Production of Kaon and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.06580067pt" id="M1" height="11.4652pt" version="1.1" viewBox="-0.0657574 -11.3994 11.9474 11.4652" width="11.9474pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-140" d="M671 0V28C608 36 593 47 562 130C495 309 432 486 368 665L336 656C270 481 202 311 134 139C98 47 84 39 20 28V0H241V28C167 38 156 47 178 115C217 236 276 383 327 530H329C375 398 437 223 484 92C499 47 489 37 424 28V0H671Z"/></g></svg> in Nucleus-Nucleus Collisions at Ultrarelativistic Energy from a Blast-Wave Model

Zhang, S.; Ma, Y. G.; Chen, J. H.; Zhong, C.

doi:https://doi.org/10.1155/2015/460590

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Volume 2015 | Article ID 460590 | https://doi.org/10.1155/2015/460590

Production of Kaon and in Nucleus-Nucleus Collisions at Ultrarelativistic Energy from a Blast-Wave Model

S. Zhang,¹Y. G. Ma,^1,2J. H. Chen,¹and C. Zhong¹

Academic Editor: Bhartendu K. Singh

Received27 Jun 2014

Accepted28 Sept 2014

Published14 Jun 2015

Abstract

The particle production of Kaon and is studied in nucleus-nucleus collisions at relativistic energy based on a chemical equilibrium blast-wave model. The transverse momentum spectra of Kaon and at the kinetic freeze-out stage from our model are in good agreement with the experimental results. The kinetic freeze-out parameters of temperature and radial flow parameter are presented for the FOPI, RHIC, and LHC energies. And the resonance decay effect is also discussed. The systematic study for beam energy dependence of the strangeness particle production will help us to better understand the properties of the matter created in heavy-ion collisions at the kinetic freeze-out stage.

1. Introduction

Study on quark-gluon plasma (QGP) [1] by ultrarelativistic heavy-ion collisions [2–5] provides an opportunity to understand the production mechanism of strangeness hadrons and the phase-space evolution in the system created; in particular, the energy dependence is thought as one of important observables to study various aspects of the QCD phase diagram [6–8] in the beam energy scan program at RHIC [9]. The s-quarks in strangeness hadrons can be a good probe to investigate the properties of the high dense and temperature matter because there should be no net strangeness content in the colliding system [10–13]. The s-quarks are all created in the reaction. Kaon is produced associated with -hyperon at FOPI energy and at higher energies, such as in the RHIC or LHC region, and it can be produced by another mechanism, the so-called pair production [2–5]. The transverse momentum distribution encodes rich physics information. It has been measured in p + p, p + nucleus, or nucleus + nucleus collisions at different energy range by the FOPI [14] and KaoS [15] collaboration at GeV, by the RHIC-STAR collaboration at GeV [16, 17] and 200 GeV [18, 19], by the LHC-ALICE collaboration [20–23] at and 7 TeV, and so forth. The resonance decay effect is also discussed in the above papers [16, 24]. Through fitting the measured transverse momentum distribution by a blast-wave model [25], one can investigate the properties of the collision system at kinetic freeze-out stage. The temperature parameter and the radial flow at kinetic freeze-out stage can provide some information about the evolution of the expanding phase space. One can also study if the system has reached kinetic equilibrium stage when the hadron interactions were completed. The resonances decay will change the production rate and the distribution of Kaon and . However, it is difficult to estimate the effect quantitatively in experiment. The blast-wave model has been applied in experimental analysis [16, 26] to study the kinetic freeze-out properties. Retière and Lisa [27] have explored in detail an analytic parameterization of the freeze-out configuration and investigated the spectra, the collective flow, and the HBT correlation of the hadrons produced in head-on nuclear collisions at top RHIC energy. In addition, the DRAGON [28] and the THERMINATOR2 [29, 30] models have been developed to study the phase-space distribution of produced hadrons at freeze-out stage. In this paper, we carry out a detailed study on the beam energy dependence of Kaon and production based on a blast-wave model. The transverse momentum distributions of Kaon and are presented. The chemical and kinetic freeze-out parameters are consistent with the ones extracted from experimental data. The resonance decay effect is also investigated and an approximate estimation of the percent of Kaon and from resonance decay to total Kaon and is achieved.

2. Blast-Wave Model with Thermal Equilibrium Mechanism

As discussed above, within the framework of the blast-wave model, the fireball created in high-energy heavy-ion collisions is assumed to be in local thermal equilibrium and expands at a four-component velocity . The phase-space distribution of hadrons emitted from the expanding fireball can be expressed as a Wigner function [27–30]:where , , and are the spin, rapidity, and transverse mass of the hadron, respectively, and is the four-component momentum. Equation (1) is formulated in a Lorentz covariant way, and are the polar coordinates, and and are the pseudorapidity and the proper time, respectively. is defined aswith () standing for the coordinates in the transverse plane and being the average transverse radius. The kinetic freeze-out temperature and the radial flow parameter are important in determining the transverse momentum spectrum. And the latter will affect the four-component velocity field. Since we are currently interested in the spectrum at midrapidity, the pseudorapidity distribution is not important. The spectrum can then be written asA thermal equilibrium model is employed to calculate the chemical components of hadrons. The particle density of species can be expressed as [28, 31–36]with the upper (lower) sign being for bosons (fermions) and being the degeneracy factor. Assuming that the chemical equilibrium condition is satisfied, (4) essentially determines the fraction of particle species . The particle yield can be described by adjusting parameters such as the chemical freeze-out temperature , the baryon chemical potential , the strangeness chemical potential , and the system volume . And then the fraction of particle species and its phase-space distribution can be calculated from (4) and (3).

3. Results and Discussion

The rapidity distributions of , proton, and are presented in Figure 1. The hadron rapidity distribution is related to the density at reaction scope. The calculated results can describe the data from the FOPI [14] and KaoS collaborations [15] for , proton, and in Ni + Ni collisions at GeV. The is mainly produced at midrapidity and is different from proton distribution at forward/backward rapidity. This results from the pronounced longitudinal expansion of proton and indicates large degree of transparency in Ni + Ni system at the FOPI energies [14]. A similar calculation for from other groups can be found in [37] and our previous results for were calculated by a transport model [38].

The collective properties of the hot and dense matter created in ultrarelativistic heavy-ion collisions at freeze-out stage can be studied through transverse momentum () distributions of identified particles. The radial flowis related to the maximum flow rapidityThe results are independent of since the dependence is averaged out after integration.

Transverse momentum () spectrum is a basic observable in ultrarelativistic heavy-ion collisions [39, 40]. By fitting the transverse momentum spectra with thermal model, information of the system created in the collisions can be obtained, such as the kinetic freeze-out temperature and the radial flow. If the spectra are identified for different particles species, the ratio between the different particles will give the chemical freeze-out temperature and baryon (strangeness) chemical potentials. In this paper, a blast-wave model with chemical equilibrium model is employed to calculate the transverse momentum () spectra of Kaon and in nucleus-nucleus collisions at ultrarelativistic energy from 2.6 GeV to 2.76 TeV corresponding to the FOPI, RHIC, and LHC energy range.

Figure 2 shows the transverse momentum distribution of and by the blast-wave model compared with the data from FOPI collaboration [14] in Ni + Ni collisions at GeV. Our results can describe the data well. The chemical temperature and the baryon chemical potential used in this calculation are similar to the ones applied in [37]. And the kinetic freeze-out parameters of temperature and radial flow are chosen from experimental results with compilation in [16]. The production of Kaon and here is near the threshold; thus, it can be a reference in Lanzhou-Cooling Storage Ring (CSR) facility and High Intensity Accelerator Facility (HIAF) in the near future. Figures 3 and 4 present the transverse momentum distributions of and at midrapidity in Au + Au central collisions at GeV and 200 GeV, respectively. The chemical and kinetic freeze-out parameters are extracted from data as in [16, 35, 36]. And for LHC energy the chemical freeze-out parameters and kinetic freeze-out temperatures were already discussed in our previous study [24] and Figure 5 presents the distribution of and in Pb + Pb central collisions at TeV. Our calculated results are in good agreement with the distribution from experiment. From Figures 2, 3, 4, and 5, it can be found that the transverse momentum distributions of are harder than those of Kaon. The slope (effective temperature) of the momentum distribution is related to both the radial flow parameter and the mass of particles (); that is, [41–43]. The radial flow will push the heavier particle to high transverse momentum; therefore, the stiffer spectrum emerges for in contrast with Kaon.

As discussed above the collective properties of the hot and dense matter created in ultrarelativistic heavy-ion collisions at freeze-out stage can be calculated through (5). Figure 6 shows the radial flow parameter as a function of centre of mass energy . It shows an increasing trend of the radial flow with the increasing of centre of mass energy . Namely, the expanding velocity of the collision system in radial direction is larger at higher energy. From Figure 6, the radial flow used in this calculation is consistent with those extracted from the experimental results [16]. It implies that these parameters are also valid for strangeness hadrons.

The resonance production rate is high in nucleus-nucleus collisions at relativistic energy. The hadrons decayed from resonances will pollute the distribution of hadrons produced in the collision [16]. However, it is difficult to measure the effect precisely in experiment due to the wide species of resonance. This can be done in model calculation, though. In our previous work [24], this effect for , , and is discussed in detail in the LHC energy range. We show the results for strangeness hadron in different energy from Figures 2, 3, 4, and 5 in this paper. In this calculation, Kaon’s and ’s resonances are all included. The Kaons (decayed from resonances) are mainly from , , and other heavy resonances whose masses are heavier than that of 2 Kaons, and ’s (decayed from resonance) are mainly from ’s and ’s resonances. From (4) and the mass of those particles mentioned above, one can estimate that the production rate from resonance decay of ’s will be more than that of Kaons. And Table 1 summarises our estimation for this effect. The percent of () from resonance decay to total () is increased with the increasing of centre of mass energy . The percentage for is higher than that for . And the effect from resonance decay to and is more significant at RHIC and LHC energy than the ones at low beam energy.

4. Summary

The blast-wave model with a chemical equilibrium model is employed to calculate the production of Kaon and in nucleus-nucleus collisions at relativistic energy. The baryon chemical potential and chemical freeze-out temperature are consistent with those extracted from experiments [16] and used in other model calculations [37]. The kinetic freeze-out properties are also discussed such as kinetic freeze-out temperature and radial flow parameter . These kinetic freeze-out parameters are in good agreement with the ones from experimental results and are found to be valid for strangeness hadrons (Kaon and ). And the resonance decay effect on strangeness production is also studied in detail in this paper. In summary, the beam energy dependence of Kaon and production can be a good probe to study the properties of the dense matter created in ultrarelativistic heavy-ion collisions. Our results shed light on the beam energy scan at RHIC and the academic activity related to strangeness production at Lanzhou-CSR facility.

Conflict of Interests

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

Acknowledgments

This work was supported in part by the Major State Basic Research Development Program in China under Contract no. 2014CB845400, the National Natural Science Foundation of China under Contract nos. 11421505, 11035009, 11220101005, 11105207, 11275250, 11322547, and U1232206, and the Knowledge Innovation Project of the Chinese Academy of Sciences under Grant no. KJCX2-EW-N01.

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Copyright

Copyright © 2015 S. Zhang et al. 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.

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