar. The v4(pT) seems higher at RHIC compared to that at LHC.(Color online) (a) Comparison ofvn(pT) at midrapidity for 30–40% collision centrality at RHIC (Au+Au collisions at sNN=200 GeV from PHENIX experiment [104]) and at LHC (Pb+Pb collisions at sNN = 2.76 TeV from ALICE experiment [105]). (b) show the ratio of vn at LHC and RHIC. (b) v2 versus pT and v2/nq versus pT/nq for pions and protons at midrapidity for 10–20% collision centrality from Au+Au collisions at sNN=200 GeV (PHENIX experiment [106]) and Pb+Pb collisions at sNN=2.76 TeV (ALICE experiment [107]).
(a)
(b)One of the most striking observations to come out from RHIC is the number of constituent quark (nq) scaling of v2(pT) for identified hadrons. The basis of such a scaling is the splitting of v2(pT) between baryons and mesons at intermediate pT (2–6 GeV/c). This is shown in the bottom panels of Figure 11(b). Such a splitting between baryon and meson v2(pT) is also observed at intermediate pT at LHC energies (seen in the top panels of Figure 11(b)). However, the degree to which nq scaling holds could be different at RHIC [106] and LHC [107] energies. The nq scaling is much more closely followed at RHIC compared to LHC. It may be noted that there are several factors which could dilute such scaling, which include energy dependence of radial flow, an admixture of higher Fock states, and consideration of a realistic momentum distribution of quarks inside a hadron [108, 109]. The observation of the baryon-meson splitting is commonly interpreted as due to substantial amount of collectivity being generated in the deconfined phase. Another important feature is that at both RHIC and LHC energies, a clear hydrodynamic feature of mass dependence of v2(pT) is observed at low pT (<2 GeV/c).Figure12 shows the charged hadron v2(pT) for 30–40% collision centrality in Au+Au collisions at sNN = 200 GeV and Pb+Pb collisions at sNN=2.76 TeV for |η|<1 [17–20]. This figure demonstrates the kinematic reach for higher energy collisions at LHC relative to RHIC. LHC data allows us to study the v2(pT) in the pT range never measured before in heavy-ion collisions. The v2(pT)~0 for pT>40 GeV/c might suggest that those particles must have been emitted very early in the interactions when the collective effects had not set in. These high transverse momentum data are useful to understand the effects of the initial geometry or path-length dependence of various properties associated with parton modification inside the hot QCD medium. In addition, it also provides significantly improved precision measurement of v2 for 12<pT<20 GeV/c.Figure 12
(Color online) Comparison ofv2(pT) at midrapidity for 30–40% collision centrality at RHIC (Au+Au collisions at sNN = 200 GeV from STAR experiment) and at LHC (Pb+Pb collisions at sNN=2.76 TeV from CMS experiment [17–20]). The shaded band about CMS data point are systematic errors and vertical lines represent statistical errors.


## 3.2.3. Flow Fluctuations

Fluctuations in azimuthal anisotropy coefficientv2 have gained quite an attention in recent times. In particular, the measurement of event-by-event v2 fluctuations can pose new constraints on the models of the initial state of the collision and their subsequent hydrodynamic evolution. In extracting event-by-event v2 fluctuations, one needs to separate nonflow effects, and so far, there is no direct method to decouple v2 fluctuations and nonflow effects in a model independent from the experimental measurements. However, several techniques exist where the nonflow effects can be minimized; for example, flow and non-flow contributions can be possibly separated to a great extent with a detailed study of two particle correlation function in Δϕ and its dependence on η and Δη. Here, we discuss another technique to extract and compare the v2 fluctuations at RHIC and LHC. We assume that the difference between v2{2} (two-particle cumulant) and v2{4} (four-particle cumulant) is dominated by v2 fluctuations, and nonflow effect is negligible for v2{4}. Then, the ratio Rv(2-4)=(v2{2}2-v2{4}2)/(v2{2}2+v2{4}2) can be considered as an estimate for v2 fluctuations in the data. Figure 13 shows the Rv(2-4) as a function of collision centrality and 〈dNch/dη〉 for RHIC [110] and LHC [107] energies. The centrality dependence of Rv(2-4) at RHIC or LHC as seen in Figure 13 could be an interplay of residual nonflow effects which increases for central collisions and multiplicity fluctuations which dominate smaller systems. It is striking to see that Rv(2-4) when presented as a function of % cross section is similar at RHIC and LHC, suggesting it reflects features associated with initial state of the collisions, for example, the event-by-event fluctuations in the eccentricity of the system. But when presented as a function of dNch/dη, it tends to suggest a different behavior for most central collisions at RHIC.(Color online) The ratioRv(2-4)=(v2{2}2-v2{4}2)/(v2{2}2+v2{4}2), an estimate of v2 fluctuations plotted as a function of collision centrality (a) and 〈dNch/dη〉 (b) for RHIC (STAR experiment: Au+Au collisions at sNN=200 GeV [110]) and LHC (ALICE: Pb+Pb collisions at sNN=2.76 TeV [107]) at midrapidity. The bands reflect the systematic errors.
(a)
(b)Recently, a great interest has been generated on extracting initial condition and flow fluctuation information from the measurement of the probability distribution ofvn at LHC. The probability density of vn can be expressed as a Gaussian function in transverse plane [111] as p(vn)=(1/2πδvn2)e-(vn-vnRP)2/(2δvn2) or as one dimensional Bessel-Gaussian function [112, 113] as p(vn)=(vn/δvn2)e-(((vn)2+(vnRP)2)/2δvn2)I0(vnRPvn/δvn2), where I0 is the modified Bessel function of the first kind and δvn is the fluctuation in vn, with δvn≈σvn for δvn≪vnRP (vn measured with respect to reaction plane).Figure14 shows the v2RP and δv2 values extracted from the v2 distributions as a function of 〈Npart〉 by fitting to the above probability functions [114]. They are compared with values of 〈v2〉 and σv2 obtained directly from the v2 distributions. The v2RP value is always smaller than the value for 〈v2〉, and it decreases to zero in the 0–2% centrality interval. The value of δv2 is close to σv2, except in the most central collisions. This leads to a value of δv2/v2RP larger than σv2/〈v2〉 over the full centrality range as shown in Figure 14(c). The value of δv2/v2RP decreases with 〈Npart〉 and reaches a minimum at 〈Npart〉≈200 but then increases for more central collisions. Thus, the event-by-event v2 distribution brings additional insight for the understanding of v2 fluctuations.(Color online) The dependence ofv2RP and 〈v2〉 (a), δv2 and σv2 (b), and δv2/v2RP and σv2/〈v2〉 (c) on 〈Npart〉 [114]. The shaded boxes indicate the systematic uncertainties.
(a)
(b)
(c)


## 3.3. Nuclear Modification Factor

Figure15 shows the RAA of various particles produced in heavy-ion collisions at RHIC and LHC. In Figure 15(a), we observe that the shape of the RAA versus pT of charged hadrons at RHIC and LHC [26, 27] is very similar for the common pT range of measurements. The values RAA at RHIC are higher compared to those at LHC energies up to pT<8 GeV/c. The higher kinematic reach of LHC in pT allows us to see the full pT evolution of RAA in high energy heavy-ion collisions. All these measurements suggest that the energy loss of partons in the medium formed in heavy-ion collisions at LHC energies is perhaps larger compared to that at RHIC. In Figure 15(b), we observe that the nuclear modification factors for d+Au collisions at sNN=200 GeV [115] and p+Pb collisions at sNN=5.02 TeV [116] are greater than unity for the pT>2 GeV/c. The values for RHIC are slightly larger compared to those for LHC. A value greater than unity for the nuclear modification factor in p(d)+A collisions is generally interpreted as due to Cronin effect [117, 118]. However, several other physics effects could influence the magnitude of the nuclear modification factor in p(d)+A collisions such as nuclear shadowing and gluon saturation effects. But the results that the nuclear modification factors in p(d)+A collisions are not below unity strengthen the argument (from experimental point of view) that a hot and dense medium of color charges is formed in A+A collisions at RHIC and LHC. In Figure 15(c), we show the RAA of particles that do not participate in strong interactions, and some of them are most likely formed in the very early stages of the collisions. These particles (photon [119, 120], W± [121], and Z [122] bosons) have an RAA~ 1, indicating that the RAA<1, observed for charged hadrons in A+A collisions, is due to the strong interactions in a dense medium consisting of color charges.(Color online) (a) Nuclear modification factorRAA of charged hadrons measured by ALICE [26] and CMS [27] experiments at midrapidity for 0–5% most central Pb+Pb collisions at sNN=2.76 TeV. For comparison, shown are the RAA of charged hadrons at midrapidity for 0–5% most central collisions measured by STAR [115] and RAA of π0 at midrapidity for 0–10% most central collisions measured by PHENIX [173] for Au+Au collisions at sNN=200 GeV. (b) Comparison of nuclear modification factor for charged hadrons versus pT at midrapidity for minimum bias collisions in d+Au collisions at sNN=200 GeV [115] and p+Pb collisions at sNN=5.02 TeV [116]. (c) The nuclear modification factor versus pT for isolated photons in central nucleus-nucleus collisions at sNN=200 GeV [119] and 2.76 TeV [120]. Also shown are the pT integrated RAA of W± [121] and Z bosons [122] at corresponding mT at LHC energies. Open and shaded boxes represents the systematic uncertainties in the experimental measurements and normalization uncertainties, respectively.
(a)
(b)
(c)


## 4. Comparison to Model Calculations

In this section, we compare some of the experimental observables discussed above with corresponding model calculations. This helps us to interpret the data at both RHIC and LHC energies. We restrict our discussion on the comparison of the models with the experimental data for charged particle production, ratio of kaon to pion yields as a function of beam energy,pT dependence of v2, and RAA for charged particles and pions. For the charged particle production, we compare the experimental data with models inspired by the perturbative QCD-based calculations (HIJING, DPMJET) with macroscopic models (statistical and hydrodynamical), microscopic models (string, transport, cascade, etc.), and calculations which are derived by the different parametrizations of the nucleon-nucleon and nucleus-nucleus lower energy data. The ratio of kaon to pion yields for different beam energies is compared with the statistical and thermal models. The transverse momentum dependence of v2 is compared with models incorporating the calculations based on hydrodynamic and transport approaches. Finally, the RAA results are compared with the perturbative QCD-based calculations with different mechanism for the parton energy loss in the presence of colored medium.


### 4.1. Charged Particle Multiplicity Density and Particle Ratio

Figure16 compares the measured charged particle pseudorapidity density at RHIC (0.2 TeV) and LHC (2.76 TeV) energies to various model calculations.(Color online) Comparison ofdNch/dη measurement at midrapidity for central heavy-ion collisions at RHIC and LHC with model predictions.
(a)
(b)Empirical extrapolation from lower energy data (named “Busza” in the figure) [123] significantly under-predicts the measurement at LHC energies. A simple power-law growth of charged-particle multiplicities near midrapidity in central Au+Au collisions seems to be followed up to RHIC energies (named as “Barshay and Kreyerhoff” in the figure) [124]. Perturbative QCD-inspired Monte Carlo event generators, the HIJING model without jet quenching [125], the Dual Parton Model [126] (named “DPMJET III” in the figure), and the Ultrarelativistic Quantum Molecular Dynamics model [127] (named “UrQMD” in the figure) are consistent with the measurement. The HIJING model results without jet quenching were also consistent with the RHIC measurements. The semimicroscopic models like LEXUS are successful in explaining the observed multiplicity at RHIC (named as “Jeon and Kapusta” in the figure) [128]. Models based on initial-state gluon density saturation have a range of predictions depending on the specifics of the implementation [129–133]. The best agreement with LHC data happens for model as described in (named as “Kharzeev et al.” and “Armesto et al.” in the figure) [131, 133]. Conclusions for RHIC energy from these models are similar. The prediction of a hybrid model based on hydrodynamics and saturation of final-state phase space of scattered partons (named as “Eskola et al.” in the figure) [134] is slightly on a higher side compared to the measurement at LHC. But such a model seems to do a reasonable job for RHIC energies [135]. Another hydrodynamic model in which multiplicity is scaled from p+p collisions overpredicts the measurement (named as “Bozek et al.” in the figure) [136]. Models incorporating constituent quark scaling and Landau hydrodynamics (named as “Sarkisyan and Sakharov” in the figure) [137, 138] and based on modified PYTHIA and hadronic re-scattering (named as “Humanic” in the figure) [139] underpredict the measurement at LHC energy. At RHIC energies, models considering minijet production in ultrarelativistic heavy-ion collisions by taking semihard parton rescatterings explicitly into account underpredict the multiplicities (named as  “Accardi” in the figure) [140]. It is also seen at RHIC energies that models based on string fusion [141] and dual string model [142] seem to work well, whereas those based on heavy-ion cascade LUCIFER model [143] underpredict the data.Figure17 shows the (dNch/dη)/(〈Npart〉/2) versus 〈Npart〉 for Pb+Pb collisions at sNN=2.76 TeV [14]. Also shown are the corresponding RHIC results scaled up by a factor 2.15. Remarkable similarity is observed in the shape of the distributions at RHIC and LHC energies. Particle production based on saturation model explains the trends nicely (named as “ALbacete and Dumitru” in the figure) [144] (published after the most central  dNch/dη value [25] was known). simple fit to the data using a power law form for the 〈Npart〉 also explains the measurements. In addition, a functional form inspired by the detailed shape of pseudorapidity distribution of charged particle multiplicity distributions at RHIC [47] explains the centrality trends nicely.Figure 17
(Color online) Centrality dependence of(dNch/dη)/(〈Npart〉/2) for Pb+Pb collisions at sNN=2.76 TeV [14] and Au+Au collisions at sNN=200 GeV. The RHIC results are scaled up by a factor of 2.15. Also shown are comparisons to theoretical model calculations [144] and some parametrization based on detail shape of dNch/dη distributions at RHIC [47] and 〈Npart〉.Strangeness production in heavy-ion collisions is a classic signature for formation of QGP [145]. The particle yield ratio K/π could reflect the strangeness enhancement in heavy-ion collisions with respect to the elementary collisions. Figure 18 shows the energy dependence of K±/π± ratio for central collisions at midrapidity. It will be interesting to see which model explains such an impressive collection of systematic data on K/π ratio. Figure 18 also shows the energy dependence of K/π ratio from various theoretical model calculations. The energy dependence of K+/π+ ratio has been interpreted using the Statistical Model of Early Stage (SMES) [146]. The model predicts first-order phase transition and the existence of mixed phase around beam energy of 7-8 GeV. The SHM or statistical hadronization model [147] assumes that the strong interactions saturate the particle production matrix elements. This means that the yield of particles is controlled predominantly by the magnitude of the accessible phase space. The system is in chemical nonequilibrium for sNN<7.6 GeV, while for higher energies, the oversaturation of chemical occupancies is observed. The statistical model [148] assumes that the ratio of entropy to T3 as a function of collision energy increases for mesons and decreases for baryons. Thus, a rapid change is expected at the crossing of the two curves, as the hadronic gas undergoes a transition from a baryon-dominated to a meson-dominated gas. The transition point is characterized by T=140 MeV, μB=410 MeV, and sNN=8.2 GeV. In the thermal model [79], the energy dependence of K±/π± is studied by including σ-meson, which is neglected in most of the models, and many higher mass resonances (m>2 GeV/c2) into the resonance spectrum employed in the statistical model calculations. The hadronic nonequilibrium kinetic model [149] assumes that the surplus of strange particles is produced in secondary reactions of hadrons generated in nuclear collisions. Then, the two important aspects are the available energy density and the lifetime of the fireball. It is suggested that these two aspects combine in such a way so as to show a sharp peak for the strangeness-to-entropy or K/π ratio as a function of beam energy. In the hadron resonance gas and hagedorn (HRG+Hagedorn) model [150], all hadrons as given in PDG with masses up to 2 GeV/c2 are included. The unknown hadron resonances in this model are included through Hagedorn’s formula for the density of states. The model assumes that the strangeness in the baryon sector decays to strange baryons and does not contribute to the kaon production. The energy dependence of K±/π± ratio seems to be best explained using HRG+Hagedorn model.Figure 18
(Color online) Energy dependence ofK±/π± ratio for central collisions at midrapidity. Errors are statistical and systematic added in quadrature. Results are also compared with various theoretical model predictions [79, 147–150].This systematic measurement ofK/π ratio reveals two interesting  pieces of  information. (a) The K+/π+ ratio shows a peak around sNN=8 GeV, while the K-/π- ratio increases monotonically; the peak indicates the role of the maximum baryon density at freeze-out around this collision energy. (b) For sNN>100 GeV, pair production becomes the dominant mechanism for K± production, so both the ratios K+/π+ and K-/π- approach the value of 0.16. Taking into account the different masses between pions and kaons, this asymptotic value corresponds to a temperature of the order of 160 MeV.


### 4.2. Azimuthal Anisotropy

The azimuthal anisotropy parameterv2, measured at RHIC and LHC, provides a unique opportunity to study the transport properties of the fundamental constituents of any visible matter, a system of quarks and gluons. Furthermore, it provides an opportunity to understand whether the underlying dynamics of the evolution of the system formed in the collisions are governed by macroscopic hydrodynamics [151–153] or by microscopic transport approach [154]. Figure 19 shows the v2 versus pT for 30–40% collision centrality Au+Au and Pb+Pb collisions at midrapidity for sNN=200 GeV and 2.76 TeV, respectively. The measurements are compared to a set of model calculations based on hydrodynamic approach (including THERMINATOR [155, 156]) and another set of calculations based on transport approach. It is observed that hydrodynamic-based models explain the v2 measurements both at RHIC and LHC energies. Transport-based models including partonic interactions (like AMPT [154]) also explain the v2 measurements. However, those transport models which do not incorporate partonic interactions like UrQMD [157, 158] fail to explain the data. The model comparison also reveals that the data favors a high degree of fluidity reflected by a small value of shear viscosity to entropy density ratio (η/s)<0.2. A more detailed comparison of the model calculations with various order azimuthal anisotropy parameters vn would in the near future give us a more quantitative picture of the temperature (or energy) dependence of transport coefficients of the system formed in the heavy-ion collisions.Figure 19
(Color online) The azimuthal anisotropy parameterv2, measured in noncentral heavy-ion collisions at midrapidity for RHIC and LHC energies. For comparison, shown are the various theoretical calculations based on hydrodynamic and transport approaches (see text for details).


### 4.3. Nuclear Modification Factor

The nuclear modification factor (RAA) is an observable used to study the structure of strongly interacting dense matter formed in heavy-ion collisions. Here, we discuss the observation of RAA<1 at high pT seen at RHIC and LHC by comparing two models within perturbative QCD- (pQCD-) based formalisms. In this picture, the high pT hadrons are expected to originate from the fragmentation of hard partons (hard scattering scales larger than QCD scales of 200 MeV). The hard partons lose energy through interactions with the hot and dense mediums, which get reflected in the observed values of RAA. The processes by which they could lose energy includes radiative energy loss and elastic energy loss. For a more elaborate discussion on these models, we refer the reader to the review article [159].In Figure20, we show a comparison between experimentally measured RAA versus pT at LHC and RHIC energies and corresponding pQCD-based model calculations. All theoretical formalisms require a microscopic model of the medium to set the input parameters for the energy loss calculation. These parameters, for example, are denoted as 〈q^〉, the transport coefficient of the medium or the gluon number density dNg/dy per unit rapidity. The parameter Pesc, on the other hand, reflects the strength of elastic energy loss put in the model calculations. Without going into deeper theoretical discussions of each model, we refer the readers to the following related publications: PQM [160], GLV [161], ASW [162], YaJEM [163], WHDG [164], and ZOWW [165]. However, for completeness and to elucidate the approach taken in the model calculations, we briefly mention two formalisms as examples: the GLV approach named after their authors Gyulassy, Levai, and Vitev and ASW approach named after the corresponding authors Armesto, Salgado and Wiedemann, where the medium is defined as separated heavy static scattering centers with color screened potentials, where as in some other formalism, a more precise definition of the medium is considered as being composed of quark gluon quasiparticles with dispersion relations and interactions given by the hard thermal loop effective theory.(Color online) Measurements of the nuclear modification factorRAA in central heavy-ion collisions at two different center-of-mass energies, as a function of pT, for pions (π±,0) [174, 175] and charged hadrons [26, 27], compared to several theoretical predictions (see text). The error bars on the points are the statistical uncertainties, and the boxes around the data points are the systematic uncertainties. Additional absolute normalization uncertainties of order 5% to 10% are not plotted. The bands for several of the theoretical calculations represent their uncertainties.
(a)
(b)We observe that most models predict thepT dependence of RAA well for collisions both at RHIC and LHC energies. The models specially capture the generally rising behavior of RAA that is observed in the data at high pT for the LHC energies. The magnitude of the predicted slope of RAA versus pT varies between models, depending on the assumptions for the jet-quenching mechanism. The models shown do not need larger values of medium density in the calculation to explain the RAA for 3<pT<20 GeV/c at RHIC and LHC for the common kinematic range. They however, require a high medium density at LHC energy to explain the values of RAA for pT>20 GeV/c.


## 4.1. Charged Particle Multiplicity Density and Particle Ratio

Figure16 compares the measured charged particle pseudorapidity density at RHIC (0.2 TeV) and LHC (2.76 TeV) energies to various model calculations.(Color online) Comparison ofdNch/dη measurement at midrapidity for central heavy-ion collisions at RHIC and LHC with model predictions.
(a)
(b)Empirical extrapolation from lower energy data (named “Busza” in the figure) [123] significantly under-predicts the measurement at LHC energies. A simple power-law growth of charged-particle multiplicities near midrapidity in central Au+Au collisions seems to be followed up to RHIC energies (named as “Barshay and Kreyerhoff” in the figure) [124]. Perturbative QCD-inspired Monte Carlo event generators, the HIJING model without jet quenching [125], the Dual Parton Model [126] (named “DPMJET III” in the figure), and the Ultrarelativistic Quantum Molecular Dynamics model [127] (named “UrQMD” in the figure) are consistent with the measurement. The HIJING model results without jet quenching were also consistent with the RHIC measurements. The semimicroscopic models like LEXUS are successful in explaining the observed multiplicity at RHIC (named as “Jeon and Kapusta” in the figure) [128]. Models based on initial-state gluon density saturation have a range of predictions depending on the specifics of the implementation [129–133]. The best agreement with LHC data happens for model as described in (named as “Kharzeev et al.” and “Armesto et al.” in the figure) [131, 133]. Conclusions for RHIC energy from these models are similar. The prediction of a hybrid model based on hydrodynamics and saturation of final-state phase space of scattered partons (named as “Eskola et al.” in the figure) [134] is slightly on a higher side compared to the measurement at LHC. But such a model seems to do a reasonable job for RHIC energies [135]. Another hydrodynamic model in which multiplicity is scaled from p+p collisions overpredicts the measurement (named as “Bozek et al.” in the figure) [136]. Models incorporating constituent quark scaling and Landau hydrodynamics (named as “Sarkisyan and Sakharov” in the figure) [137, 138] and based on modified PYTHIA and hadronic re-scattering (named as “Humanic” in the figure) [139] underpredict the measurement at LHC energy. At RHIC energies, models considering minijet production in ultrarelativistic heavy-ion collisions by taking semihard parton rescatterings explicitly into account underpredict the multiplicities (named as  “Accardi” in the figure) [140]. It is also seen at RHIC energies that models based on string fusion [141] and dual string model [142] seem to work well, whereas those based on heavy-ion cascade LUCIFER model [143] underpredict the data.Figure17 shows the (dNch/dη)/(〈Npart〉/2) versus 〈Npart〉 for Pb+Pb collisions at sNN=2.76 TeV [14]. Also shown are the corresponding RHIC results scaled up by a factor 2.15. Remarkable similarity is observed in the shape of the distributions at RHIC and LHC energies. Particle production based on saturation model explains the trends nicely (named as “ALbacete and Dumitru” in the figure) [144] (published after the most central  dNch/dη value [25] was known). simple fit to the data using a power law form for the 〈Npart〉 also explains the measurements. In addition, a functional form inspired by the detailed shape of pseudorapidity distribution of charged particle multiplicity distributions at RHIC [47] explains the centrality trends nicely.Figure 17
(Color online) Centrality dependence of(dNch/dη)/(〈Npart〉/2) for Pb+Pb collisions at sNN=2.76 TeV [14] and Au+Au collisions at sNN=200 GeV. The RHIC results are scaled up by a factor of 2.15. Also shown are comparisons to theoretical model calculations [144] and some parametrization based on detail shape of dNch/dη distributions at RHIC [47] and 〈Npart〉.Strangeness production in heavy-ion collisions is a classic signature for formation of QGP [145]. The particle yield ratio K/π could reflect the strangeness enhancement in heavy-ion collisions with respect to the elementary collisions. Figure 18 shows the energy dependence of K±/π± ratio for central collisions at midrapidity. It will be interesting to see which model explains such an impressive collection of systematic data on K/π ratio. Figure 18 also shows the energy dependence of K/π ratio from various theoretical model calculations. The energy dependence of K+/π+ ratio has been interpreted using the Statistical Model of Early Stage (SMES) [146]. The model predicts first-order phase transition and the existence of mixed phase around beam energy of 7-8 GeV. The SHM or statistical hadronization model [147] assumes that the strong interactions saturate the particle production matrix elements. This means that the yield of particles is controlled predominantly by the magnitude of the accessible phase space. The system is in chemical nonequilibrium for sNN<7.6 GeV, while for higher energies, the oversaturation of chemical occupancies is observed. The statistical model [148] assumes that the ratio of entropy to T3 as a function of collision energy increases for mesons and decreases for baryons. Thus, a rapid change is expected at the crossing of the two curves, as the hadronic gas undergoes a transition from a baryon-dominated to a meson-dominated gas. The transition point is characterized by T=140 MeV, μB=410 MeV, and sNN=8.2 GeV. In the thermal model [79], the energy dependence of K±/π± is studied by including σ-meson, which is neglected in most of the models, and many higher mass resonances (m>2 GeV/c2) into the resonance spectrum employed in the statistical model calculations. The hadronic nonequilibrium kinetic model [149] assumes that the surplus of strange particles is produced in secondary reactions of hadrons generated in nuclear collisions. Then, the two important aspects are the available energy density and the lifetime of the fireball. It is suggested that these two aspects combine in such a way so as to show a sharp peak for the strangeness-to-entropy or K/π ratio as a function of beam energy. In the hadron resonance gas and hagedorn (HRG+Hagedorn) model [150], all hadrons as given in PDG with masses up to 2 GeV/c2 are included. The unknown hadron resonances in this model are included through Hagedorn’s formula for the density of states. The model assumes that the strangeness in the baryon sector decays to strange baryons and does not contribute to the kaon production. The energy dependence of K±/π± ratio seems to be best explained using HRG+Hagedorn model.Figure 18
(Color online) Energy dependence ofK±/π± ratio for central collisions at midrapidity. Errors are statistical and systematic added in quadrature. Results are also compared with various theoretical model predictions [79, 147–150].This systematic measurement ofK/π ratio reveals two interesting  pieces of  information. (a) The K+/π+ ratio shows a peak around sNN=8 GeV, while the K-/π- ratio increases monotonically; the peak indicates the role of the maximum baryon density at freeze-out around this collision energy. (b) For sNN>100 GeV, pair production becomes the dominant mechanism for K± production, so both the ratios K+/π+ and K-/π- approach the value of 0.16. Taking into account the different masses between pions and kaons, this asymptotic value corresponds to a temperature of the order of 160 MeV.


## 4.2. Azimuthal Anisotropy

The azimuthal anisotropy parameterv2, measured at RHIC and LHC, provides a unique opportunity to study the transport properties of the fundamental constituents of any visible matter, a system of quarks and gluons. Furthermore, it provides an opportunity to understand whether the underlying dynamics of the evolution of the system formed in the collisions are governed by macroscopic hydrodynamics [151–153] or by microscopic transport approach [154]. Figure 19 shows the v2 versus pT for 30–40% collision centrality Au+Au and Pb+Pb collisions at midrapidity for sNN=200 GeV and 2.76 TeV, respectively. The measurements are compared to a set of model calculations based on hydrodynamic approach (including THERMINATOR [155, 156]) and another set of calculations based on transport approach. It is observed that hydrodynamic-based models explain the v2 measurements both at RHIC and LHC energies. Transport-based models including partonic interactions (like AMPT [154]) also explain the v2 measurements. However, those transport models which do not incorporate partonic interactions like UrQMD [157, 158] fail to explain the data. The model comparison also reveals that the data favors a high degree of fluidity reflected by a small value of shear viscosity to entropy density ratio (η/s)<0.2. A more detailed comparison of the model calculations with various order azimuthal anisotropy parameters vn would in the near future give us a more quantitative picture of the temperature (or energy) dependence of transport coefficients of the system formed in the heavy-ion collisions.Figure 19
(Color online) The azimuthal anisotropy parameterv2, measured in noncentral heavy-ion collisions at midrapidity for RHIC and LHC energies. For comparison, shown are the various theoretical calculations based on hydrodynamic and transport approaches (see text for details).


## 4.3. Nuclear Modification Factor

The nuclear modification factor (RAA) is an observable used to study the structure of strongly interacting dense matter formed in heavy-ion collisions. Here, we discuss the observation of RAA<1 at high pT seen at RHIC and LHC by comparing two models within perturbative QCD- (pQCD-) based formalisms. In this picture, the high pT hadrons are expected to originate from the fragmentation of hard partons (hard scattering scales larger than QCD scales of 200 MeV). The hard partons lose energy through interactions with the hot and dense mediums, which get reflected in the observed values of RAA. The processes by which they could lose energy includes radiative energy loss and elastic energy loss. For a more elaborate discussion on these models, we refer the reader to the review article [159].In Figure20, we show a comparison between experimentally measured RAA versus pT at LHC and RHIC energies and corresponding pQCD-based model calculations. All theoretical formalisms require a microscopic model of the medium to set the input parameters for the energy loss calculation. These parameters, for example, are denoted as 〈q^〉, the transport coefficient of the medium or the gluon number density dNg/dy per unit rapidity. The parameter Pesc, on the other hand, reflects the strength of elastic energy loss put in the model calculations. Without going into deeper theoretical discussions of each model, we refer the readers to the following related publications: PQM [160], GLV [161], ASW [162], YaJEM [163], WHDG [164], and ZOWW [165]. However, for completeness and to elucidate the approach taken in the model calculations, we briefly mention two formalisms as examples: the GLV approach named after their authors Gyulassy, Levai, and Vitev and ASW approach named after the corresponding authors Armesto, Salgado and Wiedemann, where the medium is defined as separated heavy static scattering centers with color screened potentials, where as in some other formalism, a more precise definition of the medium is considered as being composed of quark gluon quasiparticles with dispersion relations and interactions given by the hard thermal loop effective theory.(Color online) Measurements of the nuclear modification factorRAA in central heavy-ion collisions at two different center-of-mass energies, as a function of pT, for pions (π±,0) [174, 175] and charged hadrons [26, 27], compared to several theoretical predictions (see text). The error bars on the points are the statistical uncertainties, and the boxes around the data points are the systematic uncertainties. Additional absolute normalization uncertainties of order 5% to 10% are not plotted. The bands for several of the theoretical calculations represent their uncertainties.
(a)
(b)We observe that most models predict thepT dependence of RAA well for collisions both at RHIC and LHC energies. The models specially capture the generally rising behavior of RAA that is observed in the data at high pT for the LHC energies. The magnitude of the predicted slope of RAA versus pT varies between models, depending on the assumptions for the jet-quenching mechanism. The models shown do not need larger values of medium density in the calculation to explain the RAA for 3<pT<20 GeV/c at RHIC and LHC for the common kinematic range. They however, require a high medium density at LHC energy to explain the values of RAA for pT>20 GeV/c.


## 5. Summary

In summary, the results on multiplicity density in pseudorapidity, HBT, azimuthal anisotropy, and nuclear modification factor from LHC experiments indicate that the fireball produced in these nuclear collisions is hotter, lives longer, and expands to a larger size at freeze-out compared to lower energies. These results also confirm the formation of a deconfined state of quarks and gluons at RHIC energies. The measurements at LHC provide a unique kinematic access to study in detail the properties (such as transport coefficients) of this system of quarks and gluons.In this review, we showed that the first set of measurements made by the three LHC experiments within the heavy-ion programs, ALICE, ATLAS, and CMS, show a high degree of consistency. These measurements include centrality dependence of charged particle multiplicity, azimuthal anisotropy, and nuclear modification factor versus transverse momentum. Next, we discussed the comparison of various measurements made at RHIC and LHC energies. LHC measurements ofdNch/dη clearly demonstrated the power law dependence of charged particle multiplicity on the beam energy. They also reconfirmed the observation at RHIC that particle production mechanism is not a simple superposition of several p+p collisions. The values of 〈mT〉, ϵBj, freeze-out volume, decoupling time for hadrons, and 〈v2〉 and 〈β〉 are larger at LHC energies compared to those at RHIC energies, even though the freeze-out temperatures are comparable. The value of the net-charge fluctuation measure is observed to rapidly approach towards a simple model-based calculation for QGP state. However, the sensitivity of this observable for a heavy-ion system as well as the lack of proper modeling of the heavy-ion system theoretically for such an observable needs careful consideration. The v2 fluctuations as a function of centrality fraction have a similar value at both RHIC and LHC. This reflects their sensitivity to initial state effects. Just like at RHIC, the RdAu and direct photon RAA measurements experimentally demonstrated that the observed RAA<1 for charged hadrons is a final state effect; also at LHC, the RpPb, direct photon, and W± and Z0RAA measurements showed that the observed RAA<1 is indeed due to formation of a dense medium of colored charges in central heavy-ion collisions. All these conclusions were further validated by the comparison of several observables to corresponding model calculations. Further, it was found that the fluid at LHC shows a comparable degree of fluidity as that at RHIC. This is reflected by a small value of shear viscosity to entropy density ratio.Measurements-related heavy quark production [166–168], dilepton production, jet-hadron correlations [169, 170], and higher-order azimuthal anisotropy [171, 172] which are now coming out of both RHIC and LHC experiments will provide a much more detailed characterization of the properties of the QCD matter formed in heavy-ion collisions.



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*Source: 761474-2013-10-31.xml*