Systematics of Kinetic Freeze-out Properties in High Energy Collisions from STAR
aa r X i v : . [ nu c l - e x ] A ug Nuclear Physics A 00 (2018) 1–4
NuclearPhysics A
Systematics of Kinetic Freeze-out Properties in High EnergyCollisions from STAR
Lokesh Kumar (for the STAR Collaboration) School of Physical Sciences,National Institute of Science Education and Research,Bhubaneswar, India - 751005
Abstract
The main aim of the RHIC Beam Energy Scan (BES) program is to explore the QCD phase diagram which includes search fora possible QCD critical point and the phase boundary between QGP and hadronic phase. We report the collision energy andcentrality dependence of kinetic freeze-out properties from the measured mid-rapidity ( | y | < .
1) light hadrons (pions, kaons,protons and their anti-particles) for Au + Au collisions at the center-of-mass energy √ s NN = T kin and average collective velocity h β i parameters are extracted from blast-wave fits to the identifiedhadron spectra and systematically compared with the results from other collision energies including those at AGS, SPS and LHC.It is found that all results fall into an anti-correlation band in the 2-dimension ( T kin , h β i ) distribution: the largest value of collectivevelocity and lowest temperature is reached in the most central collisions at the highest collision energy. The energy dependence ofthese freeze-out parameters are discussed. Keywords:
Freeze-out, transverse momentum spectra, beam energy scan
1. Introduction
The ultra-relativistic heavy-ion collisions are expected to produce a hot and dense form of matter called QuarkGluon Plasma (QGP) [1]. The fireball produced in these collisions thermalizes rapidly leading to expansion andcooling of the system. Subsequently, the hadronization takes place and the particles get detected in the detectors.During this process, two important stages occur as described below. The point in time after the collisions when theinelastic interactions among the particles stop is referred to as chemical freeze-out. The yields of most of the producedparticles get fixed at chemical freeze-out. The statistical thermal models have successfully described the chemicalfreeze-out stage with unique system parameters such as chemical freeze-out temperature T ch and baryon chemicalpotential µ B [1, 2, 3]. Even after the chemical freeze-out, the elastic interactions among the particles are still ongoingwhich could lead to change in the momentum of the particles. After some time, when the inter-particle distancebecomes so large that the elastic interactions stop, the system is said to have undergone kinetic freeze-out. At thisstage, the transverse momentum p T spectra of the produced particles get fixed. The hydrodynamics inspired modelssuch as the Blast Wave Model [1, 4, 5] have described the kinetic freeze-out scenario with a common temperature T kin and average transverse radial flow velocity h β i which reflects the expansion in transverse direction. A list of members of the STAR Collaboration and acknowledgements can be found at the end of this issue. okesh Kumar / Nuclear Physics A 00 (2018) 1–4 -2 -1 Au+Au 7.7 GeV -2-1 Au+Au 11.5 GeV + π + Kp - π - Kp BW fits -2-1 fit ranges (|y|<0.1) T p: 0.5-1.3 GeV/c π K: 0.25-1.4 GeV/cp: 0.4-1.3 GeV/c -2 -1 Au+Au 19.6 GeV -1 Au+Au 27 GeV (GeV/c) T p -2-1 Au+Au 39 GeV - d y ) ( G e V / c ) T dp T p π N / ( d Figure 1. Invariant yields of π ± , K ± , and p ( ¯ p ) versus transverse momentum in 0–5% central Au + Au collisions at √ s NN = Quantum Chromo Dynamics (QCD), a theory of strong interactions, suggests that the phase diagram has two mainphases: QGP and hadron gas. Lattice QCD predicts that the transition between hadron gas and QGP is a crossover [6]at µ B ∼
0. At high µ B , the transition is expected to be a first order [7, 8]. In between, one expects the position of thecritical point, where the first order phase transition line ends [9, 10]. The experiments at RHIC focus on exploring theQCD phase diagram, locating a critical point and determining the phase boundary between hadron and QGP phase. Inview of these, a Beam Energy Scan (BES) program was started at RHIC [11, 12, 13, 14]. The first phase of the BESprogram yielded many interesting results as a function of energy or µ B related to the search for critical point and phaseboundary [15, 16]. The kinetic freeze-out parameters provide important information about the collision dynamics.The vast range of data collected in the BES program allows for the systematic study of kinetic freeze-out parametersand to see their energy dependence trends. The BES results presented here are obtained for Au + Au collisions at √ s NN = | y | < ff ects.As mentioned earlier the kinetic freeze-out parameters T kin and h β i of the system can be obtained using thehydrodynamics-motivated blast wave model. The model assumes that the particles are locally thermalized at ki-netic freeze-out temperature and are moving with a common transverse collective flow velocity [4, 5]. Assuming aradially boosted thermal source, with a kinetic freeze-out temperature T kin and a transverse radial flow velocity β , thetransverse momentum p T distribution of the particles can be given by dNp T d p T ∝ Z R r dr m T I p T sinh ρ ( r ) T kin ! × K m T cosh ρ ( r ) T kin ! , (1)where m T = q p T + m , m being mass of a hadron, ρ ( r ) = tanh − β , and I and K are the modified Bessel functions.We use the flow velocity profile of the form β = β S ( r / R ) n , where β S is the surface velocity, r / R is the relative radialposition in the thermal source, and n is the exponent of flow velocity profile. Average transverse radial flow velocity h β i can then be obtained as: h β i = + n β S .Figure 1 shows the invariant yields of π ± , K ± , and p ( ¯ p ) versus p T for | y | < + Au collisionsat √ s NN = p T spectra of π, K , p at all energies studied. The low p T part of pion spectra is a ff ected byresonance decays due to which the pion spectra is fitted above p T > / c . The fit parameters are T kin , h β i , and n .The p T spectra can also be characterized by obtaining h p T i or h m T i , where m T is the transverse mass of theparticles. Figure 2 shows the energy dependence of h m T i − m for π ± , K ± , and p ( ¯ p ). The star symbols show results2 okesh Kumar / Nuclear Physics A 00 (2018) 1–4 (GeV) NN s10 100 1000 ) - m ( G e V / c 〉 T m 〈 + π BES + π - π BES - π (a) (GeV) NN s10 100 1000 + K BES + K - K BES - K (b) (GeV) NN s10 100 1000 (c) Figure 2. Energy dependence of h m T i − m for (a) π ± , (b) K ± , and (c) p ( ¯ p ) in central heavy-ion collisions. (c) 〉 β 〈 ( M e V ) k i n T Pb+Pb 2.76 TeVAu+Au 200 GeVAu+Au 62.4 GeVAu+Au 39 GeVAu+Au 27 GeVAu+Au 19.6 GeVAu+Au 11.5 GeVAu+Au 7.7 GeV
STAR Preliminary centralperipheral
Figure 3. Variation of T kin with h β i for di ff erent energies and centralities. The centrality increases from left to right for a given energy. The datapoints other than BES energies are taken from Refs. [5, 20]. from the BES while the data points for AGS, SPS, top RHIC, and LHC energies (represented by open circles andsquares), are taken from the references [5, 18, 19, 20]. It can be seen that h m T i − m increases with energy at lowerenergies, remains almost constant at the BES energies and then increases again towards higher energies up to theLHC. If the system is assumed to be in a thermodynamic equilibrium, h m T i − m can be related to temperature and √ s NN can be related to entropy of the system ( dN / dy ∝ log ( √ s NN ). In view of this, the constant value of h m T i − m canbe interpreted as a signature of first order phase transition [21]. However, more studies may be needed to understandthis behavior [22].Figure 3 shows the variation of T kin with h β i for di ff erent energies and centralities. T kin increases from central toperipheral collisions suggesting a longer lived fireball in central collisions, while h β i decreases from central to periph-eral collisions suggesting more rapid expansion in central collisions. Furthermore, we observe that these parametersshow a two-dimensional anti-correlation band. Higher values of T kin correspond to lower values of h β i and vice-versa.Figure 4 (left panel) shows the energy dependence of kinetic and chemical freeze-out temperatures for centralheavy-ion collisions. We observe that the values of kinetic and chemical freeze-out temperatures are similar around √ s NN = √ s NN = T kin is almost constant around the 7.7–39 GeV and then decreasesup to the LHC energies. The separation between T ch and T kin increases with increasing energy. This might suggestthe e ff ect of increasing hadronic interactions between chemical and kinetic freeze-out when we go towards higherenergies [1]. Figure 4 (right panel) shows the average transverse radial flow velocity plotted as a function of √ s NN .The h β i increases very rapidly at lower energies, remains almost constant for √ s NN = h β i reflects the expansion in the transverse direction, it is observed that thisexpansion velocity is constant around √ s NN = okesh Kumar / Nuclear Physics A 00 (2018) 1–4 (GeV) NN s10 100 1000 T ( M e V ) ch T kin T BES ch T BES kin T ch T kin T Andronic et al. ch T Cleymans et al. ch Tcentral collisions STAR Preliminary (GeV) NN s10 100 1000 ( c ) 〉 β 〈 STAR Preliminarycentral collisions
Figure 4. Left panel: Energy dependence of kinetic and chemical freeze-out temperatures for central heavy-ion collisions. The curves representvarious theoretical predictions [23, 24]. Right panel: Energy dependence of average transverse radial flow velocity for central heavy-ion collisions.The data points other than BES energies are taken from the Refs. [5, 18, 19, 20] and references therein.
2. Conclusions
We have presented a systematic study of kinetic freeze-out parameters in heavy-ion collisions with results fromthe RHIC BES program. The T kin increases from central to peripheral collisions suggesting a longer lived fireballin central collisions, while h β i decreases from central to peripheral collisions suggesting more rapid expansion incentral collisions. The kinetic freeze-out temperature suggests a decrease from lower ( √ s NN ∼ √ s NN ∼ √ s NN ∼ √ s NN = h m T i − m for π , K , p , and ¯ p also shows similar constant behavior around lower BES energies which could be related to first-order phase transitionsignature. References [1] J. Adams et al. (STAR Collaboration), Nucl. Phys. A , 28 (2005).[2] A. Andronic, F. Beutler, P. Braun-Munzinger, K. Redlich and J. Stachel, Phys. Lett. B , 312 (2009) [arXiv:0804.4132 [hep-ph]].[3] S. Wheaton and J. Cleymans, Comput. Phys. Commun. , 84 (2009) [hep-ph / , 2462 (1993) [nucl-th / et al. (STAR Collaboration), Phys. Rev. C , 034909 (2009); ibid. Phys. Rev. C , 024911 (2010).[6] Y. Aoki, G. Endroli, Z. Fodor, S. D. Katz and K. K. Szabo, Nature , 074507 (2008).[8] E. S. Bowman and J. I. Kapusta, Phys. Rev. C , 015202 (2009).[9] M. A. Stephanov, Prog. Theor. Phys. Suppl. , 139 (2004) [Int. J. Mod. Phys. A , 4387 (2005)] [hep-ph / , 1525 (2011) [arXiv:1105.3934 [hep-ph]].[11] L. Kumar (for STAR Collaboration), Nucl. Phys. A , 275C (2009); ibid Nucl. Phys. A , 125 (2011).[12] B. Mohanty, Nucl. Phys. A , 899C (2009).[13] B. I. Abelev et al. (STAR Collaboration), Phys. Rev. C , 024911 (2010).[14] M. M. Aggarwal et al. (STAR Collaboration), arXiv:1007.2613.[15] L. Kumar (STAR Collaboration), Nucl. Phys. A , no. issue, 256c (2013) [arXiv:1211.1350 [nucl-ex]].[16] L. Kumar, Mod. Phys. Lett. A , 1330033 (2013) [arXiv:1311.3426 [nucl-ex]].[17] M. Anderson et al. , NIM A , 659 (2003); W. J. Llope et al. NIM B , 306 (2005).[18] S. V. Afanasiev et al. (NA49 Collaboration), Phys. Rev. C , 054902 (2002); C. Alt et al. (NA49 Collaboration), Phys. Rev. C , 024903(2008); ibid. , 044910 (2006); T. Anticic et al. (NA49 Collaboration), Phys. Rev. C , 024902 (2004).[19] L. Ahle et al. (E866 Collaboration and E917 Collaboration), Phys. Lett. B , 53 (2000); ibid. , 1 (2000); J. L. Klay et al. (E895Collaboration), Phys. Rev. Lett. , 102301 (2002).[20] B. Abelev et al. (ALICE Collaboration), Phys. Rev. C , no. 4, 044910 (2013) [arXiv:1303.0737 [hep-ex]].[21] L. Van Hove, Phys. Lett. B , 138 (1982).[22] B. Mohanty et al. , Phys. Rev. C , 021901 (2008) and references therein.[23] J. Cleymans, H. Oeschler, K. Redlich and S. Wheaton, Phys. Rev. C , 034905 (2006) [hep-ph / , 237C (2010) [arXiv:0911.4931 [nucl-th]]., 237C (2010) [arXiv:0911.4931 [nucl-th]].