Constraining Particle Production Mechanism in Au+Au Collisions at RHIC Energies Using A Multi Phase Transport Model

We study the production of pions, kaons, and (anti-) protons in A Multi Phase Transport (AMPT) Model in Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 27, and 200 GeV. We present the centrality and energy dependence of various bulk observables such as invariant yields as a function of transverse momentum $p_T$, particle yields $dN/dy$, average transverse momentum $\langle p_T \rangle$ and various particle ratios, and compare them with experimental data. Both default and string melting (SM) versions of the AMPT model are used with three different sets of initial conditions. We observe that neither the default nor the SM model could consistently describe the centrality dependence of all observables at the above energies with any one set of initial conditions. The energy dependence behavior of the experimental observables for 0--5\% central collisions is in general better described by the default AMPT model using the default HIJING parameters for Lund string fragmentation and 3mb parton scattering cross-section.


I. INTRODUCTION
Relativistic collisions of heavy ions make it possible to subject nuclear matter to the extreme energy densities required for a possible deconfinement of quarks and gluons. A dense matter with partonic degrees of freedom, often called the quark-gluon plasma (QGP), is expected to form in the initial moments after the collision [1][2][3][4]. Exploring the quantum chromodynamics (QCD) phase diagram to understand the properties of quark matter is one of the most important goals of high-energy heavy ion experiments [5][6][7]. Comparing the results obtained from theoretical models with the experimental data helps in understanding the space-time evolution of QGP and many of its other properties. The QCD phase diagram is usually plotted as temperature (T) versus baryon chemical potential (µ B ). Assuming a thermalized system is reached in heavy-ion collisions, both T and µ B can be varied by changing the collision energy [8][9][10]. To this end, the Beam Energy Scan program at the Relativistic Heavy Ion Collider (RHIC), completed its first phase of operation in 2010 and 2011 [11][12][13][14][15][16][17][18]. The measurements of the bulk properties of identified hadrons using the BES data were recently published [18]. The measurements from STAR cover the µ B interval from 20 to 450 MeV. This is also believed to be the region in which the transition from hadronic matter to QGP takes place [19][20][21][22][23][24][25].
In this paper, we have studied Au + Au collisions at √ s N N = 7.7, 27 and 200 GeV using a multi-phase transport (AMPT) model and compared bulk properties such as transverse momentum p T spectra, multiplicity densities dN/dy, average transverse momentum p T and particle ratios with the experimental data. For this study we have used three different sets of parameters for both the default and string melting (SM) versions of the AMPT model.
The paper is organized as follows. In Section II we give a brief description of the AMPT model and its pa-rameters. In Section III A we present the comparison of transverse momentum spectra between models and experimental data. In Section III B and Section III C we study the centrality dependence of particle yields and average transverse momenta respectively and compare the results with experimental data. The centrality and energy dependence of various particle ratios are discussed in Section III D and Section III E respectively. We summarize in Section IV.

II. THE AMPT MODEL
In this section, we give a short description of the AMPT model and its parameters. The AMPT model was developed to give a coherent description of the dynamics of relativistic heavy-ion collisions [26] and has been used extensively to study them at various energies and environments. It is a hydrid transport model and has four main components: the initial conditions, partonic interactions, hadronization and hadronic interactions [26]. Initial conditions are obtained from the Heavy Ion Jet Interaction Generator (HIJING) model [27]. Hard minijet partons are produced perturbatively if the momentum transfer is more than a threshold (p 0 = 2 GeV/c) and soft strings are produced otherwise. Depending on the version of AMPT model used, default or string melting, the soft strings are either retained or are completely converted to partons.
Zhangs's Parton Cascade (ZPC) [28] is used for partonic interactions. The differential scattering cross section is given by Where σ is the parton-parton scattering cross section, t is the standard Mandelstam variable for four-momentum transfer, α s is the strong coupling constant and µ is the Debye screening mass in partonic matter.

arXiv:1910.11558v1 [hep-ph] 25 Oct 2019
In the default model, only the minijet partons take part in the ZPC and the energy stored in the excited strings is only released after hadrons are formed. For the default model, after the partons stop interacting, they combine with their parent strings. Hadronization of these strings take place using the Lund string fragmentation model [29,30]. The longitudinal momentum of the hadrons generated is given by the Lund string fragmentation function f (z) ∝ z −1 (1 − z) a exp(−bm 2 T /z), z being the light-cone momentum fraction of the hadron of transverse mass m T with respect to the fragmenting string. The average squared transverse momentum p 2 T of the produced particles is proportional to the string tension κ, i.e. the energy stored per unit length of a string, and depends on the Lund string fragmentation parameters as In the string melting version, hadronization takes place via a quark coalescence model in which the nearest partons are combined to form mesons and baryons. The dynamics of the hadronic matter is described by A Relativistic Transport (ART) model which includes mesonmeson, meson-baryon, baryon-baryon, elastic and inelastic scatterings [31]. The parton density in ZPC for the SM version is quite dense as all HIJING strings are converted to partons. As a result the SM version was found to reasonably fit the elliptic flow at RHIC [26]. We have chosen the three parameter sets as given in Table I by taking guidance from earlier studies as detailed below. The parton scattering cross-section is given as σ ≈ 9πα 2 s /(2µ 2 ). Thus, the value of σ depends on a given combination of α s and µ. It has been observed that the multiplicity is not much sensitive to the parton scattering cross-section σ [32] but σ seems to affect the elliptic flow such that larger parton scattering cross-section leads to large elliptic flows [32].
It has been observed that the default HIJING values for the Lund string fragmentation parameters (a = 0.5 and b = 0.9 GeV −2 ) in set B were able to describe the pp data when used in the AMPT default model but underestimated the charged particle yield in central Pb + Pb collisions at the top SPS energy [33][34][35]. For Pb+Pb collisions at LHC energies, the AMPT SM model with default HIJING values for the Lund string fragmentation parameters (a = 0.5 and b = 0.9 GeV −2 ) in set B was able to reproduce the yield and elliptic flow of charged particles but underestimated the p T spectrum except at low p T [32,33].
From Eq.(2) it is clear that parameters a and b determine the p T distribution of the particles. For larger a and b there will be a smaller average square transverse momentum that will produce a steeper p T spectra (with large slope), while their smaller values will lead to a flatter distribution. It has been reported that the values of a = 2.2 and b = 0.5 GeV −2 produce larger multiplicity density as compared to other values of a and b [32]. Thus, the modified values of a = 2.2 and b = 0.5 GeV −2 (Set C) were used to fit the charged particle yield in Pb+Pb collisions at SPS [33,35]. For heavy-ion collisions at RHIC energies, the default AMPT model with these parameters was found to reasonable fit the rapidity and pseudo-rapidity density and the p T spectra but underestimate the elliptic flow [33,35]. On using the AMPT SM with same parameters, the elliptic flow and two-pion HBT were reproduced but the charged particle yield was overestimated while the slopes of the p T spectra were underestimated [26,33].
In order to simultaneously fit the rapidity density, p T spectrum and elliptic flow of pions and kaons at low p T in Au+Au collisions at RHIC energies, the AMPT SM model was used with modified Lund string fragmentation parameters a = 0.55 and b = 0.15 GeV −2 in Set A [33].
Thus we observe that each of these sets satisfactorily describe the heavy-ion data at different energies from various experiments. The availability of centrality dependent results at the RHIC for a vast range of energies allows us to test the validity of the said parameters at these conditions. We generated AMPT events for Au+Au collisions at three energies viz., the lowest RHIC energy (7.7 GeV), an intermediate energy (27 GeV) and the top RHIC energy of 200 GeV. The events are generated using both string melting and default versions of the AMPT. In each of these versions, we use the three sets of parameters as listed in table I to generate the events. About 20k events are used for the analysis at each energy, for each set and for each of the two versions of the model. The centrality selection is done in the same way as in the experimental data [18]. Thus, the AMPT data are divided into nine centrality classes 0-5%, 5-10%, 10-20%, 20-30%, 30-40%, 40-50%, 50-60%, 60-70%, and 70-80%.

III. RESULTS
We present the mid-rapidity (|y| < 0.1) transverse momentum p T spectra, particle yields dN/dy, average transverse momentum p T and ratios of identified particles π ± , K ± , p andp at √ s N N = 7.7, 27 and 200 GeV.
The results are obtained for both AMPT SM and default versions at each energy and using three different sets of parameters listed in          A. Transverse Momentum Spectra Figure 1 shows the invariant yield versus p T in Au+Au collisions at √ s N N = 27 GeV for positively charged particles (π + , K + , p). The results are shown using the set B parameters just for representation. The top three panels represent the results for default AMPT version while the AMPT string melting results are shown in the bottom three panels. Results from the nine collision centralities 0-5%, 5-10%, 10-20%, 20-30%, 30-40%, 40-50%, 60-70% and 70-80% are shown. The invariant yield decreases with increasing p T and also while going from central to peripheral collisions. On comparing the inverse slopes of the spectra for three particles, we observe that they follow the order p > K > π. The same behavior is observed at 7.7 and 200 GeV and for all parameter sets. The negatively charged particles (not presented here) also show similar behavior. GeV, set B parameters describe the π + spectra better. Both the K + and p spectra are described better by the set A parameters at this energy. At 27 GeV (plots not presented here), the π + spectra is described well by set C parameters. The K + and p spectra are explained better by set A parameters. At 200 GeV, the set A and B parameters describe the π + and K + while set A describes the p spectra better as compared to the other sets.
For string melting, at 7.7, 27 (plots not presented here) and 200 GeV, set A parameters describe the π + and p spectra well for 0-5% centrality. The K + spectra at 7.7 GeV are under-predicted by all sets by about a factor of 2 with set A parameters showing a better p T dependence. At 27 GeV, the data over model ratio comes closer to unity for set A parameters but is still under-predicted. At 200 GeV, the ratio of data to model for K + becomes less than unity. Thus, the ratio of data to model for K + decreases with increasing energy from about 2 at 7.7 GeV to just less than unity at 200 GeV using set A parameters. This suggests that the string melting version is important for description of kaons towards higher centerof-mass collision energies but does not characterize lower energy collisions well.
To summarize the observations from Fig. 2   Au + Au collisions from default (top two rows) and string melting (bottom two rows) versions of the AMPT model using parameter sets A, B and C. Experimental data from the STAR collaboration [18,36] are shown by solid circles. The data/model ratios are presented at the bottom of each panel.
• The pion spectra at 7.7 GeV is described well by SM model set A parameters. At 27 GeV, it is described better by default set A paramaters. At 200 GeV, it is described by both default and SM set A parameters.
• The kaon spectra at 7.7 and 27 GeV is described better by default set A parameters. At 200 GeV, it is described OK by default set A parameters but is slightly overestimated.
• The proton spectra at 7.7 and 27 GeV is described well by SM set A parameters at low p T and by default set A parameters at high p T . At 200 GeV, the spectra is described OK by both default and SM set A parameters.
The spectra comparison are quantized by comparing particle yields, average transverse momenta, and particle ratios. Figure 3 shows the centrality dependence of yield dN/dy normalized by half the number of participants N part /2 for π + , K + and protons in Au+Au collisions at 7.7, 27 and 200 GeV. The results from the default version are shown in the top three rows, while those using the string melting version are shown in the bottom three rows. The results using the three sets of parameters in both the model versions are compared with the experimental data. The experimental data show an increase of yield from peripheral to central collisions suggesting particle production by both soft and hard processes.

B. Particle Yields (dN/dy)
In default version, the dN/dy/(0.5 N part ) of π + at 7.7 GeV is described by set B parameters at all N part values. At 27 GeV, set C parameters agree with data at all N part values, but N part dependence is flat as opposed to the data in which it increases from peripheral to central collisions. At 200 GeV, none of the sets could explain the behavior observed in data for all N part values. The set A parameters could only describe the data for N part > 100 while set C parameters agree with data for N part < 40. The K + yields at 7.7 GeV are not explained by any of the parameter sets for all N part . The set A parameters can only describe the data for N part < 120. At 27 GeV, K + yields are better described by set C parameters for all N part , while at 200 GeV, the set A parameters describe the K + yields for all N part . The proton yields are described by all the parameter sets at all N part for 7.7 GeV, but none of them work for 27 GeV other than set A and C at N part < 30. Whereas at 200 GeV, none of the parameters could explain the p yields at any centrality.
For the AMPT model with string melting, the dN/dy/(0.5 N part ) of π + at 7.7 GeV is described by all the parameters at all N part values. However, the set C parameters show a rather flat behavior as opposed to the slight increase from peripheral to central collisions. At 27 GeV, the set C parameters describe the π + yields at all N part values but set A and B parameters are closer in agreement with the data in peripheral collisions. At 200 GeV, in central collisions ( N part > 100), pion yields are well described by set B parameters while those in peripheral collisions ( N part < 130) are described by set C parameters. The K + yields are only described by set A parameters below N part 50 at 7.7 GeV, below N part 130 by set C parameters at 27 GeV and for all N part by set C parameters at 200 GeV. The proton yields at 7.7 GeV are described by all parameter sets at all N part , at 27 GeV by set A parameters at all N part , and at 200 GeV by set B parameters for N part > 220 and by set C parameters for N part < 90 but not by any parameter set at the most peripheral point.
To summarize the observations for all centralities: • The pion yield is described by set C parameters for √ s N N ≤ 27 GeV for SM model, but by none of the models at 200 GeV. However, the 200 GeV pion yield is constrained between Set A and C at all N part for both versions of AMPT.
• The kaon yield at 7.7 GeV is not explained at all N part by any set with either versions (the models underestimate the data), explained at 27 GeV by the default model with set C parameters and also at 200 GeV by the default model with set A parameters and by the SM model with set C parameters. Thus, at 7.7 GeV, the strange particle production is not explained by AMPT model.
• The proton yield at 7.7 GeV is explained by all parameter sets with both the models, at 27 GeV by set A parameters with SM model, but by none of the models at 200 GeV. However, the 200 GeV proton yield is constrained between Set B and C at all N part for the AMPT SM version.
• In general, for most cases, it is observed that the Set C parameters corresponding to largest a = 2.2 give higher yields while Set B corresponding to smallest a = 0.5 give smaller yields as expected.
C. Average Transverse Momentum ( pT ) Figure 4 shows the centrality dependence of average transverse momentum p T for π + , K + and protons, in   Using the default version, p T of π + at 7.7 GeV is described by set C parameters for all N part . At 27 GeV, set A and set C parameters agree with data at N part > 220. While the set A parameters do not follow the behavior of data, set B and C reproduce the data qualitatively and tend to agree with it at the last two peripheral points. At 200 GeV, none of the sets could explain the behavior observed in data for all N part values. The set B parameters only describe the most peripheral data. The K + p T at 7.7 GeV can only be explained by set A parameters for N part > 220, and by sets B and C for N part < 170. At 27 GeV, K + p T are better described by set A parameters for N part > 150. Set A shows a flat behavior with N part . However, sets B and C only qualitatively describe the experimental data. At 200 GeV, set A parameters describe the K + p T for N part > 150. Both set B and C parameters underestimate the data at all N part . For protons at 7.7 GeV p T are described by set A parameters for N part > 50 and by both set B and C below N part ≈ 80. At 27 GeV, set A parameters describe the protons' p T for N part > 220. For peripheral collisions, set B and C parameters give closer p T values to experimental data but underestimate nevertheless. At 200 GeV, the set A parameters could explain the p p T for all N part values except the two peripheral bins. The other two parameter sets underestimated the data quite significantly.
For AMPT string melting, the p T of π + at 7.7 GeV is described by set A parameters at three mid-central collisions but under(over) estimated at central(peripheral) collisions. Sets B and C can only describe the data at the last three peripheral bins. At 27 GeV, the set A parameters could explain the data for N part ≥ 70 while set B and C parameters could only agree with data at the most peripheral bin. Increasing the energy further to 200 GeV leads to the overestimation of data by set A parameters with only the most central point sufficiently close to the data. Set C can describe the data at three most peripheral and set B at the two most peripheral points. The K + p T at 7.7 GeV are described by set A parameters for four mid-central points but under(over) estimated at central(peripheral) collisions. The set C parameters tend to describe the data below N part 90. Increasing the energy to 27 GeV, for K + , leads to better agreement also in central collisions by set A parameters. These parameters describe the data for all but last two most peripheral N part values. Increasing the energy further to 200 GeV, for K + , does not change the results much for set A parameters which still describe the data from mid-central to central collisions. Using set C parameters for K + , the model agrees with data at the most peripheral point. The proton p T at 7.7 GeV are described by set A parameters at all N part except at the most peripheral bin. The set C parameters seem to describe the data at peripheral collisions below N part ≈ 100. At 27 GeV, the set A parameters describe the proton data at all but the two most central and the most peripheral point. The other two parameter sets underestimate the data. At 200 GeV, the set A parameters only describe the proton data at most peripheral bin and underestimate the data for all other N part values. The sets B and C underestimate the data at all N part values.
To summarize the above observations: • The p T of pion at 7.7 GeV is described at all N part by default AMPT set C parameters. At 27 GeV, it is described by AMPT SM set A parameters for only N part > 50 and is constrained between sets A and C below that. At 200 GeV, it is explained by none of the models but constrained between sets A and B for both the default and SM versions.
• The kaon p T at 7.7 GeV is described partially by default AMPT set A parameters for N part > 220, and by default AMPT set B and C parameters for N part < 170. At 27 GeV, it is explained by SM set A parameters for all N part except at the two most peripheral points. For the two most peripheral bins, it is constrained between SM sets A and C. At 200 GeV, it is explained by default and SM set A parameters for N part > 100. Below that, it is constrained better between SM sets A and C.
• The proton p T at 7.7 GeV is described by SM set A parameters at all N part except the most peripheral bin. The SM sets B and C describe the peripheral bin. At 27 GeV, again, SM set A parameters work better for all but the most peripheral bin and two most central bins. At 200 GeV, the proton p T is explained at all but last two peripheral bins by default set A parameters. The last two bins are constrained between default sets A and B.

D. Particle Ratios
In Fig. 5, we show the centrality dependence of various antiparticle to particle (π − /π + , K − /K + ,p/p) ratios at mid-rapidity (|y| < 0.1) in Au + Au collisions at √ s N N = 7.7, 27 and 200 GeV obtained from the default (top three rows) and SM (bottom three rows) AMPT model using the three parameter sets A, B and C. The results are again compared with the corresponding experimental data. The default AMPT model could reasonably predict the π − /π + ratio at the three energies with all the parameter cases. The K − /K + ratio at 7.7 GeV is mostly underestimated by set A parameters while the set B and set C parameters give closer values to data in general. At 27 GeV, the results with the three parameter sets are close to each other and the data agreeing marginally with the data. At 200 GeV, the K − /K + ratio is mostly underestimated by three parameter sets but matches with the data in peripheral collisions. Thep/p ratio at 7.7 GeV is mostly overestimated by all the three parameter sets. For N part < 90 (except the most peripheral bin), set B   : Centrality dependence of antiparticle to particle (π − /π + , K − /K + ,p/p) ratios at mid-rapidity (|y| < 0.1) in Au + Au collisions at √ sNN = 7.7, 27, and 200 GeV from the AMPT default and SM models. Results are presented using the parameter sets A, B and C. Experimental data from the STAR collaboration [18,36] are shown by solid circles.  6: Centrality dependence of mixed particle (K + /π + , K − /π − , p/π + ,p/π − ) ratios at mid-rapidity (|y| < 0.1) in Au + Au collisions at √ sNN = 7.7, 27, and 200 GeV from the default and AMPT SM models. Results are presented using the parameter sets A,B and C. Experimental data from the STAR collaboration [18,36] are shown by solid circles.
parameters explain the data. At 27 GeV, thep/p ratio is explained by set B parameters for N part > 100. At 200 GeV, all the three parameter sets seem to describe thē p/p ratio, only with the exception of the most peripheral point by set A parameters.
Similar to the default model, the AMPT model with string melting could reasonably predict the π − /π + ratio at the three energies with all the three parameter cases. The K − /K + ratio at 7.7 GeV is generally described by set C parameters for central collisions N part > 150. Set B parameters could only explain the ratio at three points before the most peripheral bin. At 27 and 200 GeV, set A parameters describe the data at all centralities. The set B parameters could also explain the data at all but two centralities. Thep/p ratio at 7.7 GeV is described by the set C parameters for all centralities except at the two most peripheral bins. At 27 GeV, the ratio is described by the set C parameters at all centralities. At 200 GeV, all three sets give similar values and close to the experimentalp/p ratio.
The mixed particle ratio results could help in better differentiating among the three parameter sets. In Fig.  6, we show the centrality dependence of various mixed (K + /π + , K − /π − , p/π + ,p/π − ) particle ratios at midrapidity (|y| < 0.1) in Au + Au collisions at √ s N N = 7.7, 27 and 200 GeV obtained from the default (top three rows) and SM (bottom three rows) AMPT model using the three parameter sets A, B and C. The results are compared with the corresponding experimental data. For default AMPT model, the K + /π + ratio at 7.7 GeV is not explained by any of the parameter sets except at very peripheral collisions. At 27 GeV, the K + /π + ratio is described by set C parameters at all N part . The set A parameters describe the data at all centralities except at the most peripheral one, while set B parameters describe the ratio at almost all N part values except in midcentral collisions. Similar conclusions could be drawn for 200 GeV except that the set A parameters now miss the data at more N part values. Same as the K + /π + ratio, the K − /π − ratio at 7.7 GeV is also not described by any of the three parameter sets except at the very peripheral points. At 27 GeV, the ratio is well explained by set C parameters for all N part . The set A parameters also describe the data at all N part except at the most peripheral bin, while set C parameters work well at peripheral collisions. Similar conclusions could be drawn at 200 GeV except that the set C parameters also miss a few points towards the peripheral collisions. Thus, in this case, set A describes the data better at all N part except the peripheral point. The p/π + ratio at 7.7 GeV is described by all parameter sets at all N part . At 27 GeV, the ratio is described by set A parameters at all N part . At 200 GeV, the p/π + ratio predicted by set A parameters is closer to data but does not agree exactly with it. Thep/π − ratio at 7.7 GeV is described by set B and C parameters at all N part except at one bin towards peripheral collisions. At 27 GeV, it is described well by set C parameters at all N part values. Set B also describes this ratio at almost all the centralities. At 200 GeV, the ratio is explained by set A parameters for all N part . For AMPT SM model, the K + /π + ratio at 7.7 GeV is not explained by any parameter set except at the most peripheral collision. It is interesting to note that no set shows even the qualitative behavior of centrality dependence observed in experimental data. At 27 GeV, the K + /π + ratio is marginally described by set A parameters for most centralities except the peripheral. However, the N part dependence is well predicted by set C parameters though they consistently underestimate the data. At 200 GeV, the set C parameters describe the data at all centralities. The set A parameters also describe the K + /π + ratio for all centralities except at the most peripheral collisions. The K − /π − ratio at 7.7 GeV is also not described by any of the three parameter sets except at the most peripheral point by set C. At 27 GeV, the ratio is well explained by set C parameters for all N part . The set A parameters also result in closer values to the data at most centralities. At 200 GeV, set C parameters describe the data at all centralities. Set A also describes the data at all centralities except at the most peripheral bin. The p/π + ratio at 7.7 GeV is described by all parameter sets at all N part . At 27 GeV, the ratio is described by set A parameters at all N part . The set B parameters describe the data for central collisions but fail at peripheral collisions while the set C parameters describe the data at peripheral collisions failing at central collisions. At 200 GeV, the p/π + ratio is described by set A and B parameters towards the central collisions ( N part > 200) and by set C parameters towards peripheral collisions ( N part < 150). Thep/π − ratio at 7.7 GeV is described by both set B and C parameters at almost all N part . At 27 GeV, the ratio is described by set C parameters from mid-central ( N part < 200) to peripheral collisions. At 200 GeV, the ratio is described by set C parameters for most N part except at a few centrality bins.
To summarize the observations from the two models (Figs. 5 and 6) : • The π − /π + ratio is described by both default and SM models using the sets A, B and C at the three energies √ s N N = 7.7, 27, and 200 GeV.
• The K − /K + ratio at 7.7 GeV is better described by SM set C parameters for N part > 150. At 27 and 200 GeV, it is described at all N part by SM set A parameters.
• Thep/p ratio at 7.7 GeV is described better by SM set C parameters for all centralities except at the last two peripheral bins. At 27 GeV, the ratio is described well by SM set C parameters and at 200 GeV, by default set B parameters at all centralities.
• The K + /π + ratio at 7.7 GeV is not described well by any of the models at all centralities, except the peripheral bins. The default model gives similar centrality dependence but underpredicts the data. At 27 GeV, this ratio is described better by default set C parameters at all N part . At 200 GeV, it is explained by both default and SM set C parameters at all centralities. Thus, at 7.7 GeV, the strange particle production is not well explained by the AMPT model.
• The K − /π − ratio results at 7.7 GeV are similar to K + /π + ratio. It is also not explained by any model at all centralities except at the peripheral bins. At 27 GeV, this ratio is described by both default and SM set C parameters. At 200 GeV, it is explained by SM set C parameters.
• The p/π + ratio at 7.7 GeV is explained by both default and SM models with all parameter sets. At 27 GeV, the ratio is described by both default and SM Set A parameters at all centralities. However, at 200 GeV, it is not explained by a single parameter set in either models at all the centralities. For central collisions, SM set A and B parameters describe the data while for peripheral collisions SM set C parameters work better.
• Thep/π − ratio at 7.7 GeV is described at most N part by both default and SM set B and C parameters. At 27 GeV, it is described by default set C parameters and is well explained at 200 GeV by default set A parameters at all N part .

E. Energy Dependence of Particle Ratios
The particle yields and ratios are used in statistical thermal models to determine the freeze-out conditions in heavy-ion collisions [8][9][10]18]. We present the energy dependence of mixed particle ratios for 0-5% central collisions that play an important role in determining the freeze-out conditions. Figure 7 presents the comparison of K ± /π ± ratios at mid-rapidity (|y| < 0.1) for 0-5% centrality in Au + Au collisions at √ s N N = 7.7, 27 and 200 GeV from the AMPT default (left panels) and SM (right panels) models with experimental data [13,18,[36][37][38][39][40][41][42][43]. The results from AMPT are presented with the parameters sets A, B and C. The experimental results of the K + /π + ratio show an interesting trend. The ratio increases with energy, reaches a maximum and then decreases and becomes almost constant at higher energies. It has been suggested that the peak position, also called "horn", in this energy dependence could be a signature of phase transition from hadronic to QGP gas [18,43]. However, the peak position also corresponds to the energy region with maximum baryon density [44]. For the default AMPT model, the three sets are consistent with data at 27 and 200 GeV. At 7.7 GeV, all the three sets under-predict the ratio significantly. However, among the three sets, the set A parameters are closest to the data. For SM, set A seems to be in better agreement with the data at 27 and 200 GeV but under-predicts the data at 7.7 GeV. Comparing between default and SM, the default set A parameters describe the energy dependence of K + /π + ratio better. The K − /π − ratio at 200 GeV is described by all three sets of the default and SM model. At 27 GeV, the set A and C parameters are consistent with the data. At 7.7 GeV, the ratio is again under-predicted by both the versions. The default model is in closer agreement with data at lower energies. Thus, it can be concluded that strangeness (kaon) production at √ s N N = 7.7 GeV is not explained by the AMPT model. Figure 8 shows the comparison of p/π + andp/π − ratios at mid-rapidity (|y| < 0.1) for 0-5% centrality in Au + Au collisions at √ s N N = 7.7, 27 and 200 GeV from the AMPT default (left panels) and SM (right panels) models with experimental data [18,36]. The results for AMPT are presented for the parameters sets A, B and C. In the default model, the set A parameters seem to describe the p/π + ratio better at the three energies. With the SM model, both sets A and B describe the data at the three energies. Thep/π − ratio from default AMPT set A parameters describe the ratio at 7.7 and 200 GeV, while set B and C parameters describe it at 7.7 and 27 GeV. Overall, the set A parameters are closest to the data. For SM model, the set C parameters describe the ratio at 7.7 and 200 GeV, while set B and C only describe the data at 7.7 GeV. Again, we observe that the default AMPT model with set A parameters works better than SM model. In general, considering the energy dependence behaviour in 0-5% central Au + Au collisions, we observe that for all observables including yields, p T and ratios, the AMPT default model with set A parameters explain the data better than the other sets and also better than AMPT SM with all the sets. The AMPT default explaining particle yields or ratios better than SM version is consistent with the earlier studies where it is mentioned that SM version is better suited to describe the elliptic flow [26].

IV. SUMMARY
This study is an attempt to the first detailed comparison of the AMPT model with experimental data of three extreme energy regions at RHIC, different centralities and various identified particles. The default and SM AMPT models were initiated with different sets of parameters (as given in Table I) and the results obtained were compared with the data from the STAR experiment. For this study, we have looked at bulk properties like transverse momentum spectra, yields, average transverse momentum and various ratios corresponding to π ± , K ± , p, andp.
GeV, and by both default and SM Set A at 200 GeV. For the kaon spectra, default Set A works better at three energies. For proton spectra, both default and SM Set A work fine at three energies. It is observed that for all centralities, pion yield is described by set C parameters at √ s N N ≤ 27 GeV with both default and SM models but by none of the models at 200 GeV. However, the 200 GeV pion yield is constrained between sets A and C at all N part for both versions of AMPT. The kaon yield at 7.7 GeV is not explained at all N part by any one set with either versions (the models underestimate the data), explained at 27 GeV by the default model with set C parameters, and also at 200 GeV by the default model with set A parameters and by the SM model with set C parameters. Thus, at 7.7 GeV, the strange particle production is not explained by AMPT model. The proton yield is explained at 7.7 GeV by all parameter sets with both models, at 27 GeV by set A parameters of SM model but by none of the models at 200 GeV. However, the 200 GeV proton yield is constrained between sets B and C at all N part for the SM version of AMPT. In general, for most cases, it is observed that the set C parameters corresponding to largest a = 2.2 give higher yields while set B corresponding to smallest a = 0.5 give smaller yields as expected.
It is observed that the p T of pion at 7.7 GeV is described at all N part by default AMPT set C parameters. At 27 GeV, it is described by AMPT SM set A parameters for only N part > 50 and is constrained between sets A and C below that. At 200 GeV, it is explained by none of the models but is constrained between sets A and B for both default and SM versions. The kaon p T at 7.7 GeV is described partially by default set A parameters for N part > 220, and by default set B and C parameters for N part < 170. At 27 GeV, it is explained by SM set A parameters for all N part except at the two most peripheral points. For the two most peripheral bins, it is constrained between SM sets A and C. At 200 GeV, it is explained by the default and SM set A parameters for N part > 100. Below that, it is constrained better between SM sets A and C. The proton p T at 7.7 GeV is described by SM set A parameters all N part except at the most peripheral bin. The SM sets B and C describe the peripheral bin. At 27 GeV, again, SM set A parameters work better for all but the most peripheral bin and two most central bins. At 200 GeV, the proton p T is explained at all but last two peripheral bins by default set A parameters. The last two bins are constrained between default set A and B.
It is observed that the π − /π + ratio is described by both default and SM models using the sets A, B and C at the three energies √ s N N = 7.7, 27 and 200 GeV. The K − /K + ratio at 7.7 GeV is better described by SM set C parameters for N part > 150. At 27 and 200 GeV, it is described for all N part by SM set A parameters. Thep/p ratio at 7.7 GeV is described better by SM set C parameters for all centralities except at the last two peripheral bins. At 27 GeV, the ratio is described well by SM set C parameters and at 200 GeV, by default set B parameters at all centralities. The K + /π + ratio at 7.7 GeV is not described well by any of the models at all centralities, except the peripheral bins. The default model gives similar centrality dependence but under predicts the data. At 27 GeV, this ratio is described better by default set C parameters at all N part . At 200 GeV, it is explained by both default and SM set C parameters at all centralities. Thus, at 7.7 GeV, the strange particle production is not explained by AMPT model. The K − /π − ratio results at 7.7 GeV are similar to K + /π + ratio. It is also not explained by any model at all centralities except the peripheral bins. At 27 GeV, this ratio is described by both default and SM set C parameters. At 200 GeV, it is explained by SM set C parameters. The p/π + ratio at 7.7 GeV is explained by both default and SM models with all parameter sets. At 27 GeV, the ratio is described by both default and SM set A parameters at all centralities. However, at 200 GeV, it is not explained by a single parameter set in either models at all the centralities. For central collisions, SM set A and B parameters describe the data while for peripheral collisions SM set C parameters work better. Thep/π − ratio at 7.7 GeV is described at most N part by both default and SM set B and C parameters. At 27 GeV, it is described by default set C parameters and is well explained at 200 GeV by default set A parameters at all N part . For the energy dependence of K + /π + ratio in 0-5% Au + Au central collisions, we observe that in case of the default AMPT model, the three sets are consistent with data at 27 and 200 GeV. At 7.7 GeV, all the three sets under-predict the ratio significantly. However, among the three sets, the set A parameters are closest to the data. For SM, set A seems to be in better agreement with the data at 27 and 200 GeV but under-predicts the data at 7.7 GeV. Comparing between default and SM, the default set A parameters describe the energy dependence of K + /π + ratio better. The K − /π − ratio at 200 GeV is described by all three sets of the default and SM model. At 27 GeV, the set A and C parameters are consistent with the data. At 7.7 GeV, the ratio is again under-predicted by both the versions. The default model is in relatively close agreement with data at lower energies. Thus, we again observe that the strangeness (kaon) production at √ s N N = 7.7 GeV is not explained by the AMPT model. The energy dependence of p/π + andp/π − ratios are also presented. In the default model, the set A parameters seem to describe the p/π + ratio better at the three energies. In the SM model, both sets A and B describe the data at the three energies. Thep/π − ratio from default AMPT set A parameters describe the ratio at 7.7 and 200 GeV, while set B and C parameters describe it at 7.7 and 27 GeV. Overall, the set A parameters are closest to the data. For SM model, the set C parameters describe the ratio at 7.7 and 200 GeV, while sets B and C only describe the data at 7.7 GeV. Again, we observe that the default AMPT model with set A parameters works better than SM model.
In general for the energy dependence behavior in 0-5% Au+Au central collisions we observe that for observables including yields, p T , and ratios, the default AMPT with set A parameters is generally better than the other sets and also better than AMPT SM with any set.
These comparisons of various bulk observables at three different energy regions and for different centralities provide help in constraining the models in a better way.