# A Review onϕ Meson Production in Heavy-Ion Collision

Authors: Md. Nasim; Vipul Bairathi; Mukesh Kumar Sharma; Bedangadas Mohanty; Anju Bhasin
Journal: Advances in High Energy Physics
 (2015)

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## Abstract

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 QCD matter from center-of-mass energies (sNN) 4.75 GeV 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 (v2) of proton is also discussed relative to corresponding effect on ϕ meson v2.


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## Body

## 1. Introduction

According to quantum chromodynamics (QCD) [1–4], at very high temperature (T) and/or at high density, a deconfined phase of quarks and gluons is expected to be present, while at low T 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.Theϕ vector meson, which is the lightest bound state of s and s- 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 K+p→Λ+K+K- as shown in Figure 1 [5]. It has a mass of 1.019445±0.000020 GeV/c2 which is comparable to the masses of the lightest baryons such as proton (0.938 GeV/c2) and Λ (1.115 GeV/c2). The interaction cross-section (σ) of the ϕ meson with nonstrange hadrons is expected to have a small value [6]. The data on coherent ϕ photo-production shows that σϕN~10mb [7]. This is about a factor of 3 times lower than σρN and σπN, about a factor of 4 times lower than σΛN and σNN, and about a factor of 2 times lower than σKN. 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 (pT) distribution of ϕ meson seems to suggest that it freezes out early compared to other hadrons [8]. The life time of the ϕ meson is ~42 fm/c. Because of longer life time the ϕ 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 ϕ meson are primarily controlled by the conditions in the early partonic phase and those can be considered as a clean probe to investigate the properties of matter created in heavy-ion collisions.Figure 1
Number of events versus square of invariant mass ofKK- pairs from the reaction K+p→Λ+K+K- in bubble chamber experiments at Brookhaven National Laboratory (BNL) [5].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 [10–13]. In the past, several possible reasons for this strangeness enhancement have been discussed. Firstly, if nucleus-nucleus reactions proceed through a deconfined stage, then strange-quark 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 ϕ(ss-) meson due to its zero net strangeness is not subjected to Canonical suppression effects. Therefore measurement of ϕ meson yield in both nucleus-nucleus and proton-proton would provide the true answer for observed strangeness enhancement.Experimentally measured results onv2 (=cos2(φ-Ψ), a measure of the azimuthal angle (φ) anisotropy of the produced particles, and Ψ is the reaction plane angle) of identified hadrons as a function of pT show that at low pT (<2 GeV/c) elliptic flow follows a pattern ordered by mass of the hadron (the v2 values are smaller for heavier hadrons than that of lighter hadrons). At the intermediate pT (2GeV/cto6GeV/c) all mesons and all baryons form two different groups [35]. When v2 and pT are scaled by the number of constituent quarks (nq) of the hadrons, the magnitude of the scaled v2 is observed to be the same for all the hadrons at the intermediate pT. 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 heavy-ion collision [36, 37]. Since ϕ meson has mass (1.0194 GeV/c2) comparable to the masses of the lightest baryons such as proton and at the same time it is a meson, the study of ϕ meson v2 would be more appropriate to understand the mass type and/or particle type (baryon-meson) dependence of v2(pT).In this review we have compiled all the available experimental measurements onϕ meson production in high energy heavy-ion collisions as a function of pT, azimuthal angle (φ), and rapidity (y). This paper is organised in the following manner. In Section 2, measurement of ϕ meson invariant yield has been presented from SPS to LHC energy. Section 3 describes the compilation of the azimuthal anisotropy measurements in ϕ meson production from all the available experimental results. Finally, the summary and conclusion have been discussed in Section 4.


## 2. Invariant Yield ofϕ Meson

### 2.1. Invariant Transverse Momentum Spectra

We have compiled the data on the invariantpT spectra of the ϕ meson measured in p+p, d+A, and A + A systems for different collision centralities at various centre-of-mass energies (sNN=17.3GeV–7TeV) [16–22] and those are shown in Figure 2. Only the statistical errors are indicated as error bars. Measurement of ϕ meson invariant yield in p+p collisions at s=7TeV 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(1)12πpTd2NdydpT=dN/dy2πTm0+Texp-m02+pT2-m0T.The blue solid lines in Figure 2 are the fits to the data with Levy function of the form given by (2)12πpTd2NdydpT=dNdyn-1n-22πnTnT+m0n-2×1+pT2+m02-m0nT-n.T is known as the inverse slope parameter, dN/dy is the ϕ meson yield per unit rapidity, m0 is the rest mass of ϕ meson, and n is the Levy function parameter. Levy function is similar in shape to an exponential function at low pT and has a power-law-like shape at higher pT. In fact, the exponential function is the limit of the Levy function as n approaches infinity. From Figure 2, it can be seen that the exponential 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 χ2/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 pT spectra (deviations from exponential distribution and more towards a power law distribution) at high pT for peripheral collisions. Tsallis function also describes the measured identified spectra equally well as Levy, which is shown in [39, 40]. Like Levy, Tsallis function describes both the low pT exponential and the high pT 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 pT for p+p and d+Au collisions whereas Levy function describes data for all pT. 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 ϕ meson production in more peripheral collisions at higher pT. Particle production at low pT 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 pT. 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 n are large in the case central A + A collisions where both Levy and exponential functions fit the data well. The dN/dy values increase from peripheral to central collisions, indicating increasing production of ϕ meson with increase in collision centrality.Table 1
Results from Levy fits to the transverse mass distributions of theϕ meson. All values are for midrapidity (|y|<0.5).
Centrality
χ
2/ndf
T (GeV)
n
d
N
/
d
y
Pb + Pb (2.76 TeV)
0–10%
4.282/5
0.5005  ±  0.0128
1.121e06  ±  1.414e06
12.41  ±  0.796
10–20%
4.793/5
0.5131 ±  0.0132
4.969e05  ±  2.6e05
8.978  ±  0.553
20–30%
3.976/5
0.4926  ±  0.0429
162  ±  681.2
6.870  ±  0.415
30–40%
1.796/5
0.4897  ±  0.0454
129.6  ±  436.7
4.190  ±  0.262
40–50%
2.25/5
0.4401  ±  0.0424
28.34  ±  21
2.605  ±  0.162
50–60%
3.177/5
0.3946  ±  0.042
15.41  ±  6.68
1.457  ±  0.094
60–70%
0.551/5
0.3801  ±  0.0432
14.68  ±  6.23
0.7157  ±  0.050
70–80%
0.910/5
0.3401  ±  0.04351
10.41 ±  3.32
0.297  ±  0.022
Au + Au (200 GeV)
0–10%
9.4/11
0.3572  ±  0.002331
102.9 ± 116
7.421  ±  0.106
10–20%
19.2/11
0.3529  ±  0.002514
93.2 ± 101
5.142  ±  0.108
20–30%
15.2/11
0.3591  ±  0.002343
41.6 ± 5.6
3.442  ±  0.071
30–40%
16.2/11
0.3595  ±  0.002448
38.9 ± 20
2.189  ±  0.045
40–50%
21.4/11
0.3153  ±  0.003802
22.7  ±  4.3
1.392  ±  0.033
50–60%
6.9/11
0.2905  ±  0.003404
0.0138  ±  1.9
0.806  ±  0.023
60–70%
7.4/11
0.2916  ±  0.002911
0.0186  ±  3.6
0.419 ±  0.014
70–80%
5.5/11
0.2430  ±  0.002543
0.0130  ±  2.3
0.202  ±  0.009
Au + Au (62.4 GeV)
0–20%
9.2/8
0.3211 ±  0.00624
9.993e06  ±  6.39e06
3.693  ±  0.353
20–40%
8.8/8
0.3217 ±  0.00353
4.24e08  ±  7.41e06
1.590  ±  0.142
40–60%
14.5/8
0.2910 ±  0.00644
9.409e07  ±  e10
0.580  ±  0.071
60–80%
6.78/6
0.2681 ±  0.001426
21.45 ± 17.89
0.151  ±  0.020
Au + Au (39 GeV)
0–10%
1.645/9
0.2995 ±  0.01611
6.619e10  ±  8.931e05
3.402  ±  0.812
10–20%
1.046/9
0.3131  ±  0.03514
1.108e07  ±  1.414e04
2.216  ± 0.278
20–30%
1.55/8
0.2996  ±  0.01301
1.532e08  ±  6.651e05
1.597  ±  0.150
30–40%
1.047/9
0.2957  ±  0.04906
945  ±  356
1.019  ±  0.0773
40–60%
1.6383/9
0.2363  ±  0.03561
24.47  ±  14.96
0.456  ±  0.057
60–80%
1.705/9
0.2110  ±  0.03410
20.2  ±  10.72
0.128  ±  0.018
Au +  Au (27 GeV)
0–10%
3.719/9
0.2861 ±  0.007709
89.17  ±  78.22
3.051  ±  0.178
10–20%
10.05/9
0.2851  ±  0.0039
56.62  ±  38.42
2.004  ± 0.0278
20–30%
12.85/9
0.2747  ±  0.01754
46.3  ±  32.98
1.345  ±  0.082
30–40%
14.06/9
0.2574  ±  0.01741
40.36  ±  30.44
0.846  ± 0.053
40–60%
2.573/9
0.2114  ±  0.01696
19.3  ±  6.155
0.404  ±  0.026
60–80%
15.946/9
0.1901  ±  0.01368
23.34  ±  7.753
0.107  ±  0.007
Au + Au (19.6 GeV)
0–10%
10.28/8
0.2803 ±  0.00466
87.17  ±  69.63
2.603  ±  0.051
10–20%
10.96/8
0.2676  ±  0.01202
59.38  ±  47.27
1.786  ± 0.037
20–30%
9.75/8
0.2367  ±  0.01038
32.32  ±  13.11
1.263  ± 0.029
30–40%
8.804/8
0.2397  ±  0.01144
33.25  ±  26.33
0.759  ± 0.018
40–60%
14.31/8
0.1947  ±  0.00865
15.19  ±  2.743
0.336  ±  0.007
60–80%
7.346/8
0.1913  ±  0.00553
15.76  ±  2.849
0.080  ±  0.001
Pb + Pb (17.3 GeV)
0–4%
1.329/2
0.1746 ± 0.01043
1000  ±  1.175e05
0.00227  ± 0.0013
Au + Au (11.5 GeV)
0–10%
6.694/7
0.2662 ±  0.009276
100.73  ±  75.39
1.733  ±  0.112
10–20%
8.171/7
0.2653  ±  0.01187
60.29  ±  42.09
1.121  ± 0.076
20–30%
4.599/7
0.2282  ±  0.02887
37.3  ±  32.05
0.772  ± 0.054
30–40%
10.18/7
0.2353  ±  0.03014
34.36  ±  30.39
0.467  ± 0.034
40–60%
2.898/7
0.1846  ±  0.02255
18.9  ±  10.09
0.205  ±  0.015
60–80%
1.034/7
0.1438  ±  0.01981
11.31  ±  3.681
0.056  ±  0.005
Au+Au (7.7 GeV)
0–10%
1.5978/4
0.3082 ±  0.03636
90.33  ±  79.97
1.21  ±  0.098
10–20%
2.8/4
0.2419  ±  0.02615
64.29  ±  40.33
0.719  ± 0.061
20–30%
2.946/4
0.1639  ±  0.07128
50.19  ±  35.39
0.518  ± 0.091
30–40%
1.299/4
0.2039  ±  0.02201
63.3± 39.39
0.275  ± 0.024
40–60%
1.833/4
0.1562  ±  0.04774
7.10  ±  6.67
0.139  ± 0.015
60–80%
2.816/4
0.1423  ±  0.0842
15.02  ±  52.03
0.033  ± 0.007Table 2
Results from exponential fits to the transverse mass distributions of theϕ meson. All values are for midrapidity (|y|<0.5).
Centrality
χ
2/ndf
T (GeV)
d
N
/
d
y
Pb + Pb (2.76 TeV)
0–10%
4.28/6
0.5005  ±  0.0128
12.41  ±  0.795
10–20%
4.793/6
0.5131 ±  0.013
8.973  ±  0.502
20–30%
4.032/6
0.5024  ±  0.0127
4.032  ±  0.412
30–40%
1.88/6
0.5027  ±  0.0130
4.171  ±  0.013
40–50%
4.036/6
0.4961  ±  0.0137
2.550  ±  0.0162
50–60%
8.356/6
0.4901  ±  0.0146
1.408  ±  0.014
60–70%
5.937/6
0.4891  ±  0.0156
0.679  ±  0.047
70–80%
10.12/6
0.4815  ±  0.0182
0.271  ±  0.024
Au + Au (200 GeV)
0–10%
11.2/12
0.3562  ±  0.002431
7.440  ±  0.106
10–20%
9.7/12
0.3522  ±  0.002614
5.371  ±  0.108
20–30%
26.7/12
0.3731  ±  0.002413
3.435  ±  0.071
30–40%
21.1/12
0.3873  ±  0.002548
2.291  ±  0.045
40–50%
26.4/12
0.3671  ±  0.00307
1.342  ±  0.033
50–60%
70/12
0.3605  ±  0.003604
0.727  ±  0.023
60–70%
54.4/12
0.3516  ±  0.003911
0.380 ±  0.014
70–80%
31.7/12
0.3330  ±  0.004543
0.170  ±  0.009
Au + Au (62.4 GeV)
0–20%
8.4/9
0.328 ±  0.00624
3.523  ±  0.353
20–40%
8.4/9
0.324 ±  0.00353
1.590  ±  0.140
40–60%
14.5/9
0.308 ±  0.00644
0.584  ±  0.072
60–80%
13.3/9
0.2791 ±  0.01426
0.152  ±  0.022
Au + Au (39 GeV)
0–10%
10.36/10
0.3015 ±  0.0052
3.549  ±  0.070
10–20%
15.54/10
0.3019  ±  0.00522
2.347  ± 0.045
20–30%
3.946/9
0.3004  ±  0.005711
1.618  ± 0.030
30–40%
12.57/10
0.2826  ±  0.00398
1.067  ± 0.019
40–60%
20.62/10
0.267  ±  0.00362
0.498  ± 0.006
60–80%
21.08/10
0.2371  ±  0.00501
0.124  ± 0.002
Au + Au (27 GeV)
0–10%
26.13/10
0.29  ±  0.00245
3.46  ±  0.036
10–20%
32.3/10
0.2873  ±  0.00227
2.152  ± 0.023
20–30%
24.93/10
0.2766  ±  0.00236
1.471  ± 0.016
30–40%
13.57/10
0.2645  ±  0.00225
0.926  ± 0.010
40–60%
25.19/10
0.2601  ±  0.00217
0.422  ± 0.004
60–80%
71.08/10
0.2296  ±  0.00250
0.100  ± 0.001
Au + Au (19.6 GeV)
0–10%
28.87/9
0.2805  ±  0.003265
2.609  ±  0.038
10–20%
15.28/9
0.2788  ±  0.003722
1.817  ± 0.026
20–30%
13.63/9
0.2608  ±  0.003246
1.187  ± 0.017
30–40%
7.811/9
0.2652  ±  0.003917
0.763  ± 0.011
40–60%
17.78/9
0.2404  ±  0.003352
0.345  ± 0.004
60–80%
10.06/9
0.2142  ±  0.003558
0.072  ± 0.001
Pb + Pb (17.3 GeV)
0–4%
1.337/3
0.1748 ± 0.01043
0.0022  ± 0.0012
Au + Au (11.5 GeV)
0–10%
11.5/8
0.2621  ±  0.006674
1.754  ±  0.047
10–20%
9.638/8
0.265  ±  0.006731
1.281  ± 0.033
20–30%
6.885/8
0.2359  ±  0.006009
0.843  ± 0.022
30–40%
1.946/8
0.2453  ±  0.005765
0.506  ± 0.013
40–60%
2.862/8
0.2071  ±  0.00545
0.235  ± 0.005
60–80%
11.12/8
0.1947  ±  0.00888
0.051  ± 0.001
Au + Au (7.7 GeV)
0–10%
3.36/5
0.3082  ±  0.03087
1.207  ±  0.069
10–20%
10.46/5
0.2553  ±  0.01811
0.783  ±  0.036
20–30%
9.767/5
0.2207  ±  0.0141
0.471  ±  0.023
30–40%
4.177/5
0.2375  ±  0.01926
0.329  ±  0.017
40–60%
0.4763/5
0.2195  ±  0.01467
0.147  ± 0.007
60–80%
3.958/5
0.1992  ±  0.02282
0.035  ±  0.002Figure 2
The invariant yield ofϕ mesons as a function of pT measured for different system and different centralities at various centre-of-mass energies [16–21]. The black dashed (blue solid) line represents an exponential (Levy) function fit to the data.
(a)
p +p INEL
(b)
p +p (NSD) 200 GeV
(c)
d + Au 200 GeV
(d)
Pb + Pb 17.3 GeV
(e)
Au + Au 7.7 Gev
(f)
Au + Au 11.5 GeV
(g)
Au + Au 19.6 GeV
(h)
Au + Au 27 GeV
(i)
Au + Au 39 GeV
(j)
Au + Au 62.4 GeV
(k)
Au + Au 200 GeV
(l)
Pb + Pb 2.76 TeV


### 2.2.ϕ Meson Yield per Unit Rapidity

In Figure3 we present all available measurements of pT integrated ϕ meson yield (dN/dy) at midrapidity as a function of centre-of-mass energy in both nucleus-nucleus [16–18, 21] and proton-proton 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 p+p collisions. The rate of increases with sNN  is higher in A + A collisions compared to p+p collisions. We have observed that the measured midrapidity yield per participant (Npart) pair, (dN/dy)/(0.5Npart), increases nonlinearly with centrality and for the same Npart(dN/dy)/(0.5Npart) increases with the collision energy of the A + A collisions. The former suggests that particle production does not scale with Npart and the latter is expected because of the increase of energy available to produce the ϕ mesons.Figure 3
Theϕ meson midrapidity yield (dN/dy) as a function of sNN for A + A [16–18, 21] and p+p collisions [18–20, 22, 23]. For RHIC BES energies (sNN=7.7–39GeV) only statistical errors are shown whereas for other energies systematic errors are added in quadrature with statistical errors.
(a)
A + A
(b)
p +p(dN/dy)×200


### 2.3. Strangeness Enhancement

The ratio of strange hadron production normalised toNpart in nucleus-nucleus collisions relative to corresponding results from p+p collisions at 200 GeV [24] is shown in the left upper panel of Figure 4. The results are plotted as a function of Npart. K-, 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 ϕ 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 K- and Λ have similar enhancement, or a mass effect, since Λ and ϕ have similar mass but different enhancement factors.Figure 4
(a) The ratio of the yields ofK-, ϕ, Λ-, and Ξ+Ξ- normalised to Npart nucleus-nucleus collisions and to corresponding yields in proton-proton collisions as a function of Npart at 62.4 and 200 GeV [24]. Error bars are quadrature sum of statistical and systematic uncertainties. (b) The ratio of Npart normalised yield of ϕ, Λ, Λ-, Ξ-, and Ω-+Ω-+ in Pb + Pb collisions to the corresponding yield in p+p (p + Be) collisions at 17.3 GeV (NA57 & NA49) [25, 26] and 2.76 TeV (ALICE) [21]. Only statistical uncertainties are shown.
(a)
(b)In heavy-ion collisions, the production ofϕ mesons is not Canonically suppressed due to its ss- structure. The p+p 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 ϕ 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, ϕ 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 ϕ meson production being related to medium density is further supported by the energy dependence shown in the lower panel of Figure 4. The ϕ meson production relative to p+p 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 Figure4 shows the enhancement in Pb + Pb with respect to p+p reference yields for ϕ, Λ, Ξ-, and Ω-+Ω-+ at sNN=2.76TeV [21]. The ϕ, Ξ, and Ω yield in p+p collisions at s=2.76TeV have been estimated by interpolating between the measured yields at s=0.9TeV and s=7TeV. The reference Λ yield in p+p collisions at sNN=2.76TeV is estimated by extrapolating from the measured yield in (inelastic) p+p collisions available up to s=0.9TeV. Details can be found in [21]. Enhancement factor increases linearly with Npart until Npart≈100; then the enhancement values seem to be saturated for higher values of Npart. Unlike SPS and RHIC, the order of ϕ enhancement is the same as Ξ- at LHC energy. We have observed that the ϕ 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 observedϕ 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.


### 2.4. Nuclear Modification Factor

In order to understand parton energy loss in the medium created in high energy heavy-ion collisions for different centralities in A + A collisions, the nuclear modification factor(RCP) is measured which is defined as follows:(3)RCP=YieldcentralYieldperipheral×NbinperipheralNbincentral,where Nbin is the average number of binary collisions for the corresponding centrality. The value of Nbin was calculated from the Monte Carlo Glauber simulation [43]. RCP value is equal to one when the nucleus-nucleus collisions are simply the superposition of nucleon-nucleon collisions. Therefore deviation of RCP from the unity would imply contribution from the nuclear medium effects, specifically jet-quenching [44]. Nuclear modification factors (RCP) of ϕ mesons at midrapidity in Au + Au collisions at sNN=7.7,11.5,19.6,27,39, and 200 GeV [17, 18] and in Pb + Pb collisions at sNN=2.76TeV [21] are shown in Figure 5. We can see that the RCP of ϕ 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 sNN≤39GeV, ϕ meson RCP is greater than or equal to unity at the intermediate pT, which indicates that at low energy the parton energy loss contribution to RCP measurement could be less important. In order to confirm that the RCP<1 is due to parton energy loss or jet-quenching phenomenon, it is important to study RCP in p + A ord + 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 RCP at high pT is expected to be greater than one.Figure 5
Theϕ meson RCP as a function of pT in Au + Au [17, 18] and Pb + Pb [21] collisions at various beam energies. Error bars are only statistical uncertainties. Bands represent normalisation error from Nbin which is approximately 20% for sNN=7.7–39 GeV, ~10% for 200 GeV, and ~7% for 2.76 TeV.Figure6 presents the pT dependence of the nuclear modification factor RAB in Au + Au andd + Au collisions at sNN=200GeV [18, 27]. The definition of RAB is the ratio of the yields of the hadron produced in the nucleus (A) + nucleus (B) collisions to the corresponding yields in the inelastic p+p collisions normalised by Nbin. The RAB of ϕ mesons ford + Au collisions show a similar enhancement trend as those for π++π- and p+p- at the intermediate pT. This enhancement ind + 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 pT. Current experimental measurements on ϕ meson RAB ind + Au do not seem to have the precision to differentiate between particle type dependence types [49, 50]. On the other hand, the RAB in Au + Au (i.e., RAA) at 200 GeV is lower than that ind + 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.Figure 6
The nuclear modification factorRAB as a function of pT in Au + Au andd + Au [18, 27] collisions at sNN=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 ϕ ind + Au and only statistical for three other cases.


### 2.5. Mean Transverse Mass

Figure7 shows the difference in mean transverse mass (mT=pT2+m02) and rest mass (m0), that is, mT-m0 for ϕ meson, as a function of centre-of-mass energy for p+p [18, 20, 22], Au + Au [17, 18], and Pb + Pb [16, 21] collisions. Due to limited statistics, result for p+p at s=900GeV 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 mT-m0 increases monotonically with sNN in p+p collisions whereas the corresponding data in A + A collisions changes slope twice as a function of center-of-mass energy. In A + A collisions, mT-m0 first increases with sNN and then stays independent of energy from approximately 17 GeV to 39 GeV, followed by again an increase with sNN. For a thermodynamic system, the mT-m0 can be interpreted as a measure of temperature of the system, and dN/dy∝ln(sNN) 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 mT-m0 for ϕ 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.Figure 7
m
T
-
m
0 as a function centre-of-mass energies in central A + A and p + p 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.


### 2.6. Particle Ratios

#### 2.6.1.ϕ/K-

The mechanism forϕ meson production in high energy collisions has remained an open issue. In an environment with many strange quarks, ϕ mesons can be produced readily through coalescence, bypassing the OZI rule [52]. On the other hand, a naive interpretation of ϕ meson production in heavy-ion collisions would be the ϕ production via kaon coalescence. In the latter case one could expect an increasing trend of ϕ/K 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 ϕ/K- ratio at midrapidity as a function of centrality [18]. Therefore, the ratio of ϕ meson yield to that of the kaons can be used to shed light on ϕ meson production mechanism. Figure 8 shows the ϕ/K- ratio as a function of number of participants for different centre-of-mass energies [18]. The UrQMD model prediction for ϕ/K- 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 ϕ/K- is independent of centrality and also centre-of-mass energy. In addition, if ϕ production is dominantly from KK- coalescence, one expects the width of the rapidity distribution of ϕ mesons to be related to those for charged kaons as 1/σϕ2=1/σK-2+1/σK+2. Measurements at SPS energies show a clear deviation of the data from the above expectation [55]. Finally, if ϕ production is dominantly from KK- coalescence it would be reflected in elliptic flow (v2) measurements. We observe at intermediate pT that the v2 of ϕ mesons and kaons are comparable (discussed in Section 3). All these measurements effectively rule out kaon coalescence as the dominant production mechanism for the ϕ meson for this energy region.Figure 8
ϕ
/
K
- ratio as a function of number of participants in Au + Au [18] and Pb + Pb [21] collision at various beam energies.


#### 2.6.2.Ω/ϕ

The production mechanism of multistrange hadrons (e.g.,ϕ and Ω) is predicted to be very sensitive to the early phase of nuclear collisions [56], because both ϕ and Ω freeze out early, have low hadronic interaction cross-section, and are purely made of strange and antistrange quarks. Therefore the ratio N(Ω)/N(ϕ) 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, N(Ω-+Ω¯+)/2N(ϕ), as a function of pT in Au + Au collisions at sNN=11.5GeV to 2760 GeV [17, 18, 21]. The dashed lines are the results from the recombination model calculation by Hwa and Yang for sNN=200GeV [57]. In this model the ϕ and Ω yields in the measured pT region are mostly from the recombination of thermal strange quarks, which were assumed to follow an exponential pT distribution. The thermal s quark distribution was determined by fitting the low pT data of kaon production. The contribution from hard parton scattering was assumed to be negligible unless pT is large. Details of this recombination model have been given in [57]. We can see from Figure 9 that, in central A + A collisions at sNN≥19.6GeV, the ratios of N(Ω-+Ω¯+)/2N(ϕ) in the intermediate pT 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 pT~4GeV/c which covers ~95% of the total yields for the ϕ and Ω. The observations imply that the production of ϕ and Ω in central Au + Au collisions is predominantly through the recombination of thermal s quarks for sNN≥19.6GeV. But at sNN=11.5GeV, the ratio at the highest measured pT shows a deviation from the trend of other energies. This may indicate a change in Ω and/or ϕ production mechanism at sNN = 11.5 GeV.Figure 9
The baryon-to-meson ratio,N(Ω-+Ω¯+)/2N(ϕ), as a function of pT in midrapidity (y<0.5) from central A + A collisions at sNN=11.5,19.6,27,39,200, and 2760 GeV [17, 18, 21]. Gray bands denote systematical errors.


## 2.1. Invariant Transverse Momentum Spectra

We have compiled the data on the invariantpT spectra of the ϕ meson measured in p+p, d+A, and A + A systems for different collision centralities at various centre-of-mass energies (sNN=17.3GeV–7TeV) [16–22] and those are shown in Figure 2. Only the statistical errors are indicated as error bars. Measurement of ϕ meson invariant yield in p+p collisions at s=7TeV 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(1)12πpTd2NdydpT=dN/dy2πTm0+Texp-m02+pT2-m0T.The blue solid lines in Figure 2 are the fits to the data with Levy function of the form given by (2)12πpTd2NdydpT=dNdyn-1n-22πnTnT+m0n-2×1+pT2+m02-m0nT-n.T is known as the inverse slope parameter, dN/dy is the ϕ meson yield per unit rapidity, m0 is the rest mass of ϕ meson, and n is the Levy function parameter. Levy function is similar in shape to an exponential function at low pT and has a power-law-like shape at higher pT. In fact, the exponential function is the limit of the Levy function as n approaches infinity. From Figure 2, it can be seen that the exponential 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 χ2/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 pT spectra (deviations from exponential distribution and more towards a power law distribution) at high pT for peripheral collisions. Tsallis function also describes the measured identified spectra equally well as Levy, which is shown in [39, 40]. Like Levy, Tsallis function describes both the low pT exponential and the high pT 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 pT for p+p and d+Au collisions whereas Levy function describes data for all pT. 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 ϕ meson production in more peripheral collisions at higher pT. Particle production at low pT 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 pT. 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 n are large in the case central A + A collisions where both Levy and exponential functions fit the data well. The dN/dy values increase from peripheral to central collisions, indicating increasing production of ϕ meson with increase in collision centrality.Table 1
Results from Levy fits to the transverse mass distributions of theϕ meson. All values are for midrapidity (|y|<0.5).
Centrality
χ
2/ndf
T (GeV)
n
d
N
/
d
y
Pb + Pb (2.76 TeV)
0–10%
4.282/5
0.5005  ±  0.0128
1.121e06  ±  1.414e06
12.41  ±  0.796
10–20%
4.793/5
0.5131 ±  0.0132
4.969e05  ±  2.6e05
8.978  ±  0.553
20–30%
3.976/5
0.4926  ±  0.0429
162  ±  681.2
6.870  ±  0.415
30–40%
1.796/5
0.4897  ±  0.0454
129.6  ±  436.7
4.190  ±  0.262
40–50%
2.25/5
0.4401  ±  0.0424
28.34  ±  21
2.605  ±  0.162
50–60%
3.177/5
0.3946  ±  0.042
15.41  ±  6.68
1.457  ±  0.094
60–70%
0.551/5
0.3801  ±  0.0432
14.68  ±  6.23
0.7157  ±  0.050
70–80%
0.910/5
0.3401  ±  0.04351
10.41 ±  3.32
0.297  ±  0.022
Au + Au (200 GeV)
0–10%
9.4/11
0.3572  ±  0.002331
102.9 ± 116
7.421  ±  0.106
10–20%
19.2/11
0.3529  ±  0.002514
93.2 ± 101
5.142  ±  0.108
20–30%
15.2/11
0.3591  ±  0.002343
41.6 ± 5.6
3.442  ±  0.071
30–40%
16.2/11
0.3595  ±  0.002448
38.9 ± 20
2.189  ±  0.045
40–50%
21.4/11
0.3153  ±  0.003802
22.7  ±  4.3
1.392  ±  0.033
50–60%
6.9/11
0.2905  ±  0.003404
0.0138  ±  1.9
0.806  ±  0.023
60–70%
7.4/11
0.2916  ±  0.002911
0.0186  ±  3.6
0.419 ±  0.014
70–80%
5.5/11
0.2430  ±  0.002543
0.0130  ±  2.3
0.202  ±  0.009
Au + Au (62.4 GeV)
0–20%
9.2/8
0.3211 ±  0.00624
9.993e06  ±  6.39e06
3.693  ±  0.353
20–40%
8.8/8
0.3217 ±  0.00353
4.24e08  ±  7.41e06
1.590  ±  0.142
40–60%
14.5/8
0.2910 ±  0.00644
9.409e07  ±  e10
0.580  ±  0.071
60–80%
6.78/6
0.2681 ±  0.001426
21.45 ± 17.89
0.151  ±  0.020
Au + Au (39 GeV)
0–10%
1.645/9
0.2995 ±  0.01611
6.619e10  ±  8.931e05
3.402  ±  0.812
10–20%
1.046/9
0.3131  ±  0.03514
1.108e07  ±  1.414e04
2.216  ± 0.278
20–30%
1.55/8
0.2996  ±  0.01301
1.532e08  ±  6.651e05
1.597  ±  0.150
30–40%
1.047/9
0.2957  ±  0.04906
945  ±  356
1.019  ±  0.0773
40–60%
1.6383/9
0.2363  ±  0.03561
24.47  ±  14.96
0.456  ±  0.057
60–80%
1.705/9
0.2110  ±  0.03410
20.2  ±  10.72
0.128  ±  0.018
Au +  Au (27 GeV)
0–10%
3.719/9
0.2861 ±  0.007709
89.17  ±  78.22
3.051  ±  0.178
10–20%
10.05/9
0.2851  ±  0.0039
56.62  ±  38.42
2.004  ± 0.0278
20–30%
12.85/9
0.2747  ±  0.01754
46.3  ±  32.98
1.345  ±  0.082
30–40%
14.06/9
0.2574  ±  0.01741
40.36  ±  30.44
0.846  ± 0.053
40–60%
2.573/9
0.2114  ±  0.01696
19.3  ±  6.155
0.404  ±  0.026
60–80%
15.946/9
0.1901  ±  0.01368
23.34  ±  7.753
0.107  ±  0.007
Au + Au (19.6 GeV)
0–10%
10.28/8
0.2803 ±  0.00466
87.17  ±  69.63
2.603  ±  0.051
10–20%
10.96/8
0.2676  ±  0.01202
59.38  ±  47.27
1.786  ± 0.037
20–30%
9.75/8
0.2367  ±  0.01038
32.32  ±  13.11
1.263  ± 0.029
30–40%
8.804/8
0.2397  ±  0.01144
33.25  ±  26.33
0.759  ± 0.018
40–60%
14.31/8
0.1947  ±  0.00865
15.19  ±  2.743
0.336  ±  0.007
60–80%
7.346/8
0.1913  ±  0.00553
15.76  ±  2.849
0.080  ±  0.001
Pb + Pb (17.3 GeV)
0–4%
1.329/2
0.1746 ± 0.01043
1000  ±  1.175e05
0.00227  ± 0.0013
Au + Au (11.5 GeV)
0–10%
6.694/7
0.2662 ±  0.009276
100.73  ±  75.39
1.733  ±  0.112
10–20%
8.171/7
0.2653  ±  0.01187
60.29  ±  42.09
1.121  ± 0.076
20–30%
4.599/7
0.2282  ±  0.02887
37.3  ±  32.05
0.772  ± 0.054
30–40%
10.18/7
0.2353  ±  0.03014
34.36  ±  30.39
0.467  ± 0.034
40–60%
2.898/7
0.1846  ±  0.02255
18.9  ±  10.09
0.205  ±  0.015
60–80%
1.034/7
0.1438  ±  0.01981
11.31  ±  3.681
0.056  ±  0.005
Au+Au (7.7 GeV)
0–10%
1.5978/4
0.3082 ±  0.03636
90.33  ±  79.97
1.21  ±  0.098
10–20%
2.8/4
0.2419  ±  0.02615
64.29  ±  40.33
0.719  ± 0.061
20–30%
2.946/4
0.1639  ±  0.07128
50.19  ±  35.39
0.518  ± 0.091
30–40%
1.299/4
0.2039  ±  0.02201
63.3± 39.39
0.275  ± 0.024
40–60%
1.833/4
0.1562  ±  0.04774
7.10  ±  6.67
0.139  ± 0.015
60–80%
2.816/4
0.1423  ±  0.0842
15.02  ±  52.03
0.033  ± 0.007Table 2
Results from exponential fits to the transverse mass distributions of theϕ meson. All values are for midrapidity (|y|<0.5).
Centrality
χ
2/ndf
T (GeV)
d
N
/
d
y
Pb + Pb (2.76 TeV)
0–10%
4.28/6
0.5005  ±  0.0128
12.41  ±  0.795
10–20%
4.793/6
0.5131 ±  0.013
8.973  ±  0.502
20–30%
4.032/6
0.5024  ±  0.0127
4.032  ±  0.412
30–40%
1.88/6
0.5027  ±  0.0130
4.171  ±  0.013
40–50%
4.036/6
0.4961  ±  0.0137
2.550  ±  0.0162
50–60%
8.356/6
0.4901  ±  0.0146
1.408  ±  0.014
60–70%
5.937/6
0.4891  ±  0.0156
0.679  ±  0.047
70–80%
10.12/6
0.4815  ±  0.0182
0.271  ±  0.024
Au + Au (200 GeV)
0–10%
11.2/12
0.3562  ±  0.002431
7.440  ±  0.106
10–20%
9.7/12
0.3522  ±  0.002614
5.371  ±  0.108
20–30%
26.7/12
0.3731  ±  0.002413
3.435  ±  0.071
30–40%
21.1/12
0.3873  ±  0.002548
2.291  ±  0.045
40–50%
26.4/12
0.3671  ±  0.00307
1.342  ±  0.033
50–60%
70/12
0.3605  ±  0.003604
0.727  ±  0.023
60–70%
54.4/12
0.3516  ±  0.003911
0.380 ±  0.014
70–80%
31.7/12
0.3330  ±  0.004543
0.170  ±  0.009
Au + Au (62.4 GeV)
0–20%
8.4/9
0.328 ±  0.00624
3.523  ±  0.353
20–40%
8.4/9
0.324 ±  0.00353
1.590  ±  0.140
40–60%
14.5/9
0.308 ±  0.00644
0.584  ±  0.072
60–80%
13.3/9
0.2791 ±  0.01426
0.152  ±  0.022
Au + Au (39 GeV)
0–10%
10.36/10
0.3015 ±  0.0052
3.549  ±  0.070
10–20%
15.54/10
0.3019  ±  0.00522
2.347  ± 0.045
20–30%
3.946/9
0.3004  ±  0.005711
1.618  ± 0.030
30–40%
12.57/10
0.2826  ±  0.00398
1.067  ± 0.019
40–60%
20.62/10
0.267  ±  0.00362
0.498  ± 0.006
60–80%
21.08/10
0.2371  ±  0.00501
0.124  ± 0.002
Au + Au (27 GeV)
0–10%
26.13/10
0.29  ±  0.00245
3.46  ±  0.036
10–20%
32.3/10
0.2873  ±  0.00227
2.152  ± 0.023
20–30%
24.93/10
0.2766  ±  0.00236
1.471  ± 0.016
30–40%
13.57/10
0.2645  ±  0.00225
0.926  ± 0.010
40–60%
25.19/10
0.2601  ±  0.00217
0.422  ± 0.004
60–80%
71.08/10
0.2296  ±  0.00250
0.100  ± 0.001
Au + Au (19.6 GeV)
0–10%
28.87/9
0.2805  ±  0.003265
2.609  ±  0.038
10–20%
15.28/9
0.2788  ±  0.003722
1.817  ± 0.026
20–30%
13.63/9
0.2608  ±  0.003246
1.187  ± 0.017
30–40%
7.811/9
0.2652  ±  0.003917
0.763  ± 0.011
40–60%
17.78/9
0.2404  ±  0.003352
0.345  ± 0.004
60–80%
10.06/9
0.2142  ±  0.003558
0.072  ± 0.001
Pb + Pb (17.3 GeV)
0–4%
1.337/3
0.1748 ± 0.01043
0.0022  ± 0.0012
Au + Au (11.5 GeV)
0–10%
11.5/8
0.2621  ±  0.006674
1.754  ±  0.047
10–20%
9.638/8
0.265  ±  0.006731
1.281  ± 0.033
20–30%
6.885/8
0.2359  ±  0.006009
0.843  ± 0.022
30–40%
1.946/8
0.2453  ±  0.005765
0.506  ± 0.013
40–60%
2.862/8
0.2071  ±  0.00545
0.235  ± 0.005
60–80%
11.12/8
0.1947  ±  0.00888
0.051  ± 0.001
Au + Au (7.7 GeV)
0–10%
3.36/5
0.3082  ±  0.03087
1.207  ±  0.069
10–20%
10.46/5
0.2553  ±  0.01811
0.783  ±  0.036
20–30%
9.767/5
0.2207  ±  0.0141
0.471  ±  0.023
30–40%
4.177/5
0.2375  ±  0.01926
0.329  ±  0.017
40–60%
0.4763/5
0.2195  ±  0.01467
0.147  ± 0.007
60–80%
3.958/5
0.1992  ±  0.02282
0.035  ±  0.002Figure 2
The invariant yield ofϕ mesons as a function of pT measured for different system and different centralities at various centre-of-mass energies [16–21]. The black dashed (blue solid) line represents an exponential (Levy) function fit to the data.
(a)
p +p INEL
(b)
p +p (NSD) 200 GeV
(c)
d + Au 200 GeV
(d)
Pb + Pb 17.3 GeV
(e)
Au + Au 7.7 Gev
(f)
Au + Au 11.5 GeV
(g)
Au + Au 19.6 GeV
(h)
Au + Au 27 GeV
(i)
Au + Au 39 GeV
(j)
Au + Au 62.4 GeV
(k)
Au + Au 200 GeV
(l)
Pb + Pb 2.76 TeV


## 2.2.ϕ Meson Yield per Unit Rapidity

In Figure3 we present all available measurements of pT integrated ϕ meson yield (dN/dy) at midrapidity as a function of centre-of-mass energy in both nucleus-nucleus [16–18, 21] and proton-proton 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 p+p collisions. The rate of increases with sNN  is higher in A + A collisions compared to p+p collisions. We have observed that the measured midrapidity yield per participant (Npart) pair, (dN/dy)/(0.5Npart), increases nonlinearly with centrality and for the same Npart(dN/dy)/(0.5Npart) increases with the collision energy of the A + A collisions. The former suggests that particle production does not scale with Npart and the latter is expected because of the increase of energy available to produce the ϕ mesons.Figure 3
Theϕ meson midrapidity yield (dN/dy) as a function of sNN for A + A [16–18, 21] and p+p collisions [18–20, 22, 23]. For RHIC BES energies (sNN=7.7–39GeV) only statistical errors are shown whereas for other energies systematic errors are added in quadrature with statistical errors.
(a)
A + A
(b)
p +p(dN/dy)×200


## 2.3. Strangeness Enhancement

The ratio of strange hadron production normalised toNpart in nucleus-nucleus collisions relative to corresponding results from p+p collisions at 200 GeV [24] is shown in the left upper panel of Figure 4. The results are plotted as a function of Npart. K-, 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 ϕ 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 K- and Λ have similar enhancement, or a mass effect, since Λ and ϕ have similar mass but different enhancement factors.Figure 4
(a) The ratio of the yields ofK-, ϕ, Λ-, and Ξ+Ξ- normalised to Npart nucleus-nucleus collisions and to corresponding yields in proton-proton collisions as a function of Npart at 62.4 and 200 GeV [24]. Error bars are quadrature sum of statistical and systematic uncertainties. (b) The ratio of Npart normalised yield of ϕ, Λ, Λ-, Ξ-, and Ω-+Ω-+ in Pb + Pb collisions to the corresponding yield in p+p (p + Be) collisions at 17.3 GeV (NA57 & NA49) [25, 26] and 2.76 TeV (ALICE) [21]. Only statistical uncertainties are shown.
(a)
(b)In heavy-ion collisions, the production ofϕ mesons is not Canonically suppressed due to its ss- structure. The p+p 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 ϕ 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, ϕ 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 ϕ meson production being related to medium density is further supported by the energy dependence shown in the lower panel of Figure 4. The ϕ meson production relative to p+p 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 Figure4 shows the enhancement in Pb + Pb with respect to p+p reference yields for ϕ, Λ, Ξ-, and Ω-+Ω-+ at sNN=2.76TeV [21]. The ϕ, Ξ, and Ω yield in p+p collisions at s=2.76TeV have been estimated by interpolating between the measured yields at s=0.9TeV and s=7TeV. The reference Λ yield in p+p collisions at sNN=2.76TeV is estimated by extrapolating from the measured yield in (inelastic) p+p collisions available up to s=0.9TeV. Details can be found in [21]. Enhancement factor increases linearly with Npart until Npart≈100; then the enhancement values seem to be saturated for higher values of Npart. Unlike SPS and RHIC, the order of ϕ enhancement is the same as Ξ- at LHC energy. We have observed that the ϕ 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 observedϕ 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.


## 2.4. Nuclear Modification Factor

In order to understand parton energy loss in the medium created in high energy heavy-ion collisions for different centralities in A + A collisions, the nuclear modification factor(RCP) is measured which is defined as follows:(3)RCP=YieldcentralYieldperipheral×NbinperipheralNbincentral,where Nbin is the average number of binary collisions for the corresponding centrality. The value of Nbin was calculated from the Monte Carlo Glauber simulation [43]. RCP value is equal to one when the nucleus-nucleus collisions are simply the superposition of nucleon-nucleon collisions. Therefore deviation of RCP from the unity would imply contribution from the nuclear medium effects, specifically jet-quenching [44]. Nuclear modification factors (RCP) of ϕ mesons at midrapidity in Au + Au collisions at sNN=7.7,11.5,19.6,27,39, and 200 GeV [17, 18] and in Pb + Pb collisions at sNN=2.76TeV [21] are shown in Figure 5. We can see that the RCP of ϕ 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 sNN≤39GeV, ϕ meson RCP is greater than or equal to unity at the intermediate pT, which indicates that at low energy the parton energy loss contribution to RCP measurement could be less important. In order to confirm that the RCP<1 is due to parton energy loss or jet-quenching phenomenon, it is important to study RCP in p + A ord + 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 RCP at high pT is expected to be greater than one.Figure 5
Theϕ meson RCP as a function of pT in Au + Au [17, 18] and Pb + Pb [21] collisions at various beam energies. Error bars are only statistical uncertainties. Bands represent normalisation error from Nbin which is approximately 20% for sNN=7.7–39 GeV, ~10% for 200 GeV, and ~7% for 2.76 TeV.Figure6 presents the pT dependence of the nuclear modification factor RAB in Au + Au andd + Au collisions at sNN=200GeV [18, 27]. The definition of RAB is the ratio of the yields of the hadron produced in the nucleus (A) + nucleus (B) collisions to the corresponding yields in the inelastic p+p collisions normalised by Nbin. The RAB of ϕ mesons ford + Au collisions show a similar enhancement trend as those for π++π- and p+p- at the intermediate pT. This enhancement ind + 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 pT. Current experimental measurements on ϕ meson RAB ind + Au do not seem to have the precision to differentiate between particle type dependence types [49, 50]. On the other hand, the RAB in Au + Au (i.e., RAA) at 200 GeV is lower than that ind + 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.Figure 6
The nuclear modification factorRAB as a function of pT in Au + Au andd + Au [18, 27] collisions at sNN=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 ϕ ind + Au and only statistical for three other cases.


## 2.5. Mean Transverse Mass

Figure7 shows the difference in mean transverse mass (mT=pT2+m02) and rest mass (m0), that is, mT-m0 for ϕ meson, as a function of centre-of-mass energy for p+p [18, 20, 22], Au + Au [17, 18], and Pb + Pb [16, 21] collisions. Due to limited statistics, result for p+p at s=900GeV 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 mT-m0 increases monotonically with sNN in p+p collisions whereas the corresponding data in A + A collisions changes slope twice as a function of center-of-mass energy. In A + A collisions, mT-m0 first increases with sNN and then stays independent of energy from approximately 17 GeV to 39 GeV, followed by again an increase with sNN. For a thermodynamic system, the mT-m0 can be interpreted as a measure of temperature of the system, and dN/dy∝ln(sNN) 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 mT-m0 for ϕ 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.Figure 7
m
T
-
m
0 as a function centre-of-mass energies in central A + A and p + p 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.


## 2.6. Particle Ratios

### 2.6.1.ϕ/K-

The mechanism forϕ meson production in high energy collisions has remained an open issue. In an environment with many strange quarks, ϕ mesons can be produced readily through coalescence, bypassing the OZI rule [52]. On the other hand, a naive interpretation of ϕ meson production in heavy-ion collisions would be the ϕ production via kaon coalescence. In the latter case one could expect an increasing trend of ϕ/K 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 ϕ/K- ratio at midrapidity as a function of centrality [18]. Therefore, the ratio of ϕ meson yield to that of the kaons can be used to shed light on ϕ meson production mechanism. Figure 8 shows the ϕ/K- ratio as a function of number of participants for different centre-of-mass energies [18]. The UrQMD model prediction for ϕ/K- 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 ϕ/K- is independent of centrality and also centre-of-mass energy. In addition, if ϕ production is dominantly from KK- coalescence, one expects the width of the rapidity distribution of ϕ mesons to be related to those for charged kaons as 1/σϕ2=1/σK-2+1/σK+2. Measurements at SPS energies show a clear deviation of the data from the above expectation [55]. Finally, if ϕ production is dominantly from KK- coalescence it would be reflected in elliptic flow (v2) measurements. We observe at intermediate pT that the v2 of ϕ mesons and kaons are comparable (discussed in Section 3). All these measurements effectively rule out kaon coalescence as the dominant production mechanism for the ϕ meson for this energy region.Figure 8
ϕ
/
K
- ratio as a function of number of participants in Au + Au [18] and Pb + Pb [21] collision at various beam energies.


### 2.6.2.Ω/ϕ

The production mechanism of multistrange hadrons (e.g.,ϕ and Ω) is predicted to be very sensitive to the early phase of nuclear collisions [56], because both ϕ and Ω freeze out early, have low hadronic interaction cross-section, and are purely made of strange and antistrange quarks. Therefore the ratio N(Ω)/N(ϕ) 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, N(Ω-+Ω¯+)/2N(ϕ), as a function of pT in Au + Au collisions at sNN=11.5GeV to 2760 GeV [17, 18, 21]. The dashed lines are the results from the recombination model calculation by Hwa and Yang for sNN=200GeV [57]. In this model the ϕ and Ω yields in the measured pT region are mostly from the recombination of thermal strange quarks, which were assumed to follow an exponential pT distribution. The thermal s quark distribution was determined by fitting the low pT data of kaon production. The contribution from hard parton scattering was assumed to be negligible unless pT is large. Details of this recombination model have been given in [57]. We can see from Figure 9 that, in central A + A collisions at sNN≥19.6GeV, the ratios of N(Ω-+Ω¯+)/2N(ϕ) in the intermediate pT 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 pT~4GeV/c which covers ~95% of the total yields for the ϕ and Ω. The observations imply that the production of ϕ and Ω in central Au + Au collisions is predominantly through the recombination of thermal s quarks for sNN≥19.6GeV. But at sNN=11.5GeV, the ratio at the highest measured pT shows a deviation from the trend of other energies. This may indicate a change in Ω and/or ϕ production mechanism at sNN = 11.5 GeV.Figure 9
The baryon-to-meson ratio,N(Ω-+Ω¯+)/2N(ϕ), as a function of pT in midrapidity (y<0.5) from central A + A collisions at sNN=11.5,19.6,27,39,200, and 2760 GeV [17, 18, 21]. Gray bands denote systematical errors.


## 2.6.1.ϕ/K-

The mechanism forϕ meson production in high energy collisions has remained an open issue. In an environment with many strange quarks, ϕ mesons can be produced readily through coalescence, bypassing the OZI rule [52]. On the other hand, a naive interpretation of ϕ meson production in heavy-ion collisions would be the ϕ production via kaon coalescence. In the latter case one could expect an increasing trend of ϕ/K 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 ϕ/K- ratio at midrapidity as a function of centrality [18]. Therefore, the ratio of ϕ meson yield to that of the kaons can be used to shed light on ϕ meson production mechanism. Figure 8 shows the ϕ/K- ratio as a function of number of participants for different centre-of-mass energies [18]. The UrQMD model prediction for ϕ/K- 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 ϕ/K- is independent of centrality and also centre-of-mass energy. In addition, if ϕ production is dominantly from KK- coalescence, one expects the width of the rapidity distribution of ϕ mesons to be related to those for charged kaons as 1/σϕ2=1/σK-2+1/σK+2. Measurements at SPS energies show a clear deviation of the data from the above expectation [55]. Finally, if ϕ production is dominantly from KK- coalescence it would be reflected in elliptic flow (v2) measurements. We observe at intermediate pT that the v2 of ϕ mesons and kaons are comparable (discussed in Section 3). All these measurements effectively rule out kaon coalescence as the dominant production mechanism for the ϕ meson for this energy region.Figure 8
ϕ
/
K
- ratio as a function of number of participants in Au + Au [18] and Pb + Pb [21] collision at various beam energies.


## 2.6.2.Ω/ϕ

The production mechanism of multistrange hadrons (e.g.,ϕ and Ω) is predicted to be very sensitive to the early phase of nuclear collisions [56], because both ϕ and Ω freeze out early, have low hadronic interaction cross-section, and are purely made of strange and antistrange quarks. Therefore the ratio N(Ω)/N(ϕ) 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, N(Ω-+Ω¯+)/2N(ϕ), as a function of pT in Au + Au collisions at sNN=11.5GeV to 2760 GeV [17, 18, 21]. The dashed lines are the results from the recombination model calculation by Hwa and Yang for sNN=200GeV [57]. In this model the ϕ and Ω yields in the measured pT region are mostly from the recombination of thermal strange quarks, which were assumed to follow an exponential pT distribution. The thermal s quark distribution was determined by fitting the low pT data of kaon production. The contribution from hard parton scattering was assumed to be negligible unless pT is large. Details of this recombination model have been given in [57]. We can see from Figure 9 that, in central A + A collisions at sNN≥19.6GeV, the ratios of N(Ω-+Ω¯+)/2N(ϕ) in the intermediate pT 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 pT~4GeV/c which covers ~95% of the total yields for the ϕ and Ω. The observations imply that the production of ϕ and Ω in central Au + Au collisions is predominantly through the recombination of thermal s quarks for sNN≥19.6GeV. But at sNN=11.5GeV, the ratio at the highest measured pT shows a deviation from the trend of other energies. This may indicate a change in Ω and/or ϕ production mechanism at sNN = 11.5 GeV.Figure 9
The baryon-to-meson ratio,N(Ω-+Ω¯+)/2N(ϕ), as a function of pT in midrapidity (y<0.5) from central A + A collisions at sNN=11.5,19.6,27,39,200, and 2760 GeV [17, 18, 21]. Gray bands denote systematical errors.


## 3. Azimuthal Anisotropy inϕ 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 [58–62]. The elliptic flow (v2) [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 ϕ meson is smaller than the other hadrons [6] and freezes out relatively early [8], its v2 remain almost unaffected by the later stage interaction. Therefore ϕ meson v2 can be considered as good and clean probe for early system created in nucleus-nucleus collisions. Further the ϕ 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 ϕ mesons would reflect the collectivity in the partonic phase. In addition, its mass is comparable to the masses of the lightest baryon (p and Λ); therefore comparison of ϕ meson v2 with that of proton and Λ will be helpful to distinguish the mass effect and/or baryon-meson effect in v2(pT).


### 3.1. Differentialϕ Meson v2

Elliptic flow ofϕ meson as a function of pT measured at midrapidity [28–31] is shown in Figure 10. The shape of ϕv2(pT) is similar for sNN=19.6GeV to 2760 GeV. But at 7.7 and 11.5 GeV, the ϕv2 values at the highest measured pT bins are observed to be smaller than other energies. Various model studies predicted that ϕ meson v2 will be small for a system with hadronic interactions [66, 67]. Small interaction cross-section of ϕ meson in hadronic phase suggests that ϕ meson v2 mostly reflects collectivity from the partonic phase; hence small ϕ meson v2 indicates less contribution to the collectivity from partonic phase. So the large ϕ meson v2 at sNN≥15GeV indicates the formation of partonic matter and small v2 at sNN≤11.5 could indicate dominance of hadron interactions.Figure 10
Theϕ meson v2(pT) at midrapidity in Au+Au collisions at sNN=7.7–62.4 GeV for 0–80% centrality [28] and at sNN=200 GeV for 0–80%, 0–30%, and 30–80% centralities [29, 30] and in Pb + Pb collisions at sNN=2.76 TeV [31] for different collisions centralities. The vertical lines are statistical uncertainties.
(a)
Au + Au 7.7 GeV
(b)
Au + Au 11.5 GeV
(c)
Au + Au 19.6 GeV
(d)
Au + Au 27 GeV
(e)
Au + Au 39 GeV
(f)
Au + Au 62.4 GeV
(g)
Au + Au 200 GeV
(h)
Pb + Pb 2.76 TeV


### 3.2. Number-of-Constituent Quark Scaling

In Figure11, the v2 scaled by number-of-constituent quarks (nq) as a function (mT-m0)/nq for identified hadrons in Au + Au collisions at sNN=7.7–200GeV are presented. We can see from Figure 11 that for sNN=19.6–200GeV the v2 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 v2 [68–70]. This is due to modification of initially developed v2 by later stage hadronic interactions and the production mechanism as implemented in the model [69]. Hence to avoid these ambiguities, the v2 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, ϕ mesons v2 are almost unaffected by later stage interaction and it will have negligible value if ϕ mesons are not produced via s and s- quark coalescence [66, 67]. Therefore, NCQ scaling of ϕ mesons v2 can be considered as the key observables for the partonic collectivity in heavy-ion collisions. As we can see from Figure 11, at sNN=7.7 and 11.5 GeV, the ϕ meson v2 deviates from the trend of the other hadrons at the highest measured pT values by 1.8σ and 2.3σ, respectively. This could be the effect for a system, where hadronic interactions are more important.Figure 11
The NCQ-scaled elliptic flow,v2/nq, versus (mT-m0)/nq for 0–80% central Au + Au collisions for selected identified particles [28–30]. Only statistical error bars are shown.
(a)
7.7 GeV
(b)
11.5 GeV
(c)
19.6 GeV
(d)
27 GeV
(e)
39 GeV
(f)
62.4 GeV
(g)
200 GeVFigure12 presents the (mT-m0)/nq dependence of v2/nq for 10–20% and 40–50% central Pb + Pb collisions for selected identified particles [31]. It can be seen that, at higher value of (mT-m0)/nq, 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.Figure 12
The NCQ-scaled elliptic flow,v2/nq, versus (mT-m0)/nq for 10–20% and 40–50% central Pb + Pb collisions for selected identified particles [31]. Only statistical error bars are shown. The figure has been taken from the presentation at Quark Matter 2014 by ALICE collaboration.
(a)
(b)


### 3.3.pT Integrated ϕ Meson v2

ThepT integrated elliptic flow (v2) can be calculated as (4)v2=∫v2pTdN/dpTdpT∫dN/dpTdpT.Figure 13 shows pT integrated ϕ meson (red star) and proton (blue circle) v2 as a function of centre-of-mass energy for 0–80% centrality [32]. One can see that for both particle species the v2 increases with increasing beam energy. ϕ meson v2 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 v2 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 v2 of ϕ mesons for sNN≥19.6GeV 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 sNN=11.5GeV. The comparison to AMPT model results indicates negligible contribution of the partonic interactions to the final measured collectivity for sNN=11.5GeV. For sNN>19.6GeV, proton and ϕ meson show similar magnitude of v2. The proton is a baryon and ϕ is a meson; in addition they are composed of different quark flavours, yet they have similar v2; this is a strong indication of large fraction of the collectivity being developed in the partonic phase. However at sNN≤19.6GeV, ϕ meson v2 values show deviation from that for proton and at sNN = 11.5 GeV ϕ meson v2 becomes small (~1.5%). This tells us that due to the lack of enough partonic interactions at lower beam energies a larger v2 could not be generated for ϕ mesons. The contribution to ϕv2 from hadronic interactions is small because of small ϕ-hadron interaction cross-sections. However the observed higher collectivity of protons compared to ϕ mesons at the lower beam energies could be due to the protons having larger hadronic interaction cross-section.Figure 13
ThepT integrated proton and ϕ meson v2 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 pT spectra were used for ϕ and proton v2 calculation [17, 33, 34]. The red and blue lines are the fit to the ϕ and proton v2 by empirical function just to guide the eye of the reader.


### 3.4. Hadronic Rescattering Effect onv2

Recent phenomenological calculation based on ideal hydrodynamical model together with the later stage hadron cascade (hydro + JAM) shows that the mass ordering ofv2 could be broken between that of ϕ meson and that of proton at low pT (pT<1.5GeV/c) [71]. This is because of late stage hadronic rescattering effects on proton v2. The model calculation was done by considering low hadronic interaction cross-section for ϕ meson and larger hadronic interaction cross-section for proton. The ratio between ϕv2 and proton v2 is shown in Figure 14 for minimum bias Au + Au collisions at sNN=200GeV. 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 pT region (pT<0.7GeV/c) for 0–30% centrality although mass of the ϕ meson (1.019 GeV/c2) is greater than mass of the proton (0.938 GeV/c2). 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 v2 which reduces its value, as predicted in the theoretical model [67, 71]. Due to small hadronic interaction cross-section ϕ meson v2 remains unaffected by later stage hadronic rescattering.Figure 14
Ratio betweenϕ and pv2 for 0–30% and 30–80% centrality in Au + Au collisions sNN = 200 GeV [29, 30].


## 3.1. Differentialϕ Meson v2

Elliptic flow ofϕ meson as a function of pT measured at midrapidity [28–31] is shown in Figure 10. The shape of ϕv2(pT) is similar for sNN=19.6GeV to 2760 GeV. But at 7.7 and 11.5 GeV, the ϕv2 values at the highest measured pT bins are observed to be smaller than other energies. Various model studies predicted that ϕ meson v2 will be small for a system with hadronic interactions [66, 67]. Small interaction cross-section of ϕ meson in hadronic phase suggests that ϕ meson v2 mostly reflects collectivity from the partonic phase; hence small ϕ meson v2 indicates less contribution to the collectivity from partonic phase. So the large ϕ meson v2 at sNN≥15GeV indicates the formation of partonic matter and small v2 at sNN≤11.5 could indicate dominance of hadron interactions.Figure 10
Theϕ meson v2(pT) at midrapidity in Au+Au collisions at sNN=7.7–62.4 GeV for 0–80% centrality [28] and at sNN=200 GeV for 0–80%, 0–30%, and 30–80% centralities [29, 30] and in Pb + Pb collisions at sNN=2.76 TeV [31] for different collisions centralities. The vertical lines are statistical uncertainties.
(a)
Au + Au 7.7 GeV
(b)
Au + Au 11.5 GeV
(c)
Au + Au 19.6 GeV
(d)
Au + Au 27 GeV
(e)
Au + Au 39 GeV
(f)
Au + Au 62.4 GeV
(g)
Au + Au 200 GeV
(h)
Pb + Pb 2.76 TeV


## 3.2. Number-of-Constituent Quark Scaling

In Figure11, the v2 scaled by number-of-constituent quarks (nq) as a function (mT-m0)/nq for identified hadrons in Au + Au collisions at sNN=7.7–200GeV are presented. We can see from Figure 11 that for sNN=19.6–200GeV the v2 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 v2 [68–70]. This is due to modification of initially developed v2 by later stage hadronic interactions and the production mechanism as implemented in the model [69]. Hence to avoid these ambiguities, the v2 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, ϕ mesons v2 are almost unaffected by later stage interaction and it will have negligible value if ϕ mesons are not produced via s and s- quark coalescence [66, 67]. Therefore, NCQ scaling of ϕ mesons v2 can be considered as the key observables for the partonic collectivity in heavy-ion collisions. As we can see from Figure 11, at sNN=7.7 and 11.5 GeV, the ϕ meson v2 deviates from the trend of the other hadrons at the highest measured pT values by 1.8σ and 2.3σ, respectively. This could be the effect for a system, where hadronic interactions are more important.Figure 11
The NCQ-scaled elliptic flow,v2/nq, versus (mT-m0)/nq for 0–80% central Au + Au collisions for selected identified particles [28–30]. Only statistical error bars are shown.
(a)
7.7 GeV
(b)
11.5 GeV
(c)
19.6 GeV
(d)
27 GeV
(e)
39 GeV
(f)
62.4 GeV
(g)
200 GeVFigure12 presents the (mT-m0)/nq dependence of v2/nq for 10–20% and 40–50% central Pb + Pb collisions for selected identified particles [31]. It can be seen that, at higher value of (mT-m0)/nq, 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.Figure 12
The NCQ-scaled elliptic flow,v2/nq, versus (mT-m0)/nq for 10–20% and 40–50% central Pb + Pb collisions for selected identified particles [31]. Only statistical error bars are shown. The figure has been taken from the presentation at Quark Matter 2014 by ALICE collaboration.
(a)
(b)


## 3.3.pT Integrated ϕ Meson v2

ThepT integrated elliptic flow (v2) can be calculated as (4)v2=∫v2pTdN/dpTdpT∫dN/dpTdpT.Figure 13 shows pT integrated ϕ meson (red star) and proton (blue circle) v2 as a function of centre-of-mass energy for 0–80% centrality [32]. One can see that for both particle species the v2 increases with increasing beam energy. ϕ meson v2 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 v2 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 v2 of ϕ mesons for sNN≥19.6GeV 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 sNN=11.5GeV. The comparison to AMPT model results indicates negligible contribution of the partonic interactions to the final measured collectivity for sNN=11.5GeV. For sNN>19.6GeV, proton and ϕ meson show similar magnitude of v2. The proton is a baryon and ϕ is a meson; in addition they are composed of different quark flavours, yet they have similar v2; this is a strong indication of large fraction of the collectivity being developed in the partonic phase. However at sNN≤19.6GeV, ϕ meson v2 values show deviation from that for proton and at sNN = 11.5 GeV ϕ meson v2 becomes small (~1.5%). This tells us that due to the lack of enough partonic interactions at lower beam energies a larger v2 could not be generated for ϕ mesons. The contribution to ϕv2 from hadronic interactions is small because of small ϕ-hadron interaction cross-sections. However the observed higher collectivity of protons compared to ϕ mesons at the lower beam energies could be due to the protons having larger hadronic interaction cross-section.Figure 13
ThepT integrated proton and ϕ meson v2 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 pT spectra were used for ϕ and proton v2 calculation [17, 33, 34]. The red and blue lines are the fit to the ϕ and proton v2 by empirical function just to guide the eye of the reader.


## 3.4. Hadronic Rescattering Effect onv2

Recent phenomenological calculation based on ideal hydrodynamical model together with the later stage hadron cascade (hydro + JAM) shows that the mass ordering ofv2 could be broken between that of ϕ meson and that of proton at low pT (pT<1.5GeV/c) [71]. This is because of late stage hadronic rescattering effects on proton v2. The model calculation was done by considering low hadronic interaction cross-section for ϕ meson and larger hadronic interaction cross-section for proton. The ratio between ϕv2 and proton v2 is shown in Figure 14 for minimum bias Au + Au collisions at sNN=200GeV. 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 pT region (pT<0.7GeV/c) for 0–30% centrality although mass of the ϕ meson (1.019 GeV/c2) is greater than mass of the proton (0.938 GeV/c2). 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 v2 which reduces its value, as predicted in the theoretical model [67, 71]. Due to small hadronic interaction cross-section ϕ meson v2 remains unaffected by later stage hadronic rescattering.Figure 14
Ratio betweenϕ and pv2 for 0–30% and 30–80% centrality in Au + Au collisions sNN = 200 GeV [29, 30].


## 4. Summary

We have presented a review on the experimentally measured data onϕ production (specifically the transverse momentum distributions and azimuthal anisotropy measurements) in high energy heavy-ion collisions. The differential (pT,φ,y) measurements of ϕ meson production have been compared from heavy-ion collisions at the SPS, RHIC, and LHC energies. Transverse momentum spectra of ϕ 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 ϕ meson production support the physical origin to be due to the enhanced production of s(s-)-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 ϕ 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 pT are observed to be equal to or higher than unity at sNN≤39GeV. This indicates that parton energy loss effect became less important and suggests dominance of hadronic interactions at the lower beam energies. The ratio N(ϕ)/N(K-) is observed to be almost constant as a function of centrality and centre-of-mass energy, disfavouring ϕ meson production through kaon coalescence. The ratio of N(Ω-+Ω¯+)/2N(ϕ) versus pT shows a similar trend for sNN≥19.6GeV, but at sNN=11.5GeV the ratio at the highest measured pT shows a deviation from the trend at other higher energies. This may suggest a change in Ω and/or ϕ production mechanism and strange quark dynamics in general at sNN=11.5GeV.The measurement ofϕ meson v2 as a function of pT and collision centrality are discussed. We observe that ϕ meson v2(pT) has similar values for sNN≥19.6GeV and NCQ scaling also holds for sNN≥19.6GeV. But at sNN=7.7 and 11.5 GeV, the ϕ meson v2 shows deviation from the other hadrons at the highest measured pT values by 1.8σ and 2.3σ, respectively. Since the v2 of ϕ mesons mostly reflect collectivity from partonic phase, therefore the small ϕv2 observed at sNN=7.7 and 11.5 GeV indicates a smaller contribution to the collectivity from partonic phase. We find that the ϕv2 can be explained by AMPT model with partonic interactions having cross-section values between 3 mb and 10 mb for sNN≥19.6GeV, but the model with and without partonic interactions overpredicts the data at sNN=7.7 and 11.5 GeV. Also at sNN>19.6GeV, proton and ϕ meson show similar magnitude of v2; however, at sNN≤19.6GeV, ϕ meson v2 shows deviation from corresponding proton values. At sNN=11.5GeV  ϕ meson 〈v2〉 value is small and is about 1.5%. This further emphasises our conclusion that at lower beam energies the hadronic interactions are dominating. In addition, we observe that the mass ordering between ϕ and proton v2 breaks down in the lower momentum range at sNN=200GeV. This could be because of the larger effect of hadronic rescattering on proton v2, which reduces the proton v2 values.The main conclusions of the review are the following. (a) The coalescence ofK+ and K- is not the dominant production mechanism for ϕ meson in high energy heavy-ion collisions. (b) The study of Ω/ϕ and comparison to quark recombination model calculations indicate that ϕ mesons are produced via coalescence of thermalized s quarks for sNN≥19.6GeV. (c) The observed ϕ meson enhancement (unaffected by Canonical suppression effects) in heavy-ion collisions suggests that strangeness enhancement is due to the formation of a dense partonic medium. (d) The nuclear modification factor measurements for ϕ mesons and the measurements of ϕ meson v2 indicate the formation of partonic media in heavy-ion collisions at sNN≥19.6GeV, while for sNN≤11.5GeV hadronic interactions dominate. (e) Finally ϕ meson production provided us with a benchmark to study the rescattering effect. The comparison of ϕ and proton v2 shows that mass ordering in v2(pT) could be broken due to effect of later stage rescattering effects on the proton distributions.



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*Source: 197930-2015-06-09.xml*