Antimatter production in central Au+Au collisions at =200 GeV
We have used the dynamically constrained phase space coalescence model to investigate the production of light nuclei (anti-nuclei) based on the 1.134 hadronic final states generated by the PACIAE model for the 0-5% most central Au+Au collisions at =200 GeV with 1 and 5 acceptances. The STAR data of , , , and yields and ratios are well reproduced by the corresponding PACIAE results. The transverse momentum distribution of () and () is also given. It turned out that the transverse momentum distribution of light nuclei is close to that of the corresponding anti-nuclei.
pacs:25.75.-q, 24.85.+p, 24.10.Lx
The nucleus-nucleus collisions at top RHIC energy produce an initial hot and dense matter (quark-gluon mater, QGM). It has been interpreted as a strongly coupled quark-gluon plasma (sQGP) (1); (2); (3); (4). This is nearly a perfect liquid composed of quarks and gluons but is not a free gas-like quark-gluon plasma (fQGP) expected by theorists and experimentalists long time ago.
The anti-nuclei production is great importance in the nuclear and particle physics, the astrophysics, and the cosmology. One believes that the matter and antimatter exist in equal abundance during the initial stage of the universe. However, a mystery exists: how this symmetry got lost in the evolution of the universe with no significant amount of antimatter being present. Because the initial fireball created in ultra-relativistic heavy ion collisions is similar to the initial stage of the universe, the study of anti-nuclei production in ultra-relativistic heavy ion collisions may light this issue. However, the study of light nuclei (anti-nuclei) production is quite hard both experimentally and theoretically because of the low production multiplicity.
The STAR collaboration has reported their measurements of and in Au+Au collisions at the top RHIC energy (5). They have measured “7017 antihypertritons () and 157 hypertritons ()” in the 89 million minimum-bias and 22 million central (“head-on”) Au+Au collision events at =200 GeV. Thus the corresponding yields are estimated to be 6.31 and 1.41, respectively. The ALICE collaboration has also published their preliminary yield of measured in the pp collisions at =7 TeV (6); (7).
On the other hand, the theoretical study of light nuclei (anti-nuclei) is usually separated into two steps. The nucleons and hyperons are first calculated with some selected models, such as the transport models. Then the light nuclei (anti-nuclei) are calculated by the phase space coalescence model (8); (9); (10) and/or the statistical model (11); (12) etc. Recently, production of light nuclei (hypernuclei) in Au+Au/Pb+Pb collisions at relativistic energies have been investigated theoretically by the coalescence+blast-wave method (13) and the UrQMD-hydro hybrid model+ thermal model (14), respectively.
We have proposed an approach studying the light nuclei (anti-nuclei) production in ultra-relativistic pp collisions by dynamically constrained phase-space coalescence model (15). This approach is based on the final hadronic state generated by a parton and hadron cascade model PACIAE (16). The calculated light nuclei (anti-nuclei) yield in non-single diffractive (NSD) pp collisions at =7 TeV is well comparing with ALICE data (6); (7). The transverse momentum distribution and rapidity distribution are also predicted for () and () in NSD pp collisions at =7 and 14 TeV. In this paper, we use this method to investigate the light nuclei (anti-nuclei) and hypernuclei (anti-hypernuclei) productions in the Au+Au collisions at =200 GeV.
The paper is organized as follows: In the Sec. II, we briefly introduce the PACIAE model and the dynamically constrained coalescence model. In Sec. III, the calculated light nuclei (anti-nuclei) and hypernuclei (anti-hypernuclei) yields, ratios, as well as the transverse momentum distributions are given and compared with the STAR data. A short summary is the content of Sec. IV.
The PYTHIA model (17) is devised for the high energy hadron-hadron () collisions. In this model, a hh collision is decomposed into the parton-parton collisions. The hard parton-parton scattering is described by the leading order perturbative QCD (LO-pQCD) parton-parton interactions with the modification of parton distribution function in a hadron. The soft parton-parton collision, a non-perturbative phenomenon, is considered empirically. The initial- and final-state QCD radiations and the multiparton interactions are also taken into account. Therefore, the consequence of a hh collision is a partonic multijet state composed of di-quarks (anti-diquarks), quarks (antiquarks) and gluons, as well as a few hadronic remnants. This is then followed by the string construction and fragmentation. A hadronic final state is obtained for a hh collision eventually.
The parton and hadron cascade model PACIAE (16) is based on PYTHIA and is devised for the nucleus-nucleus collisions mainly. In the PACIAE model, first of all the nucleus-nucleus collision is decomposed into the nucleon-nucleon (NN) collisions according to the collision geometry and NN total cross section. Each NN collision is described by the PYTHIA model with the string fragmentation switches-off and the di-quarks (anti-diquarks) randomly breaks into quarks (anti-quarks). So the consequence of a NN collision is now a partonic initial state composed of quarks, anti-quarks, and gluons. Provided all NN collisions are exhausted, one obtains a partonic initial state for a nucleus-nucleus collision. This partonic initial state is regarded as the quark-gluon matter (QGM) formed in the relativistic nucleus-nucleus collisions. Secondary, the parton rescattering proceeds. The rescattering among partons in QGM is randomly considered by the 2 2 LO-pQCD parton-parton interaction cross sections (18). In addition, a factor is introduced here to include the higher order and the non-perturbative corrections. Thirdly, the hadronization follows after the parton rescattering. The partonic matter can be hadronized by the Lund string fragmentation regime (17) and/or the phenomenological coalescence model (16). Finally, the hadronic matter proceeds rescattering until the hadronic freeze-out (the exhaustion of the hadron-hadron collision pairs). We refer to (16) for the details.
In quantum statistical mechanics (19) one can not precisely define both position and momentum of a particle in the six dimension phase space, because of the uncertainty principle
We can only say this particle lies somewhere within a six dimension quantum “box” or “state” with volume of . A particle state occupies a volume of in the six dimension phase space (19). Therefore one can estimate the yield of a single particle by
where and are the Hamiltonian and energy of the particle, respectively. Similarly, the yield of N particle cluster can be estimated by
Therefore the yield in our dynamically constrained phase space coalescence model, for instance, is assumed to be
here () and () are the energy and momentum of particles , respectively. In Eq. (4), and stand for, respectively, the rest mass and diameter of , refers to the allowed mass uncertainty, and is the vector distance between particles and .
Iii Calculations and results
As the hadron position and momentum distributions from transport model simulation are discrete, the integral over continuous distributions in Eq. (4) should be replaced by the sum over discrete distributions. In a single event of the final hadronic state obtained from transport model simulation, the configuration of (++) system can be expressed as
where the subscripts , , , and refers to the distance between and the center-of-mass of , , and for instance. Then the third constraint (diameter constraint) in Eq. (4) is correspondingly replaced by
where refers to the radius of .
Each of the above configuration contributes a partial yield of
to the . So the total yield of in a single event is the sum of the above partial yield over the configurations of Eq. (6) and their combinations. An average over events is required at the end.
|The STAR data were taken from (20)|
In the PACIAE simulations we assume that the hyperons heavier than already decay. The model parameters are fixed on the default values given in PYTHIA. However, the K factor as well as the parameters parj(1), parj(2), and parj(3), relevant to the strange production in PYTHIA (17), are roughly fitted to the STAR data of , , , and in the 0-5% most central Au+Au collisions at =200 GeV (20), as shown in Tab. 1. The fitted parameters of =3 (default value is 1 or 1.5 (17)), parj(1)=0.12 (0.1), parj(2)=0.55 (0.3), and parj(3)=0.65 (0.4) are used to generate 1.134 final hadronic states by the PACIAE model for the 0-5% most central Au+Au collisions at =200 with 1 and 5 acceptances. Then (), (), as well as () yields and ratios are calculated by the dynamically constrained phase-space coalescence model. The calculated results are denoted as “PACIAE” later.
Figure 1 shows the calculated hadron yields (solid triangles) in the Au+Au collisions at =200 GeV. The open circles in this figure are the experimental data taken from (12). One sees in this figure that the PACIAE results well agree with the experimental data.
|Nucleus||Exp. data||PACIAE||Ref. (13)||Ref. (14)|
|taken from Tab. I in (13).|
|taken from Fig. 6 in (14).|
|taken from (12).|
|calculated with =0.0003 GeV.|
|estimated from (5).|
|calculated with =0.00015 GeV.|
|equal to 1.41E-06/0.82 (0.82 is taken from (5)).|
|equal to 6.31E-07/0.89 (0.89 is taken from (5)).|
In the Tab. 2 , , , , , and yields are given. The STAR yield of () is estimated by the () yield of 1.41E-06 (6.31E-07) divides by the ratio of to ( to ) of 0.82 (0.89) (5). We see in this table that the agreements between experimental data and PACIAE results are well.
We give the ratios of anti-nuclei to nuclei in Tab. 3. One sees again in this table that the PACIAE results are well comparing with the STAR data.
We plot in Fig. 2 the calculated , , , , , and transverse momentum distributions in the Au+Au collisions at =200 GeV. Figure 2 (a), (b), and (c) are the calculated ditribution for (), (), and (), respectively. The pattern of transverse momentum distribution is consistent with the distribution of in the Pb+Pb collisions at =2.76 TeV (7). The peak of distribution in the Pb+Pb collision is located at higher than the one in the Au+Au collision because of the different reaction energy. The strong fluctuation showing in the panel (b) and (c) indicates that the 1.134 events are still not enough for these distributions.
The PACIAE results of light nuclei (anti-nuclei) average transverse momentum in the Au+Au collisions at =200 GeV are given in Tab. 4. Here we see that the average transverse momentum of light nuclei is nearly equal to the one of corresponding anti-nuclei. This feature is already seen in the hadron (anti-hadron) production.
In summary, we have employed the dynamically constrained phase space coalescence model to investigate the light nuclei (anti-nuclei) production based on the final hadronic state generated by the PACIAE model for the 0-5% most central Au+Au collisions at =200 GeV with 1 and 5 acceptances. The calculated PACIAE results of () yield of 0.085 (0.041) is close to the experimental datum of 0.098 (0.045) (12). The PACIAE yields of , , , and as well as their ratios are also consistent with the STAR data (5). The PACIAE results of light nuclei (anti-nuclei) transverse momentum distributions are also given. The consistency between the PACIAE results and the corresponding experimental data demonstrates that the PACIAE+dynamically constrained phase space coalescence method is able to describe the production of light nuclei (anti-nuclei) and hypernuclei (anti-hypernuclei) in the relativity heavy ion collisions.
Finally, we acknowledge the financial support from NSFC (11105227, 11075217, 11175070, 11047142, 10975062) in China and SUT-NRU project (17/2555) in Thailand. GC thanks Dr. Huan Chen for improving the English.
- I. Arsene, et al., BRAHMS Collaboration, Nucl. Phys. A 757, 1 (2005).
- B. B. Back, et al., PHOBOS Collaboration, Nucl. Phys. A 757, 28 (2005).
- J. Admas, et al., STAR Collaboration, Nucl. Phys. A 757, 102 (2005).
- K. Adcox, et al., PHENIX Collaboration, Nucl. Phys. A 757, 184 (2005).
- The STAR Collaboration, Science 328, 58 (2010); arXiv:1003.2030v1.
- N. Sharma, ALICE Collaboration, arXiv:1104.3311v1.
- N. Sharma, ALICE Collaboration,J. Phys. G: Nucl. Part. Phys. 38 124189 (2011); arXiv:1109.4836v1.
- R. Mattiello, H. Sorge, H. Stöcker, and W. Greiner, Phys. Rev. C 55 1443 (1997).
- Lie-Wen Chen and Che Ming Ko, Phys. Rev. C 73 044903 (2006).
- S. Zhang, J. H. Chen, H. Crawford, D. Keane, Y. G. Ma, and Z. B. Xu, Phys. Lett. B 684, 224 (2010), and references therein.
- V. Topor Pop and S. Das Gupta, Phys. Rev. C 81 054911 (2010), and references therein.
- A. Andronic, P. Braun-Munzinger, J. Stachel, and H. Stöcker, Phys.Lett. B 697 203 (2011); arXiv:1010.2995v1.
- L. Xue, Y. G. Ma, J. H. Chen, and S. Zhang, Phys. Rev. C 85 064912 (2012).
- J. Steinheimer, K. Gudima, A. Botvina, I. Mishustin, M. Bleicher, and H. Stoecker, arXiv:1203.2547v2 [nucl-th].
- Y.L. Yan, G. Chen, X.M. Li,D. M. Zhou, M.J. Wang, S.Y. Hu, L. Ye,B.H. Sa, Phys. Rev. C 85 024907(2012).
- Ben-Hao Sa, Dai-Mei Zhou, Yu-Liang Yan, Xiao-Mei Li, Sheng-Qin Feng, Bao-Guo Dong, and Xu Cai, Comput. Phys. Commun. 183, 333 (2012); arXiv:1104.1238v1.
- T. Sjöstrand, S. Mrenna, and P. Skands, J. High Energy Phys. JHEP05, 026 (2006).
- B. L. Combridge, J. Kripfgang, and J. Ranft, Phys. Lett. B 70, 234 (1977).
- K. Stowe, A introduction to thermodynamics and statistical mechanics, Combridge, 2007; R. Kubo, Statistical Mechanics, North-Holland Publishing Company, Amsterdam, 1965.
- STAR Collaboration, J. Adams et al., Phys. Rev. Lett. 98 , 062301 (2007)