A Review on [varphi] Meson Production in Heavy-Ion Collision

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 ([subscript]sNN[/subscript] ) 4.75 GeV to 2.76 TeV. The [varphi] 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 [varphi] meson production in heavy-ion experiments. Mainly, we discuss the energy dependence of [varphi] 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 ([subscript]v2[/subscript] ) of proton is also discussed relative to corresponding effect on [varphi] meson [subscript]v2[/subscript] .

Md. Nasim 1 and Vipul Bairathi 2 and Mukesh Kumar Sharma 3 and Bedangadas Mohanty 2 and Anju Bhasin 3

Academic Editor:Fu-Hu Liu

1, Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095, USA
2, School of Physical Sciences, National Institute of Science Education and Research, Bhubaneswar 751005, India
3, Physics Department, University of Jammu, Jammu 180001, India

Received 29 July 2014; Accepted 2 October 2014; 9 June 2015

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³ .

1. Introduction

According to quantum chromodynamics (QCD) [1-4], at very high temperature ( [figure omitted; refer to PDF] ) and/or at high density, a deconfined phase of quarks and gluons is expected to be present, while at low [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] vector meson, which is the lightest bound state of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] as shown in Figure 1 [5]. It has a mass of [figure omitted; refer to PDF] GeV/ [figure omitted; refer to PDF] which is comparable to the masses of the lightest baryons such as proton (0.938 GeV/ [figure omitted; refer to PDF] ) and [figure omitted; refer to PDF] (1.115 GeV/ [figure omitted; refer to PDF] ). The interaction cross-section [figure omitted; refer to PDF] of the [figure omitted; refer to PDF] meson with nonstrange hadrons is expected to have a small value [6]. The data on coherent [figure omitted; refer to PDF] photo-production shows that [figure omitted; refer to PDF] [7]. This is about a factor of 3 times lower than [figure omitted; refer to PDF] and [figure omitted; refer to PDF] , about a factor of 4 times lower than [figure omitted; refer to PDF] and [figure omitted; refer to PDF] , and about a factor of 2 times lower than [figure omitted; refer to PDF] . 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 [figure omitted; refer to PDF] distribution of [figure omitted; refer to PDF] meson seems to suggest that it freezes out early compared to other hadrons [8]. The life time of the [figure omitted; refer to PDF] meson is ~42 fm/c. Because of longer life time the [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] 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 of [figure omitted; refer to PDF] pairs from the reaction [figure omitted; refer to PDF] in bubble chamber experiments at Brookhaven National Laboratory (BNL) [5].

[figure omitted; refer to PDF]

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 [figure omitted; refer to PDF] meson due to its zero net strangeness is not subjected to Canonical suppression effects. Therefore measurement of [figure omitted; refer to PDF] meson yield in both nucleus-nucleus and proton-proton would provide the true answer for observed strangeness enhancement.

Experimentally measured results on [figure omitted; refer to PDF] ( [figure omitted; refer to PDF] , a measure of the azimuthal angle [figure omitted; refer to PDF] anisotropy of the produced particles, and [figure omitted; refer to PDF] is the reaction plane angle) of identified hadrons as a function of [figure omitted; refer to PDF] show that at low [figure omitted; refer to PDF] (<2 GeV/c) elliptic flow follows a pattern ordered by mass of the hadron (the [figure omitted; refer to PDF] values are smaller for heavier hadrons than that of lighter hadrons). At the intermediate [figure omitted; refer to PDF] ( [figure omitted; refer to PDF] ) all mesons and all baryons form two different groups [35]. When [figure omitted; refer to PDF] and [figure omitted; refer to PDF] are scaled by the number of constituent quarks [figure omitted; refer to PDF] of the hadrons, the magnitude of the scaled [figure omitted; refer to PDF] is observed to be the same for all the hadrons at the intermediate [figure omitted; refer to PDF] . 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 [figure omitted; refer to PDF] meson has mass (1.0194 GeV/ [figure omitted; refer to PDF] ) comparable to the masses of the lightest baryons such as proton and at the same time it is a meson, the study of [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] would be more appropriate to understand the mass type and/or particle type (baryon-meson) dependence of [figure omitted; refer to PDF] .

In this review we have compiled all the available experimental measurements on [figure omitted; refer to PDF] meson production in high energy heavy-ion collisions as a function of [figure omitted; refer to PDF] , azimuthal angle [figure omitted; refer to PDF] , and rapidity [figure omitted; refer to PDF] . This paper is organised in the following manner. In Section 2, measurement of [figure omitted; refer to PDF] meson invariant yield has been presented from SPS to LHC energy. Section 3 describes the compilation of the azimuthal anisotropy measurements in [figure omitted; refer to PDF] meson production from all the available experimental results. Finally, the summary and conclusion have been discussed in Section 4.

2. Invariant Yield of [figure omitted; refer to PDF] Meson

2.1. Invariant Transverse Momentum Spectra

We have compiled the data on the invariant [figure omitted; refer to PDF] spectra of the [figure omitted; refer to PDF] meson measured in [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and A + A systems for different collision centralities at various centre-of-mass energies [figure omitted; refer to PDF] [16-22] and those are shown in Figure 2. Only the statistical errors are indicated as error bars. Measurement of [figure omitted; refer to PDF] meson invariant yield in [figure omitted; refer to PDF] collisions at [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] The blue solid lines in Figure 2 are the fits to the data with Levy function of the form given by [figure omitted; refer to PDF] [figure omitted; refer to PDF] is known as the inverse slope parameter, [figure omitted; refer to PDF] is the [figure omitted; refer to PDF] meson yield per unit rapidity, [figure omitted; refer to PDF] is the rest mass of [figure omitted; refer to PDF] meson, and [figure omitted; refer to PDF] is the Levy function parameter. Levy function is similar in shape to an exponential function at low [figure omitted; refer to PDF] and has a power-law-like shape at higher [figure omitted; refer to PDF] . In fact, the exponential function is the limit of the Levy function as [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] /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 [figure omitted; refer to PDF] spectra (deviations from exponential distribution and more towards a power law distribution) at high [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] exponential and the high [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] for [figure omitted; refer to PDF] and [figure omitted; refer to PDF] collisions whereas Levy function describes data for all [figure omitted; refer to PDF] . 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 [figure omitted; refer to PDF] meson production in more peripheral collisions at higher [figure omitted; refer to PDF] . Particle production at low [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] . 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 [figure omitted; refer to PDF] are large in the case central A + A collisions where both Levy and exponential functions fit the data well. The [figure omitted; refer to PDF] values increase from peripheral to central collisions, indicating increasing production of [figure omitted; refer to PDF] meson with increase in collision centrality.

Table 1: Results from Levy fits to the transverse mass distributions of the [figure omitted; refer to PDF] meson. All values are for midrapidity ( [figure omitted; refer to PDF] ).

	Centrality	[figure omitted; refer to PDF] /ndf	[figure omitted; refer to PDF] (GeV)	[figure omitted; refer to PDF]	[figure omitted; refer to PDF]
Pb + Pb (2.76 TeV)	0-10%	4.282/5	0.5005 ± 0.0128	1.121 [figure omitted; refer to PDF] ± 1.414 [figure omitted; refer to PDF]	12.41 ± 0.796
10-20%	4.793/5	0.5131 ± 0.0132	4.969 [figure omitted; refer to PDF] ± 2.6 [figure omitted; refer to PDF]	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	9.993 [figure omitted; refer to PDF] ± 6.39 [figure omitted; refer to PDF]	3.693 ± 0.353
20-40%	8.8/8	0.3217 ± 0.00353	4.24 [figure omitted; refer to PDF] ± 7.41 [figure omitted; refer to PDF]	1.590 ± 0.142
40-60%	14.5/8	0.2910 ± 0.00644	9.409 [figure omitted; refer to PDF] ± [figure omitted; refer to PDF]	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	6.619 [figure omitted; refer to PDF] ± 8.931 [figure omitted; refer to PDF]	3.402 ± 0.812
10-20%	1.046/9	0.3131 ± 0.03514	1.108 [figure omitted; refer to PDF] ± 1.414 [figure omitted; refer to PDF]	2.216 ± 0.278
20-30%	1.55/8	0.2996 ± 0.01301	1.532 [figure omitted; refer to PDF] ± 6.651 [figure omitted; refer to PDF]	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 ± 1.175 [figure omitted; refer to PDF]	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 [figure omitted; refer to PDF] 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 ± 0.007

Table 2: Results from exponential fits to the transverse mass distributions of the [figure omitted; refer to PDF] meson. All values are for midrapidity ( [figure omitted; refer to PDF] ).

	Centrality	[figure omitted; refer to PDF] /ndf	[figure omitted; refer to PDF] (GeV)	[figure omitted; refer to PDF]
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 ± 0.002

Figure 2: The invariant yield of [figure omitted; refer to PDF] mesons as a function of [figure omitted; refer to PDF] 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

[figure omitted; refer to PDF]

(b) p + p (NSD) 200 GeV

[figure omitted; refer to PDF]

(c) d + Au 200 GeV

[figure omitted; refer to PDF]

(d) Pb + Pb 17.3 GeV

[figure omitted; refer to PDF]

(e) Au + Au 7.7 Gev

[figure omitted; refer to PDF]

(f) Au + Au 11.5 GeV

[figure omitted; refer to PDF]

(g) Au + Au 19.6 GeV

[figure omitted; refer to PDF]

(h) Au + Au 27 GeV

[figure omitted; refer to PDF]

(i) Au + Au 39 GeV

[figure omitted; refer to PDF]

(j) Au + Au 62.4 GeV

[figure omitted; refer to PDF]

(k) Au + Au 200 GeV

[figure omitted; refer to PDF]

(l) Pb + Pb 2.76 TeV

[figure omitted; refer to PDF]

2.2. [figure omitted; refer to PDF] Meson Yield per Unit Rapidity

In Figure 3 we present all available measurements of [figure omitted; refer to PDF] integrated [figure omitted; refer to PDF] meson yield [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] collisions. The rate of increases with [figure omitted; refer to PDF] is higher in A + A collisions compared to [figure omitted; refer to PDF] collisions. We have observed that the measured midrapidity yield per participant [figure omitted; refer to PDF] pair, [figure omitted; refer to PDF] , increases nonlinearly with centrality and for the same [figure omitted; refer to PDF] [figure omitted; refer to PDF] increases with the collision energy of the A + A collisions. The former suggests that particle production does not scale with [figure omitted; refer to PDF] and the latter is expected because of the increase of energy available to produce the [figure omitted; refer to PDF] mesons.

Figure 3: The [figure omitted; refer to PDF] meson midrapidity yield [figure omitted; refer to PDF] as a function of [figure omitted; refer to PDF] for A + A [16-18, 21] and [figure omitted; refer to PDF] collisions [18-20, 22, 23]. For RHIC BES energies [figure omitted; refer to PDF] only statistical errors are shown whereas for other energies systematic errors are added in quadrature with statistical errors.

(a) A + A

[figure omitted; refer to PDF]

(b) p + p [figure omitted; refer to PDF]

[figure omitted; refer to PDF]

2.3. Strangeness Enhancement

The ratio of strange hadron production normalised to [figure omitted; refer to PDF] in nucleus-nucleus collisions relative to corresponding results from [figure omitted; refer to PDF] collisions at 200 GeV [24] is shown in the left upper panel of Figure 4. The results are plotted as a function of [figure omitted; refer to PDF] . [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] and [figure omitted; refer to PDF] have similar enhancement, or a mass effect, since [figure omitted; refer to PDF] and [figure omitted; refer to PDF] have similar mass but different enhancement factors.

Figure 4: (a) The ratio of the yields of [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] normalised to [figure omitted; refer to PDF] nucleus-nucleus collisions and to corresponding yields in proton-proton collisions as a function of [figure omitted; refer to PDF] at 62.4 and 200 GeV [24]. Error bars are quadrature sum of statistical and systematic uncertainties. (b) The ratio of [figure omitted; refer to PDF] normalised yield of [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] in Pb + Pb collisions to the corresponding yield in [figure omitted; refer to PDF] ( [figure omitted; refer to PDF] + Be) collisions at 17.3 GeV (NA57 & NA49) [25, 26] and 2.76 TeV (ALICE) [21]. Only statistical uncertainties are shown.

(a) [figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF]

In heavy-ion collisions, the production of [figure omitted; refer to PDF] mesons is not Canonically suppressed due to its [figure omitted; refer to PDF] structure. The [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] 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, [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] meson production being related to medium density is further supported by the energy dependence shown in the lower panel of Figure 4. The [figure omitted; refer to PDF] meson production relative to [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] reference yields for [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] at [figure omitted; refer to PDF] [21]. The [figure omitted; refer to PDF] , [figure omitted; refer to PDF] , and [figure omitted; refer to PDF] yield in [figure omitted; refer to PDF] collisions at [figure omitted; refer to PDF] have been estimated by interpolating between the measured yields at [figure omitted; refer to PDF] and [figure omitted; refer to PDF] . The reference [figure omitted; refer to PDF] yield in [figure omitted; refer to PDF] collisions at [figure omitted; refer to PDF] is estimated by extrapolating from the measured yield in (inelastic) [figure omitted; refer to PDF] collisions available up to [figure omitted; refer to PDF] . Details can be found in [21]. Enhancement factor increases linearly with [figure omitted; refer to PDF] until [figure omitted; refer to PDF] ; then the enhancement values seem to be saturated for higher values of [figure omitted; refer to PDF] . Unlike SPS and RHIC, the order of [figure omitted; refer to PDF] enhancement is the same as [figure omitted; refer to PDF] at LHC energy. We have observed that the [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] is measured which is defined as follows: [figure omitted; refer to PDF] where [figure omitted; refer to PDF] is the average number of binary collisions for the corresponding centrality. The value of [figure omitted; refer to PDF] was calculated from the Monte Carlo Glauber simulation [43]. [figure omitted; refer to PDF] value is equal to one when the nucleus-nucleus collisions are simply the superposition of nucleon-nucleon collisions. Therefore deviation of [figure omitted; refer to PDF] from the unity would imply contribution from the nuclear medium effects, specifically jet-quenching [44]. Nuclear modification factors ( [figure omitted; refer to PDF] ) of [figure omitted; refer to PDF] mesons at midrapidity in Au + Au collisions at [figure omitted; refer to PDF] , and 200 GeV [17, 18] and in Pb + Pb collisions at [figure omitted; refer to PDF] [21] are shown in Figure 5. We can see that the [figure omitted; refer to PDF] of [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] , [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] is greater than or equal to unity at the intermediate [figure omitted; refer to PDF] , which indicates that at low energy the parton energy loss contribution to [figure omitted; refer to PDF] measurement could be less important. In order to confirm that the [figure omitted; refer to PDF] is due to parton energy loss or jet-quenching phenomenon, it is important to study [figure omitted; refer to PDF] in [figure omitted; refer to PDF] + 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 [figure omitted; refer to PDF] at high [figure omitted; refer to PDF] is expected to be greater than one.

Figure 5: The [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] as a function of [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] which is approximately 20% for [figure omitted; refer to PDF] GeV, ~10% for 200 GeV, and ~7% for 2.76 TeV.

[figure omitted; refer to PDF]

Figure 6 presents the [figure omitted; refer to PDF] dependence of the nuclear modification factor [figure omitted; refer to PDF] in Au + Au and d + Au collisions at [figure omitted; refer to PDF] [18, 27]. The definition of [figure omitted; refer to PDF] is the ratio of the yields of the hadron produced in the nucleus (A) + nucleus (B) collisions to the corresponding yields in the inelastic [figure omitted; refer to PDF] collisions normalised by [figure omitted; refer to PDF] . The [figure omitted; refer to PDF] of [figure omitted; refer to PDF] mesons for d + Au collisions show a similar enhancement trend as those for [figure omitted; refer to PDF] and [figure omitted; refer to PDF] at the intermediate [figure omitted; refer to PDF] . 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 [figure omitted; refer to PDF] . Current experimental measurements on [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] in d + Au do not seem to have the precision to differentiate between particle type dependence types [49, 50]. On the other hand, the [figure omitted; refer to PDF] in Au + Au (i.e., [figure omitted; refer to PDF] ) 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.

Figure 6: The nuclear modification factor [figure omitted; refer to PDF] as a function of [figure omitted; refer to PDF] in Au + Au and d + Au [18, 27] collisions at [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] in d + Au and only statistical for three other cases.

[figure omitted; refer to PDF]

2.5. Mean Transverse Mass

Figure 7 shows the difference in mean transverse mass [figure omitted; refer to PDF] and rest mass [figure omitted; refer to PDF] , that is, [figure omitted; refer to PDF] for [figure omitted; refer to PDF] meson, as a function of centre-of-mass energy for [figure omitted; refer to PDF] [18, 20, 22], Au + Au [17, 18], and Pb + Pb [16, 21] collisions. Due to limited statistics, result for [figure omitted; refer to PDF] at [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] increases monotonically with [figure omitted; refer to PDF] in [figure omitted; refer to PDF] collisions whereas the corresponding data in A + A collisions changes slope twice as a function of center-of-mass energy. In A + A collisions, [figure omitted; refer to PDF] first increases with [figure omitted; refer to PDF] and then stays independent of energy from approximately 17 GeV to 39 GeV, followed by again an increase with [figure omitted; refer to PDF] . For a thermodynamic system, the [figure omitted; refer to PDF] can be interpreted as a measure of temperature of the system, and [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] for [figure omitted; refer to PDF] 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: [figure omitted; refer to PDF] as a function centre-of-mass energies in central A + A and [figure omitted; refer to PDF] + [figure omitted; refer to PDF] 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.

[figure omitted; refer to PDF]

2.6. Particle Ratios

2.6.1. [figure omitted; refer to PDF]

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

Figure 8: [figure omitted; refer to PDF] ratio as a function of number of participants in Au + Au [18] and Pb + Pb [21] collision at various beam energies.

[figure omitted; refer to PDF]

2.6.2. [figure omitted; refer to PDF] / [figure omitted; refer to PDF]

The production mechanism of multistrange hadrons (e.g., [figure omitted; refer to PDF] and [figure omitted; refer to PDF] ) is predicted to be very sensitive to the early phase of nuclear collisions [56], because both [figure omitted; refer to PDF] and [figure omitted; refer to PDF] freeze out early, have low hadronic interaction cross-section, and are purely made of strange and antistrange quarks. Therefore the ratio [figure omitted; refer to PDF] 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, [figure omitted; refer to PDF] , as a function of [figure omitted; refer to PDF] in Au + Au collisions at [figure omitted; refer to PDF] to 2760 GeV [17, 18, 21]. The dashed lines are the results from the recombination model calculation by Hwa and Yang for [figure omitted; refer to PDF] [57]. In this model the [figure omitted; refer to PDF] and [figure omitted; refer to PDF] yields in the measured [figure omitted; refer to PDF] region are mostly from the recombination of thermal strange quarks, which were assumed to follow an exponential [figure omitted; refer to PDF] distribution. The thermal [figure omitted; refer to PDF] quark distribution was determined by fitting the low [figure omitted; refer to PDF] data of kaon production. The contribution from hard parton scattering was assumed to be negligible unless [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] , the ratios of [figure omitted; refer to PDF] in the intermediate [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] which covers ~95% of the total yields for the [figure omitted; refer to PDF] and [figure omitted; refer to PDF] . The observations imply that the production of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] in central Au + Au collisions is predominantly through the recombination of thermal [figure omitted; refer to PDF] quarks for [figure omitted; refer to PDF] . But at [figure omitted; refer to PDF] , the ratio at the highest measured [figure omitted; refer to PDF] shows a deviation from the trend of other energies. This may indicate a change in [figure omitted; refer to PDF] and/or [figure omitted; refer to PDF] production mechanism at [figure omitted; refer to PDF] = 11.5 GeV.

Figure 9: The baryon-to-meson ratio, [figure omitted; refer to PDF] , as a function of [figure omitted; refer to PDF] in midrapidity [figure omitted; refer to PDF] from central A + A collisions at [figure omitted; refer to PDF] , and 2760 GeV [17, 18, 21]. Gray bands denote systematical errors.

[figure omitted; refer to PDF]

3. Azimuthal Anisotropy in [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] [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 [figure omitted; refer to PDF] meson is smaller than the other hadrons [6] and freezes out relatively early [8], its [figure omitted; refer to PDF] remain almost unaffected by the later stage interaction. Therefore [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] can be considered as good and clean probe for early system created in nucleus-nucleus collisions. Further the [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] mesons would reflect the collectivity in the partonic phase. In addition, its mass is comparable to the masses of the lightest baryon [figure omitted; refer to PDF] and [figure omitted; refer to PDF] ; therefore comparison of [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] with that of proton and [figure omitted; refer to PDF] will be helpful to distinguish the mass effect and/or baryon-meson effect in [figure omitted; refer to PDF] .

3.1. Differential [figure omitted; refer to PDF] Meson [figure omitted; refer to PDF]

Elliptic flow of [figure omitted; refer to PDF] meson as a function of [figure omitted; refer to PDF] measured at midrapidity [28-31] is shown in Figure 10. The shape of [figure omitted; refer to PDF] is similar for [figure omitted; refer to PDF] to 2760 GeV. But at 7.7 and 11.5 GeV, the [figure omitted; refer to PDF] values at the highest measured [figure omitted; refer to PDF] bins are observed to be smaller than other energies. Various model studies predicted that [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] will be small for a system with hadronic interactions [66, 67]. Small interaction cross-section of [figure omitted; refer to PDF] meson in hadronic phase suggests that [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] mostly reflects collectivity from the partonic phase; hence small [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] indicates less contribution to the collectivity from partonic phase. So the large [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] at [figure omitted; refer to PDF] indicates the formation of partonic matter and small [figure omitted; refer to PDF] at [figure omitted; refer to PDF] could indicate dominance of hadron interactions.

Figure 10: The [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] at midrapidity in Au+Au collisions at [figure omitted; refer to PDF] GeV for 0-80% centrality [28] and at [figure omitted; refer to PDF] GeV for 0-80%, 0-30%, and 30-80% centralities [29, 30] and in Pb + Pb collisions at [figure omitted; refer to PDF] TeV [31] for different collisions centralities. The vertical lines are statistical uncertainties.

(a) Au + Au 7.7 GeV

[figure omitted; refer to PDF]

(b) Au + Au 11.5 GeV

[figure omitted; refer to PDF]

(c) Au + Au 19.6 GeV

[figure omitted; refer to PDF]

(d) Au + Au 27 GeV

[figure omitted; refer to PDF]

(e) Au + Au 39 GeV

[figure omitted; refer to PDF]

(f) Au + Au 62.4 GeV

[figure omitted; refer to PDF]

(g) Au + Au 200 GeV

[figure omitted; refer to PDF]

(h) Pb + Pb 2.76 TeV

[figure omitted; refer to PDF]

3.2. Number-of-Constituent Quark Scaling

In Figure 11, the [figure omitted; refer to PDF] scaled by number-of-constituent quarks [figure omitted; refer to PDF] as a function [figure omitted; refer to PDF] for identified hadrons in Au + Au collisions at [figure omitted; refer to PDF] are presented. We can see from Figure 11 that for [figure omitted; refer to PDF] the [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] [68-70]. This is due to modification of initially developed [figure omitted; refer to PDF] by later stage hadronic interactions and the production mechanism as implemented in the model [69]. Hence to avoid these ambiguities, the [figure omitted; refer to PDF] 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, [figure omitted; refer to PDF] mesons [figure omitted; refer to PDF] are almost unaffected by later stage interaction and it will have negligible value if [figure omitted; refer to PDF] mesons are not produced via [figure omitted; refer to PDF] and [figure omitted; refer to PDF] quark coalescence [66, 67]. Therefore, NCQ scaling of [figure omitted; refer to PDF] mesons [figure omitted; refer to PDF] can be considered as the key observables for the partonic collectivity in heavy-ion collisions. As we can see from Figure 11, at [figure omitted; refer to PDF] and 11.5 GeV, the [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] deviates from the trend of the other hadrons at the highest measured [figure omitted; refer to PDF] values by 1.8 [figure omitted; refer to PDF] and 2.3 [figure omitted; refer to PDF] , respectively. This could be the effect for a system, where hadronic interactions are more important.

Figure 11: The NCQ-scaled elliptic flow, [figure omitted; refer to PDF] , versus [figure omitted; refer to PDF] for 0-80% central Au + Au collisions for selected identified particles [28-30]. Only statistical error bars are shown.

(a) 7.7 GeV

[figure omitted; refer to PDF]

(b) 11.5 GeV

[figure omitted; refer to PDF]

(c) 19.6 GeV

[figure omitted; refer to PDF]

(d) 27 GeV

[figure omitted; refer to PDF]

(e) 39 GeV

[figure omitted; refer to PDF]

(f) 62.4 GeV

[figure omitted; refer to PDF]

(g) 200 GeV

[figure omitted; refer to PDF]

Figure 12 presents the [figure omitted; refer to PDF] dependence of [figure omitted; refer to PDF] for 10-20% and 40-50% central Pb + Pb collisions for selected identified particles [31]. It can be seen that, at higher value of [figure omitted; refer to PDF] , 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, [figure omitted; refer to PDF] , versus [figure omitted; refer to PDF] 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) [figure omitted; refer to PDF]

(b) [figure omitted; refer to PDF]

3.3. [figure omitted; refer to PDF] Integrated [figure omitted; refer to PDF] Meson [figure omitted; refer to PDF]

The [figure omitted; refer to PDF] integrated elliptic flow [figure omitted; refer to PDF] can be calculated as [figure omitted; refer to PDF] Figure 13 shows [figure omitted; refer to PDF] integrated [figure omitted; refer to PDF] meson (red star) and proton (blue circle) [figure omitted; refer to PDF] as a function of centre-of-mass energy for 0-80% centrality [32]. One can see that for both particle species the [figure omitted; refer to PDF] increases with increasing beam energy. [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] of [figure omitted; refer to PDF] mesons for [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] . The comparison to AMPT model results indicates negligible contribution of the partonic interactions to the final measured collectivity for [figure omitted; refer to PDF] . For [figure omitted; refer to PDF] , proton and [figure omitted; refer to PDF] meson show similar magnitude of [figure omitted; refer to PDF] . The proton is a baryon and [figure omitted; refer to PDF] is a meson; in addition they are composed of different quark flavours, yet they have similar [figure omitted; refer to PDF] ; this is a strong indication of large fraction of the collectivity being developed in the partonic phase. However at [figure omitted; refer to PDF] , [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] values show deviation from that for proton and at [figure omitted; refer to PDF] = 11.5 GeV [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] becomes small (~1.5%). This tells us that due to the lack of enough partonic interactions at lower beam energies a larger [figure omitted; refer to PDF] could not be generated for [figure omitted; refer to PDF] mesons. The contribution to [figure omitted; refer to PDF] from hadronic interactions is small because of small [figure omitted; refer to PDF] -hadron interaction cross-sections. However the observed higher collectivity of protons compared to [figure omitted; refer to PDF] mesons at the lower beam energies could be due to the protons having larger hadronic interaction cross-section.

Figure 13: The [figure omitted; refer to PDF] integrated proton and [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] spectra were used for [figure omitted; refer to PDF] and proton [figure omitted; refer to PDF] calculation [17, 33, 34]. The red and blue lines are the fit to the [figure omitted; refer to PDF] and proton [figure omitted; refer to PDF] by empirical function just to guide the eye of the reader.

[figure omitted; refer to PDF]

3.4. Hadronic Rescattering Effect on [figure omitted; refer to PDF]

Recent phenomenological calculation based on ideal hydrodynamical model together with the later stage hadron cascade (hydro + JAM) shows that the mass ordering of [figure omitted; refer to PDF] could be broken between that of [figure omitted; refer to PDF] meson and that of proton at low [figure omitted; refer to PDF] ( [figure omitted; refer to PDF] ) [71]. This is because of late stage hadronic rescattering effects on proton [figure omitted; refer to PDF] . The model calculation was done by considering low hadronic interaction cross-section for [figure omitted; refer to PDF] meson and larger hadronic interaction cross-section for proton. The ratio between [figure omitted; refer to PDF] and proton [figure omitted; refer to PDF] is shown in Figure 14 for minimum bias Au + Au collisions at [figure omitted; refer to PDF] . 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 [figure omitted; refer to PDF] region [figure omitted; refer to PDF] for 0-30% centrality although mass of the [figure omitted; refer to PDF] meson (1.019 GeV/ [figure omitted; refer to PDF] ) is greater than mass of the proton (0.938 GeV/ [figure omitted; refer to PDF] ). 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 [figure omitted; refer to PDF] which reduces its value, as predicted in the theoretical model [67, 71]. Due to small hadronic interaction cross-section [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] remains unaffected by later stage hadronic rescattering.

Figure 14: Ratio between [figure omitted; refer to PDF] and [figure omitted; refer to PDF] for 0-30% and 30-80% centrality in Au + Au collisions [figure omitted; refer to PDF] = 200 GeV [29, 30].

[figure omitted; refer to PDF]

4. Summary

We have presented a review on the experimentally measured data on [figure omitted; refer to PDF] production (specifically the transverse momentum distributions and azimuthal anisotropy measurements) in high energy heavy-ion collisions. The differential [figure omitted; refer to PDF] measurements of [figure omitted; refer to PDF] meson production have been compared from heavy-ion collisions at the SPS, RHIC, and LHC energies. Transverse momentum spectra of [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] meson production support the physical origin to be due to the enhanced production of [figure omitted; refer to PDF] -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 [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] are observed to be equal to or higher than unity at [figure omitted; refer to PDF] . This indicates that parton energy loss effect became less important and suggests dominance of hadronic interactions at the lower beam energies. The ratio [figure omitted; refer to PDF] is observed to be almost constant as a function of centrality and centre-of-mass energy, disfavouring [figure omitted; refer to PDF] meson production through kaon coalescence. The ratio of [figure omitted; refer to PDF] versus [figure omitted; refer to PDF] shows a similar trend for [figure omitted; refer to PDF] , but at [figure omitted; refer to PDF] the ratio at the highest measured [figure omitted; refer to PDF] shows a deviation from the trend at other higher energies. This may suggest a change in [figure omitted; refer to PDF] and/or [figure omitted; refer to PDF] production mechanism and strange quark dynamics in general at [figure omitted; refer to PDF] .

The measurement of [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] as a function of [figure omitted; refer to PDF] and collision centrality are discussed. We observe that [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] has similar values for [figure omitted; refer to PDF] and NCQ scaling also holds for [figure omitted; refer to PDF] . But at [figure omitted; refer to PDF] and 11.5 GeV, the [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] shows deviation from the other hadrons at the highest measured [figure omitted; refer to PDF] values by 1.8 [figure omitted; refer to PDF] and 2.3 [figure omitted; refer to PDF] , respectively. Since the [figure omitted; refer to PDF] of [figure omitted; refer to PDF] mesons mostly reflect collectivity from partonic phase, therefore the small [figure omitted; refer to PDF] observed at [figure omitted; refer to PDF] and 11.5 GeV indicates a smaller contribution to the collectivity from partonic phase. We find that the [figure omitted; refer to PDF] can be explained by AMPT model with partonic interactions having cross-section values between 3 mb and 10 mb for [figure omitted; refer to PDF] , but the model with and without partonic interactions overpredicts the data at [figure omitted; refer to PDF] and 11.5 GeV. Also at [figure omitted; refer to PDF] , proton and [figure omitted; refer to PDF] meson show similar magnitude of [figure omitted; refer to PDF] ; however, at [figure omitted; refer to PDF] , [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] shows deviation from corresponding proton values. At [figure omitted; refer to PDF] [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] and proton [figure omitted; refer to PDF] breaks down in the lower momentum range at [figure omitted; refer to PDF] . This could be because of the larger effect of hadronic rescattering on proton [figure omitted; refer to PDF] , which reduces the proton [figure omitted; refer to PDF] values.

The main conclusions of the review are the following. (a) The coalescence of [figure omitted; refer to PDF] and [figure omitted; refer to PDF] is not the dominant production mechanism for [figure omitted; refer to PDF] meson in high energy heavy-ion collisions. (b) The study of [figure omitted; refer to PDF] and comparison to quark recombination model calculations indicate that [figure omitted; refer to PDF] mesons are produced via coalescence of thermalized [figure omitted; refer to PDF] quarks for [figure omitted; refer to PDF] . (c) The observed [figure omitted; refer to PDF] 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 [figure omitted; refer to PDF] mesons and the measurements of [figure omitted; refer to PDF] meson [figure omitted; refer to PDF] indicate the formation of partonic media in heavy-ion collisions at [figure omitted; refer to PDF] , while for [figure omitted; refer to PDF] hadronic interactions dominate. (e) Finally [figure omitted; refer to PDF] meson production provided us with a benchmark to study the rescattering effect. The comparison of [figure omitted; refer to PDF] and proton [figure omitted; refer to PDF] shows that mass ordering in [figure omitted; refer to PDF] could be broken due to effect of later stage rescattering effects on the proton distributions.

Acknowledgments

Financial assistance from the SwarnaJayanti Fellowship of the Department of Science and Technology. Government of India, is gratefully acknowledged. Md. Nasim is supported by DOE Grant of Department of Physics and Astronomy, UCLA, USA.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

[1] F. Karsch, "Lattice results on QCD thermodynamics," Nuclear Physics A , vol. 698, no. 1-4, pp. 199-208, 2002.

[2] R. V. Gavai, S. Gupta, "On the critical end point of QCD," Physical Review D , vol. 71, no. 11, 2005.

[3] K. G. Wilson, "Confinement of quarks," Physical Review D , vol. 10, pp. 2445, 1974.

[4] S. Bethke, "Experimental tests of asymptotic freedom," Progress in Particle and Nuclear Physics , vol. 58, no. 2, pp. 351-386, 2007.

[5] L. Bertanza, V. Brisson, P. L. Connolly, "Possible Resonances in the Ξπ and KK- Systems," Physical Review Letters , vol. 9, no. 4, pp. 180-183, 1962.

[6] A. Shor Physical Review Letters , vol. 54, no. 11, pp. 1122-1125, 1985.

[7] A. Sibirtsev, H.-W. Hammer, U.-G. Meißner, A. W. Thomas The European Physical Journal , vol. 29, no. 2, pp. 209-220, 2006.

[8] J. Adams, M. M. Aggarwal, Z. Ahammed, "Experimental and theoretical challenges in the search for the quark-gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions," Nuclear Physics A , vol. 757, no. 1-2, pp. 102-183, 2005.

[9] P. Koch, B. Müllerb, J. Rafelskic, "Strangeness in relativistic heavy ion collisions," Physics Reports , vol. 142, no. 4, pp. 167-262, 1986.

[10] T. Alber, H. Appelshauser, J. Bachler, "Strange particle production in nuclear collisions at 200 GeV per nucleon," Zeitschrift für Physik C , vol. 64, no. 2, pp. 195-207, 1994.

[11] P. G. Jones, "Hadron yields and hadron spectra from the NA49 experiment," Nuclear Physics A , vol. 610, pp. 188c, 1996.

[12] F. Sikler, J. Bachlerf, D. Barna, "Hadron production in nuclear collisions from the NA49 experiment at 158 GeV/c. A," Nuclear Physics A , vol. 611, no. 1-4, pp. 45-54, 1996.

[13] C. Hohne, "Strangeness production in nuclear collisions-recent results from experiment NA49," Nuclear Physics A , vol. 611, pp. 485-488, 1999.

[14] J. Rafelski, B. Müller, "Strangeness production in the quark-gluon plasma," Physical Review Letters , vol. 48, no. 16, pp. 1066-1069, 1982.

[15] K. Redlich, A. Tounsi, "Strangeness enhancement and energy dependence in heavy ion collisions," European Physical Journal C , vol. 24, no. 4, pp. 589-594, 2002.

[16] C. Alt, T. Anticic, B. Baatar, "Energy dependence of [varphi] meson production in central Pb + Pb collisions at _sNN =6 to 17 GeV," Physical Review C , vol. 78, no. 4, 2008.

[17] M. Nasim, "Probing the QCD phase diagram with measurements of [varphi]-meson production and elliptic flow in heavy-ion collisions at STAR," Journal of Physics: Conference Series , vol. 509, no. 1, 2014.

[18] B. I. Abelev, "Measurements of [varphi] meson production in relativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC)," Physical Review C , vol. 49, 2009.

[19] B. Abelev, A. Abrahantes Quintana, D. Adamova, "Strange particle production in proton-proton collisions at s = 0.9 TeV with ALICE at the LHC," The European Physical Journal C , vol. 71, pp. 1594, 2011.

[20] B. Abelev, J. Adam, D. Adamova, "Production of K^{[low *]} (892)° and [varphi] (1020) in pp collisions at s=7 TeV,", article 2183 The European Physical Journal C , vol. 72, 2012.

[21] B. B. Abelev, J. Adam, D. Adamova, " ^{K * ( 892 ) 0} and Φ(1020) production in Pb-Pb collisions at _sNN =2.76 TeV," In press, http://arxiv.org/abs/1404.0495

[22] S. V. Afanasiev, T. Anticicu, J. Bachler, "Production of [straight phi]-mesons in p + p , p + Pb and central Pb + Pb collisions at E_beam = 158 A GeV," Physics Letters B , vol. 491, no. 1-2, pp. 59-66, 2000.

[23] T. Akesson, "Inclusive vector-meson production in the central region of pp collisions at s = 63 GeV," Nuclear Physics B , vol. 203, no. 1, pp. 27-99, 1982.

[24] B. I. Abelev, M. M. Aggarwal, Z. Ahammed, "Energy and system size dependence of [varphi] meson production in Cu + Cu and Au + Au collisions," Physics Letters B , vol. 673, pp. 183-191, 2009.

[25] F. Antinori, P. Bacon, A. Badala, "Enhancement of hyperon production at central rapidity in 158 A GeV/c Pb-Pb collisions," Journal of Physics G , vol. 32, no. 4, article 427, 2006.

[26] S. V. Afanasev, T. Anticic, J. Bachler, "Production of [straight phi] -mesons in p + p , p + Pb and central Pb + Pb collisions at E_beam = 158A GeV," Physics Letters B , vol. 491, pp. 59, 2000.

[27] A. Adare, S. Afanasiev, C. Aidala, "Nuclear modification factors of [varphi] mesons in d+Au, Cu+Cu, and Au+Au collisions at _sNN =200," Physical Review C , vol. 83, no. 2, 2011.

[28] L. Adamczyk, J. K. Adkins, G. Agakishiev, "Elliptic flow of identified hadrons in Au+Au collisions at _sNN =7.7-62.4 GeV," Physical Review C , vol. 88, 2013.

[29] M. Nasim, The STAR Collaboration, "Systematic investigation of partonic collectivity through centrality dependence of elliptic flow of multi-strange hadrons in Au+Au collisions at _sNN =200 GeV," Nuclear Physics A , vol. 904-905, pp. 413c-416c, 2013.

[30] R. Haque, M. K. Sharma STAR presentation at QM2014

[31] B. Abelev, "Elliptic flow of identified hadrons in Pb-Pb collisions at _sNN =2.76 TeV," http://arxiv.org/abs/1405.4632

[32] M. Nasim, "Using [varphi] -meson elliptic flow to map the strength of the partonic interaction," Physical Review C , vol. 89, 2014.

[33] L. Kumar, "STAR results from the RHIC beam energy scan-I," Nuclear Physics A , vol. 904-905, pp. 256c-263c, 2013.

[34] S. Das, The STAR Collaboration, "Study of freeze-out dynamics in STAR at RHIC beam energy scan program,", conference 1 Journal of Physics: Conference Series , vol. 509, 2014.

[35] J. Adams, C. Adler, M. M. Aggarwal, "Particle-type dependence of azimuthal anisotropy and nuclear modification of particle production in Au+Au collisions at _sNN =200 GeV," Physical Review Letters , vol. 92, no. 5, 2004.

[36] D. Molnar, S. A. Voloshin, "Elliptic flow at large transverse momenta from quark coalescence," Physical Review Letters , vol. 91, no. 9, 2003.

[37] R. J. Fries, B. Müller, C. Nonaka, S. A. Bass, "Hadronization in heavy-ion collisions: recombination and fragmentation of partons," Physical Review Letters , vol. 90, no. 20, 2003.

[38] G. Aad, T. Abajyan, B. Abbott, "The differential production cross section of the [varphi] (1020) meson in s=7 TeV pp collisions measured with the ATLAS detector," The European Physical Journal C , vol. 74, pp. 2895, 2014.

[39] V. Khachatryan, A. M. Sirunyan, A. Tumasyan, "Transverse-momentum and pseudorapidity distributions of charged hadrons in pp collisions at s=7 TeV," Physical Review Letters , vol. 105, 2010.

[40] S. Chatrchyan, V. Khachatryan, A. M. Sirunyan, "Study of the inclusive production of charged pions, kaons, and protons in pp collisions at s = 0.9, 2.76, and 7 TeV," The European Physical Journal C , vol. 72, pp. 2164, 2012.

[41] V. Blobel, H. Fesefeldt, H. Franz, "Test of the Zweig selection rule in Φ production by pp collisions," Physics Letters B , vol. 59, no. 1, pp. 88-92, 1975.

[42] A. Sibirtsev, J. Haidenbauer, U.-G. Meissner, "Aspects of phi-meson production in proton-proton collisions," The European Physical Journal A , vol. 27, no. 3, pp. 263-268, 2006.

[43] M. L. Miller, K. Reygers, S. J. Sanders, P. Steinberg, "Glauber modeling in high-energy nuclear collisions," Annual Review of Nuclear and Particle Science , vol. 57, pp. 205-243, 2007.

[44] X. N. Wang, M. Gyulassy, "Gluon shadowing and jet quenching in A+A collisions at s =200A GeV," Physical Review Letters , vol. 68, no. 10, pp. 1480-1483, 1992.

[45] J. W. Cronin, H. J. Frisch, M. J. Shochet, J. P. Boymond, P. A. Piroue, R. L. Sumner, "Production of hadrons at large transverse momentum at 200, 300, and 400 GeV," Physical Review D , vol. 11, pp. 3105, 1975.

[46] M. Lev, B. Petersson, "Nuclear effects at large transverse momentum in a QCD parton model," Zeitschrift für Physik C Particles and Fields , vol. 21, no. 1, pp. 155-161, 1983.

[47] A. Accardi, M. Gyulassy, "Cronin effect vs. geometrical shadowing in d + Au collisions at RHIC," Physics Letters B: Nuclear, Elementary Particle and High-Energy Physics , vol. 586, no. 3-4, pp. 244-253, 2004.

[48] G. Papp, P. Levai, G. Fai, "Saturating Cronin effect in ultrarelativistic proton-nucleus collisions," Physical Review C , vol. 61, no. 2, 1999.

[49] R. C. Hwa, C. B. Yang, R. J. Fries, "Forward production in d+Au collisions by parton recombination," Physical Review C , vol. 71, no. 2, 2005.

[50] B. I. Abelev, J. Adams, M. M. Aggarwal, "Rapidity and species dependence of particle production at large transverse momentum for d + Au collisions at _sNN =200 GeV," Physical Review C , vol. 76, 2007.

[51] L. van Hove, "Multiplicity dependence of p_t spectrum as a possible signal for a phase transition in hadronic collisions," Physics Letters B , vol. 118, no. 1-3, pp. 138-140, 1982.

[52] N. Isgur, H. B. Thacker, "Origin of the Okubo-Zweig-Iizuka rule in QCD," Physical Review D , vol. 64, no. 9, 2001.

[53] S. A. Bass, M. Belkacem, M. Bleicher, "Microscopic models for ultrarelativistic heavy ion collisions," Progress in Particle and Nuclear Physics , vol. 41, pp. 255-369, 1998.

[54] M. Bleicher, E. Zabrodin, C. Spieles, "Relativistic hadron-hadron collisions in the ultra-relativistic quantum molecular dynamics model," Journal of Physics G: Nuclear and Particle Physics , vol. 25, no. 9, article 1859, 1999.

[55] C. Alt, T. Anticic, B. Baatar, "System-size dependence of strangeness production in nucleus-nucleus collisions at _sNN =17.3 GeV," Physical Review Letters , vol. 94, no. 5, 2005.

[56] J. Adams, C. Adler, M. M. Aggarwal, "Multistrange Baryon Production in Au-Au Collisions at _sNN = 130 GeV," Physical Review Letters , vol. 92, no. 18, 2004.

[57] R. C. Hwa, C. B. Yang, "Production of strange particles at intermediate p_T in central Au+Au collisions at high energies," Physical Review C , vol. 75, pp. 054904, 2007.

[58] P. F. Kolb, U. Heinz, "Emission angle dependent HBT at RHIC and beyond," Nuclear Physics A , vol. 715, pp. 653c-656c, 2003.

[59] D. Teaney, J. Lauret, E. V. Shuryak, "Flow at the SPS and RHIC as a quark-gluon plasma signature," Physical Review Letters , vol. 86, no. 21, pp. 4783-4786, 2001.

[60] P. F. Kolb, U. Heinz, "Hydrodynamic description of ultrarelativistic heavy-ion collisions," http://arxiv.org/abs/nucl-th/0305084

[61] P. F. Kolba, P. Huovinend, U. Heinza, H. Heiselberge, "Elliptic flow at SPS and RHIC: from kinetic transport to hydrodynamics," Physics Letters B , vol. 500, no. 3-4, pp. 232-240, 2001.

[62] H. Sorge, "Elliptical flow: a signature for early pressure in ultrarelativistic nucleus-nucleus collisions," Physical Review Letters , vol. 78, pp. 2309-2312, 1997.

[63] J. Y. Ollitrault, "Anisotropy as a signature of transverse collective flow," Physical Review D , vol. 46, pp. 229, 1992.

[64] P. Huovinen, P. F. Kolb, U. Heinz, "Radial and elliptic flow at RHIC: further predictions," Physics Letters B , vol. 503, pp. 58-64, 2001.

[65] A. M. Poskanzer, S. A. Voloshin, "Methods for analyzing anisotropic flow in relativistic nuclear collisions," Physical Review C , vol. 58, no. 3, pp. 1671-1678, 1998.

[66] B. Mohanty, N. Xu, "Probe of the QCD phase diagram with phi-mesons in high-energy nuclear collisions," Journal of Physics G , vol. 36, no. 6, 2009.

[67] M. Nasim, B. Mohanty, N. Xu, "Elliptic flow of [varphi] mesons as a sensitive probe for the onset of the deconfinement transition in high energy heavy-ion collisions," Physical Review C , vol. 87, no. 1, 2013.

[68] P. Bhaduri, S. Chattopadhyay, "Differential elliptic flow of identified hadrons and constituent quark number scaling at the GSI Facility for Antiproton and Ion Research (FAIR)," Physical Review C , vol. 81, 2010.

[69] K. J. Wu, F. Liu, N. Xu, "The number-of-quark scaling of v2 in _sNN = 9.2 GeV Au+Au collisions," Nuclear Physics A , vol. 834, no. 1, pp. 303c-305c, 2010.

[70] M. Bleicher, X. Zhu, "Is constituent quark scaling a unique sign of parton recombination?," European Physical Journal C , vol. 49, no. 1, pp. 303-308, 2007.

[71] T. Hirano, U. Heinz, D. Kharzeev, R. Lacey, Y. Nara, "Mass ordering of differential elliptic flow and its violation for [varphi] mesons," Physical Review C , vol. 77, 2008.