A Review on φ Meson Production in Heavy-Ion Collision

The main aim of the relativistic heavy-ion experiment is to create extremely hot and dense matter and study the QCD phase structure. With this motivation, experimental program started in the early 1990s at the Brookhaven Alternating Gradient Synchrotron (AGS) and the CERN Super Proton Synchrotron (SPS) followed by Relativistic Heavy Ion Collider (RHIC) at Brookhaven and recently at Large Hadron Collider (LHC) at CERN.These experiments allowed us to study the QCDmatter from center-of-mass energies (√sNN) 4.75GeV to 2.76 TeV. The φ meson, due to its unique properties, is considered as a good probe to study the QCD matter created in relativistic collisions. In this paper we present a review on the measurements of φ meson production in heavy-ion experiments. Mainly, we discuss the energy dependence of φ meson invariant yield and the production mechanism, strangeness enhancement, parton energy loss, and partonic collectivity in nucleus-nucleus collisions. Effect of later stage hadronic rescattering on elliptic flow (V 2 ) of proton is also discussed relative to corresponding effect on φmeson V 2 .


Introduction
According to quantum chromodynamics (QCD) [1][2][3][4], at very high temperature () and/or at high density, a deconfined phase of quarks and gluons is expected to be present, while at low  and low density the quarks and gluons are known to be confined inside hadrons.The heavy-ion collisions (A + A) provide a unique opportunity to study QCD matter in the laboratory experiments.The medium created in the heavy-ion collision is very hot and dense and also extremely short-lived (∼5-10 fm/c).In experiments, we are only able to detect the freely streaming final state particles emerging from the collisions.Using the information carried by these particles as probes, we try to understand the properties of the medium created in the collision.
The  vector meson, which is the lightest bound state of  and  quarks, is considered as a good probe for the study of QCD matter formed in heavy-ion collisions.It was discovered at Brookhaven National Laboratory in 1962 through the reaction  +  → Λ +  +  as shown in Figure 1 [5].It has a mass of 1.019445 ± 0.000020 GeV/c 2 which is comparable to the masses of the lightest baryons such as proton (0.938 GeV/c 2 ) and Λ (1.115 GeV/c 2 ).The interaction cross-section () of the  meson with nonstrange hadrons is expected to have a small value [6].The data on coherent  photo-production shows that   ∼ 10 mb [7].This is about a factor of 3 times lower than   and   , about a factor of 4 times lower than  Λ and   , and about a factor of 2 times lower than   .Therefore its production is expected to be less affected by the later stage hadronic interactions in the evolution of the system formed in heavy-ion collisions.A hydrodynamical inspired study of transverse momentum (  ) distribution of  meson seems to suggest that it freezes out early compared to other hadrons [8].The life time of the  meson is ∼42 fm/c.Because of longer life time the  meson will mostly decay outside the fireball and therefore its daughters will not have much time to rescatter in the hadronic phase.Therefore, properties of  meson are primarily controlled by the conditions in the early partonic phase and those can be considered as a clean probe 2 Advances in High Energy Physics 58 events Figure 1: Number of events versus square of invariant mass of  pairs from the reaction  +  → Λ +  +  in bubble chamber experiments at Brookhaven National Laboratory (BNL) [5].
to investigate the properties of matter created in heavy-ion collisions.
Strange particle production is one of the observables that is expected to deliver detailed information on the reaction dynamics of relativistic nucleus-nucleus collisions [9].In experiments at the CERN SPS accelerator it was found that the ratio of the number of produced kaons to that of pions is higher by a factor of about two compared to that in proton-proton reactions at the same energy [10][11][12][13].In the past, several possible reasons for this strangeness enhancement have been discussed.Firstly, if nucleus-nucleus reactions proceed through a deconfined stage, then strangequark production should be enhanced relative to a no QGP scenario [14].Alternative ideas of Canonical suppression of strangeness in small systems (proton-proton) as a source of strangeness enhancement in high energy nucleus-nucleus collisions have been proposed [15].This led to a lot of ambiguity in understanding the true physical origin of the observed enhancement in the strange particle production in high energy heavy-ion collisions.The () meson due to its zero net strangeness is not subjected to Canonical suppression effects.Therefore measurement of  meson yield in both nucleus-nucleus and proton-proton would provide the true answer for observed strangeness enhancement.
Experimentally measured results on V 2 (= ⟨cos 2( − Ψ)⟩, a measure of the azimuthal angle () anisotropy of the produced particles, and Ψ is the reaction plane angle) of identified hadrons as a function of   show that at low   (<2 GeV/c) elliptic flow follows a pattern ordered by mass of the hadron (the V 2 values are smaller for heavier hadrons than that of lighter hadrons).At the intermediate   (2 GeV/c to 6 GeV/c) all mesons and all baryons form two different groups [35].When V 2 and   are scaled by the number of constituent quarks (  ) of the hadrons, the magnitude of the scaled V 2 is observed to be the same for all the hadrons at the intermediate   .This observation is known as number-of-constituent quark scaling (NCQ scaling).This effect has been interpreted as collectivity being developed at the partonic stage of the evolution of the system in heavyion collision [36,37].Since  meson has mass (1.0194 GeV/c 2 ) comparable to the masses of the lightest baryons such as proton and at the same time it is a meson, the study of  meson V 2 would be more appropriate to understand the mass type and/or particle type (baryon-meson) dependence of V 2 (  ).
In this review we have compiled all the available experimental measurements on  meson production in high energy heavy-ion collisions as a function of   , azimuthal angle (), and rapidity ().This paper is organised in the following manner.In Section 2, measurement of  meson invariant yield has been presented from SPS to LHC energy.Section 3 describes the compilation of the azimuthal anisotropy measurements in  meson production from all the available experimental results.Finally, the summary and conclusion have been discussed in Section 4.

Invariant Yield of 𝜙 Meson
2.1.Invariant Transverse Momentum Spectra.We have compiled the data on the invariant   spectra of the  meson measured in  + ,  + A, and A + A systems for different collision centralities at various centre-of-mass energies (√  = 17.3 GeV-7 TeV) [16][17][18][19][20][21][22] and those are shown in Figure 2.Only the statistical errors are indicated as error bars.Measurement of  meson invariant yield in  +  collisions at √ = 7 TeV by the ATLAS collaboration [38] is consistent with that from the ALICE experiment and hence is not shown in Figure 2. The dashed black lines in Figure 2 are fits to the experimental data using an exponential function of the form The blue solid lines in Figure 2 are the fits to the data with Levy function of the form given by is known as the inverse slope parameter, / is the  meson yield per unit rapidity,  0 is the rest mass of  meson, and  is the Levy function parameter.Levy function is similar in shape to an exponential function at low   and has a power-law-like shape at higher   .In fact, the exponential function is the limit of the Levy function as  approaches infinity.From Figure 2, it can be seen that the exponential Advances in High Energy Physics 3   and Levy functions both fit the central collision data equally well.However, with decreasing centrality, the exponential fits diverge from the data at higher transverse momentum and the Levy function fits the data better.The  2 /ndf values are larger for exponential function fits in peripheral collisions compared to Levy function fits (see Tables 1 and 2).This indicates a change in shape of the   spectra (deviations from exponential distribution and more towards a power law distribution) at high   for peripheral collisions.Tsallis function also describes the measured identified spectra    [16][17][18]21] and  +  collisions [18-20, 22, 23].For RHIC BES energies (√  = 7.7-39 GeV) only statistical errors are shown whereas for other energies systematic errors are added in quadrature with statistical errors.equally well as Levy, which is shown in [39,40].Like Levy, Tsallis function describes both the low   exponential and the high   power law behaviors.The Tsallis function has two parameters while number of parameters for Levy is three.The exponential function fails to explain data at high   for  +  and  + Au collisions whereas Levy function describes data for all   .This evolution in the shape of the spectra from exponential-like in central collisions to more power-law-like in peripheral collisions reflects the increasing contribution from pQCD (hard) processes to  meson production in more peripheral collisions at higher   .Particle production at low   is expected to be due to nonperturbative soft processes and with sufficient interactions the system could be thermalized, and that is why both exponential and Levy functions fit the data for all centralities at low   .All the Levy and exponential fit parameters for A + A collisions are given in Tables 1  and 2. One can see that the values of parameter  are large in the case central A + A collisions where both Levy and exponential functions fit the data well.The / values increase from peripheral to central collisions, indicating increasing production of  meson with increase in collision centrality.

𝜙 Meson Yield per Unit Rapidity.
In Figure 3 we present all available measurements of   integrated  meson yield (/) at midrapidity as a function of centre-of-mass energy in both nucleus-nucleus [16][17][18]21] and protonproton collisions [18-20, 22, 23].For A + A collisions, different centralities are shown by different marker styles in Figure 3(a).The measured midrapidity yield increases with centrality and for the same centrality it increases with the collision energy for both A + A and  +  collisions.The rate of increases with √  is higher in A + A collisions compared to  +  collisions.We have observed that the measured midrapidity yield per participant ( part ) pair, (/)/(0.5part ), increases nonlinearly with centrality and for the same  part (/)/(0.5part ) increases with the collision energy of the A + A collisions.The former suggests that particle production does not scale with  part and the latter is expected because of the increase of energy available to produce the  mesons.

Strangeness Enhancement.
The ratio of strange hadron production normalised to ⟨ part ⟩ in nucleus-nucleus collisions relative to corresponding results from + collisions at 200 GeV [24] is shown in the left upper panel of Figure 4.The results are plotted as a function of ⟨ part ⟩.  − , Λ, and Ξ are found to exhibit an enhancement (value > 1) that increases with the number of strange valence quarks.Furthermore, the observed enhancement in these open-strange hadrons increases with collision centrality, reaching a maximum for the most central collisions.However, the enhancement of  meson production from Cu + Cu and Au + Au collisions shows a deviation in ordering in terms of the number of strange constituent quarks.Such deviation is also observed in central Pb + Pb collisions at SPS energy (as shown in the right bottom panel of Figure 4).The difference in the ordering does not seem to be a baryon-meson effect, since  − and Λ have similar enhancement, or a mass effect, since Λ and  have similar mass but different enhancement factors.
In heavy-ion collisions, the production of  mesons is not Canonically suppressed due to its  structure.The  +  collisions at RHIC are at an energy which is ∼25 times higher than energies where violations of the Okubo-Zweig-Iizuka (OZI) rule were reported [41,42].The observed enhancement of  meson production then is a clear indication for the   formation of a dense partonic medium being responsible for the strangeness enhancement in Au + Au collisions at 200 GeV.Furthermore,  mesons do not follow the strange quark ordering as expected in the Canonical picture for the production of other strange hadrons.The observed enhancement in  meson production being related to medium density is further supported by the energy dependence shown in the lower panel of Figure 4.The  meson production relative to  +  collisions is larger at higher beam energy, a trend opposite to that predicted in Canonical models for other strange hadrons.
The right upper panel of Figure 4 shows the enhancement in Pb + Pb with respect to  +  reference yields for , Λ, Ξ − , and Ω − + Ω + at √  = 2.76 TeV [21].The , Ξ, and Ω yield in  +  collisions at √ = 2.76 TeV have been estimated by interpolating between the measured yields at √ = 0.9 TeV and √ = 7 TeV.The reference Λ yield in  +  collisions at √  = 2.76 TeV is estimated by extrapolating from the measured yield in (inelastic)  +  collisions available up to √ = 0.9 TeV.Details can be found in [21].Enhancement factor increases linearly with  part until  part ≈ 100; then the enhancement values seem to be saturated for higher values of  part .Unlike SPS and RHIC, the order of  enhancement is the same as Ξ − at LHC energy.We have observed that the  enhancement at central collisions increases from SPS to RHIC energy but the enhancement factor is comparable, within errors, to the values at RHIC and LHC.These findings tell us that the observed  meson enhancement is not due to the Canonical suppression effects.Therefore this enhancement is very likely due to the formation of a deconfined medium.Since other strange hadrons also emerge from the same system, their enhancement is most likely also  due to formation of deconfined matter or quark-gluon plasma (QGP) in heavy-ion collisions.

Nuclear Modification Factor.
In order to understand parton energy loss in the medium created in high energy heavyion collisions for different centralities in A + A collisions, the nuclear modification factor ( CP ) is measured which is defined as follows: where ⟨ bin ⟩ is the average number of binary collisions for the corresponding centrality.The value of  bin was calculated from the Monte Carlo Glauber simulation [43]. CP value is equal to one when the nucleus-nucleus collisions are simply the superposition of nucleon-nucleon collisions.Therefore deviation of  CP from the unity would imply contribution from the nuclear medium effects, specifically jet-quenching [44].Nuclear modification factors ( CP ) of  mesons at midrapidity in Au + Au collisions at √  = 7.7, 11.5, 19.6, 27, 39, and 200 GeV [17,18] and in Pb + Pb collisions at √  = 2.76 TeV [21] are shown in Figure 5.We can see that the  CP of  mesons goes below unity at 200 GeV and 2.76 TeV in nucleus-nucleus collisions.The most feasible explanation of this observation to date is due to the energy loss of the partons traversing the high density QCD medium.This implies that a deconfined medium of quarks and gluons was formed at 200 GeV and 2.76 TeV [18,21].For √  ≤ 39 GeV,  meson  CP is greater than or equal to unity at the intermediate   , which indicates that at low energy the parton energy loss contribution to  CP measurement could be less important.In order to confirm that the  CP < 1 is due to parton energy loss or jet-quenching phenomenon, it is important to study  CP in  + A or d + A collisions.Nuclear modifications in such systems are expected to be effected by the Cronin effect [45] and not by QGP effect.Due to the Cronin effect the value of  CP at high   is expected to be greater than one.
Figure 6 presents the   dependence of the nuclear modification factor  AB in Au + Au and d + Au collisions at √  = 200 GeV [18,27].The definition of  AB is the ratio of the yields of the hadron produced in the nucleus (A) + nucleus (B) collisions to the corresponding yields in the inelastic  +  collisions normalised by  bin .The  AB of  mesons for d + Au collisions show a similar enhancement trend as those for  + +  − and  +  at the intermediate   .This enhancement in d + Au collisions was attributed to be due to the Cronin effect [45].The Cronin enhancement may result either from momentum broadening due to multiple soft [46] (or semihard [47,48]) scattering in the initial state or from final state interactions as suggested in the recombination model.These mechanisms lead to different particle type and/or mass dependence in the nuclear modification factors as a function of   .Current experimental measurements on  meson  AB in d + Au do not seem to have the precision to differentiate between particle type dependence types [49,50].On the other hand, the  AB in Au + Au (i.e.,  AA ) at 200 GeV is lower than that in d + Au at 200 GeV and is less than unity [27].These features are consistent with the scenario of energy loss of the partons in a QGP medium formed in central Au + Au collisions.

Mean Transverse Mass.
Figure 7 shows the difference in mean transverse mass (  = √ 2  +  2 0 ) and rest mass ( 0 ), that is, ⟨  ⟩− 0 for  meson, as a function of centre-of-mass energy for  +  [18,20,22], Au + Au [17,18], and Pb + Pb [16,21] collisions.Due to limited statistics, result for  +  at √ = 900 GeV is not shown.The data points in Figure 7 are connected by the lines to guide the eye of the reader.One can see that ⟨  ⟩− 0 increases monotonically with √  in + collisions whereas the corresponding data in A + A collisions changes slope twice as a function of center-of-mass energy.In A + A collisions, ⟨  ⟩ −  0 first increases with √  and then stays independent of energy from approximately 17 GeV to 39 GeV, followed by again an increase with √  .For a thermodynamic system, the ⟨  ⟩ −  0 can be interpreted as a measure of temperature of the system, and / ∝ ln(√  ) may represent its entropy.In such a scenario, this observation could reflect the characteristic signature of a first order phase transition [51].Then the constant value of ⟨  ⟩−  0 for  meson from 17 GeV to 39 GeV could be interpreted as a formation of a mixed phase of a QGP and hadrons during the evolution of the heavy-ion system.

Particle Ratios
2.6.1./ − .The mechanism for  meson production in high energy collisions has remained an open issue.In an environment with many strange quarks,  mesons can be produced readily through coalescence, bypassing the OZI rule [52].On the other hand, a naive interpretation of  meson production in heavy-ion collisions would be the  production via kaon coalescence.In the latter case one could expect an increasing trend of / ratio as function of collision centrality and centre-of-mass energy.Models that include hadronic rescatterings such as UrQMD [53,54] have predicted an increase of the / − ratio at midrapidity as a function of centrality [18].Therefore, the ratio of  meson yield to that of the kaons can be used to shed light on  meson production mechanism.Figure 8 shows the / − ratio as a Figure 8: / − ratio as a function of number of participants in Au + Au [18] and Pb + Pb [21] collision at various beam energies.function of number of participants for different centre-ofmass energies [18].The UrQMD model prediction for / − in Au + Au 200 GeV collisions is shown by red dashed line.However, this prediction was disproved from experimental data.It is clear from Figure 8 that / − is independent of centrality and also centre-of-mass energy.In addition, if  production is dominantly from  coalescence, one expects the width of the rapidity distribution of  mesons to be related to those for charged kaons as 1/ 2  = 1/ 2  − + 1/ 2  + .Measurements at SPS energies show a clear deviation of the data from the above expectation [55].Finally, if  production is dominantly from  coalescence it would be reflected in elliptic flow (V 2 ) measurements.We observe at intermediate   that the V 2 of  mesons and kaons are comparable (discussed in Section 3).All these measurements effectively rule out kaon coalescence as the dominant production mechanism for the  meson for this energy region.
2.6.2.Ω/.The production mechanism of multistrange hadrons (e.g.,  and Ω) is predicted to be very sensitive to the early phase of nuclear collisions [56], because both  and Ω freeze out early, have low hadronic interaction cross-section, and are purely made of strange and antistrange quarks.Therefore the ratio (Ω)/() is expected to reflect the information of strange quark dynamics in the early stage of the system created in the nucleus-nucleus collision [57].Figure 9 shows the baryon-to-meson ratio in strangeness sector, (Ω − + Ω + )/2(), as a function of   in Au + Au collisions at √  = 11.5 GeV to 2760 GeV [17,18,21].The dashed lines are the results from the recombination model calculation by Hwa and Yang for √  = 200 GeV [57].In this model the  and Ω yields in the measured   region are mostly from the recombination of thermal strange quarks, which were assumed to follow an exponential   distribution.The thermal  quark distribution was determined by fitting the low   data of kaon production.The contribution from hard parton scattering was assumed to be negligible unless   is large.Details of this recombination model have been given in [57].We can see from Figure 9

Azimuthal Anisotropy in 𝜙 Meson Production
In noncentral nucleus-nucleus collisions, the initial spatial anisotropy is transformed into a final state momentum anisotropy in the produced particle distributions because of pressure gradient developed due to the interactions among the systems constituents [58][59][60][61][62].The elliptic flow (V 2 ) [63-65] is a measure of the second order azimuthal anisotropy of the produced particles in the momentum space.It can be used as probe for the properties of the medium created in the heavy-ion collisions.Because of its self-quenching nature, it carries information from the early phase.Although elliptic flow is an early time phenomenon, its magnitude might still be affected by the later stage hadronic interactions.Since the hadronic interaction cross-section of  meson is smaller than the other hadrons [6] and freezes out relatively early [8], its V 2 remain almost unaffected by the later stage interaction.Therefore  meson V 2 can be considered as good and clean probe for early system created in nucleus-nucleus collisions.
Further the  mesons seem to be formed by coalescence of strange quarks and antiquarks in a deconfined medium of quarks and gluons; hence the measurement of collectivity in  mesons would reflect the collectivity in the partonic phase.In addition, its mass is comparable to the masses of the lightest baryon ( and Λ); therefore comparison of  meson V 2 with that of proton and Λ will be helpful to distinguish the mass effect and/or baryon-meson effect in V 2 (  ).
Elliptic flow of  meson as a function of   measured at midrapidity [28][29][30][31] is shown in Figure 10.The shape of  V 2 (  ) is similar for √  = 19.6GeV to 2760 GeV.But at 7.7 and 11.5 GeV, the  V 2 values at the highest measured   bins are observed to be smaller than other energies.Various model studies predicted that  meson V 2 will be small for a system with hadronic interactions [66,67].Small interaction cross-section of  meson in hadronic phase suggests that  meson V 2 mostly reflects collectivity from the partonic phase; hence small  meson V 2 indicates less contribution to the collectivity from partonic phase.So the large  meson V 2 at √  ≥ 15 GeV indicates the formation of partonic matter and small V 2 at √  ≤ 11.5 could indicate dominance of hadron interactions.

Number-of-Constituent
Quark Scaling.In Figure 11, the V 2 scaled by number-of-constituent quarks (  ) as a function (  −  0 )/  for identified hadrons in Au + Au collisions at √  = 7.7-200 GeV are presented.We can see from Figure 11 that for √  = 19.6-200GeV the V 2 values follow a universal scaling for all the measured hadrons.This observation is known as the NCQ scaling.The observed NCQ scaling at RHIC can be explained by considering particle production mechanism via the quark recombination model and can be considered as a good signature of partonic collectivity [36,37].Therefore, such a scaling should vanish for a purely hadronic system if formed in the heavy-ion collisions at the lower energies.At the same time the study of NCQ scaling of identified hadrons from UrQMD model shows that the pure hadronic medium can also reproduce such scaling in V 2 [68][69][70].This is due to modification of initially developed V 2 by later stage hadronic interactions and the production mechanism as implemented in the model [69].Hence to avoid these ambiguities, the V 2 of those particles which do not interact with hadronic interaction will be the clean and good probe for early dynamics in heavy-ion collisions.Due to small hadronic interaction cross-section,  mesons V 2 are almost unaffected by later stage interaction and it will have negligible value if  mesons are not produced via  and  quark coalescence [66,67].Therefore, NCQ scaling of  mesons V 2 can be considered as the key observables for the partonic collectivity in heavy-ion collisions.As we can see from Figure 11, at √  = 7. GeV for 0-80% centrality [28] and at √  = 200 GeV for 0-80%, 0-30%, and 30-80% centralities [29,30] and in Pb + Pb collisions at √  = 2.76 TeV [31] for different collisions centralities.The vertical lines are statistical uncertainties.deviates from the trend of the other hadrons at the highest measured   values by 1.8 and 2.3, respectively.This could be the effect for a system, where hadronic interactions are more important.Figure 12 presents the (  −  0 )/  dependence of V 2 /  for 10-20% and 40-50% central Pb + Pb collisions for selected identified particles [31].It can be seen that, at higher value of (  −  0 )/  , the scaling is not good compared to that observed at RHIC energies.There are deviations at the level of ±20% with respect to the reference ratio as shown in [31].This larger deviation at LHC energy could be related to observed large radial flow at LHC compared to RHIC.

𝑝
The   integrated elliptic flow (⟨V 2 ⟩) can be calculated as Figure 13 shows   integrated  meson (red star) and proton (blue circle) V 2 as a function of centre-of-mass energy for 0-80% centrality [32].One can see that for both particle species the ⟨V 2 ⟩ increases with increasing beam energy. meson ⟨V 2 ⟩ from a multiphase transport (AMPT) model for three different scenarios is shown by shaded bands.Green band corresponds to AMPT default model which includes only hadronic interaction whereas black and yellow bands correspond to AMPT with string melting scenario with parton-parton cross-sections of 3 mb and 10 mb, respectively.In contrast to observations from the data, the ⟨V 2 ⟩ values from model remain constant for all the energies.This is because they have been obtained for a fixed parton-parton interaction cross-section.The ⟨V ).This tells us that due to the lack of enough partonic interactions at lower beam energies a larger ⟨V 2 ⟩ could not be generated for  mesons.The contribution to  ⟨V 2 ⟩ from hadronic interactions is small because of small -hadron interaction cross-sections.However the observed higher collectivity of protons compared to  mesons at the lower beam energies could be due to the protons having larger hadronic interaction cross-section.

Hadronic Rescattering
Effect on V 2 .Recent phenomenological calculation based on ideal hydrodynamical model together with the later stage hadron cascade (hydro + JAM) shows that the mass ordering of V 2 could be broken between that of  meson and that of proton at low   (  < 1.5 GeV/c) [71].This is because of late stage hadronic rescattering effects on proton V 2 .The model calculation was done by considering low hadronic interaction cross-section for  meson and larger hadronic interaction cross-section for proton.The ratio between  V 2 and proton V 2 is shown in Figure 14 for Advances in High Energy Physics The   integrated proton and  meson V 2 for various centre-of-mass energies for 0-80% centrality in Au + Au collisions [32].Vertical lines are the statistical error and systematic errors are shown by cap symbol.For lower RHIC energies, STAR preliminary   spectra were used for  and proton ⟨V 2 ⟩ calculation [17,33,34].The red and blue lines are the fit to the  and proton V 2 by empirical function just to guide the eye of the reader.
minimum bias Au + Au collisions at √  = 200 GeV.The data from the STAR experiment are shown by solid red square and blue solid circle [29,30].Solid red square and blue solid circle correspond to 0-30% and 30-80% centralities, respectively.The ratios are larger than unity at low   region (  < 0.7 GeV/c) for 0-30% centrality although mass of the  meson (1.019 GeV/c 2 ) is greater than mass of the proton (0.938 GeV/c 2 ).This is qualitatively consistent with the model calculation using hydro + JAM shown by red bands.Therefore this observation is consistent with the physical scenario of larger effect of hadronic rescattering on proton V 2 which reduces its value, as predicted in the theoretical model [67,71].Due to small hadronic interaction cross-section  meson V 2 remains unaffected by later stage hadronic rescattering.

Summary
We have presented a review on the experimentally measured data on  production (specifically the transverse momentum distributions and azimuthal anisotropy measurements) in high energy heavy-ion collisions.The differential (  , , ) measurements of  meson production have been compared from heavy-ion collisions at the SPS, RHIC, and LHC energies.Transverse momentum spectra of  meson for different centralities, different energies, and different collision systems are presented.The shape of the transverse momentum distribution changes from exponential to Levy functional form as one goes from central to peripheral collisions at a given beam energy.This indicates an increasing contribution of   hard processes in the peripheral collisions.The centrality and energy dependence of the enhancement in  meson production support the physical origin to be due to the enhanced production of ()-quarks in a dense partonic medium formed in high energy heavy-ion collisions.We have discussed beam energy dependence of the nuclear modification factors of  meson.The values of nuclear modification factors are less than unity for beam energies of 200 GeV and 2.76 TeV, indicating formation of a dense medium with color degrees of freedom.The nuclear modification factor values at the intermediate   are observed to be equal to or higher than unity at √  ≤ 39GeV.This indicates that parton energy loss effect became less important and suggests dominance of hadronic interactions at the lower beam energies.The ratio ()/( − ) is observed to be almost constant as a function of centrality and centre-ofmass energy, disfavouring  meson production through kaon coalescence.The ratio of (Ω − +Ω + )/2() versus   shows a similar trend for √  ≥ 19.6 GeV, but at √  = 11.5 GeV the ratio at the highest measured   shows a deviation from the trend at other higher energies.This may suggest a change in Ω and/or  production mechanism and strange quark dynamics in general at √  = 11.5 GeV.The measurement of  meson V 2 as a function of   and collision centrality are discussed.We observe that  meson V 2 (  ) has similar values for √  ≥ 19.6 GeV and NCQ scaling also holds for √  ≥ 19.6 GeV.But at √  = 7.7 and 11.5 GeV, the  meson V 2 shows deviation from the other hadrons at the highest measured   values by 1.8 and 2.3, respectively.Since the V 2 of  mesons mostly reflect collectivity from partonic phase, therefore the small  V 2 observed at √  = 7.7 and 11.5 GeV indicates a smaller contribution to the collectivity from partonic phase.We

Au + Au 200 Figure 6 :
Figure 6: The nuclear modification factor  AB as a function of   in Au + Au and d + Au [18, 27] collisions at √  = 200 GeV.Rectangular bands show the uncertainties associated with estimation of number of binary collisions.Error bars are quadrature sum of statistical and systematic uncertainties for  in d + Au and only statistical for three other cases.

2 )Figure 7 :
Figure 7: ⟨  ⟩− 0 as a function centre-of-mass energies in central A + A and  +  collisions.Only statistical errors are shown.The dashed and solid lines are the straight lines connected to the data to guide the eye of the reader.
that, in central A + A collisions at √  ≥ 19.6 GeV, the ratios of (Ω − + Ω + )/2() in the intermediate   range are explained by the recombination model with thermal strange quarks and show a similar trend.The model agrees well with the trend of the data up to   ∼ 4 GeV/c which covers ∼95% of the total yields for the  and Ω.The observations imply that the production of  and Ω in central Au + Au collisions is predominantly through the recombination of thermal  quarks for √  ≥ 19.6 GeV.But at √  = 11.5 GeV, the ratio at the highest measured   shows a deviation from the trend of other energies.This may indicate a change in Ω and/or  production mechanism at √  = 11.5 GeV.

3 Figure 13 :
Figure13:The   integrated proton and  meson V 2 for various centre-of-mass energies for 0-80% centrality in Au + Au collisions[32].Vertical lines are the statistical error and systematic errors are shown by cap symbol.For lower RHIC energies, STAR preliminary   spectra were used for  and proton ⟨V 2 ⟩ calculation[17,33,34].The red and blue lines are the fit to the  and proton V 2 by empirical function just to guide the eye of the reader.

Table 1 :
Results from Levy fits to the transverse mass distributions of the  meson.All values are for midrapidity (|| < 0.5).

Table 2 :
Results from exponential fits to the transverse mass distributions of the  meson.All values are for midrapidity (|| < 0.5).
GeV.The comparison to AMPT model results indicates negligible contribution of the partonic interactions to the final measured collectivity for √  = 11.5 GeV.For √  > 19.6 GeV, proton and  meson show similar magnitude of ⟨V 2 ⟩.The proton is a baryon and  is a meson; in addition they are composed of different quark flavours, yet they have similar ⟨V 2 ⟩; this is a strong indication of large fraction of the collectivity being developed in the partonic phase.However at √  ≤ 19.6 GeV,  meson ⟨V 2 ⟩ values show deviation from that for proton and at √  = 11.5 GeV  meson ⟨V 2 ⟩ becomes small (∼1.5% 2 ⟩ of  mesons for √  ≥ 19.6 GeV can be explained by the AMPT with string melting (SM) version, by varying the parton-parton cross-section.On the other hand, both the AMPT-SM and the AMPT default models overpredict data at √  = 11.5