Event fluctuation of charged particle eccentricity and elliptic

Event fluctuation of charged particle eccentricity and elliptic flow in Pb-Pb collisions at √s =2. 76 Te. V Gang Chen China University of Geosciences, Wuhan, China Collaborators Yu-Liang Yan, Ben-Hao Sa (CIAE, China) Dai-Mei zhou (CCNU, China) Workshop on Collectivity in RHC, Crete, Greece, Sept. 14 -20, 2014.

Outline • Introduction • Analysis Method • The Results • Summary Workshop on Collectivity in RHC, Crete, Greece, Sept. 14 -20, 2014.

The A-A collisions consists of the four stages as follows after initial state.

Elliptic flow in Heavy Ion Collisions

Elliptic flow in Heavy Ion Collisions py px The overlap region in peripheral collisions is not symmetric in coordinate space Interactions among constituents generates a pressure gradient which transforms the initial spatial anisotropy into the observed momentum anisotropy

Elliptic flow in Heavy Ion Collisions

STAR+PHENIX Emitting medium is composed of unconfined, flowing quarks.

Valence quark scaling appears to fail over whole PT range.

Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs Zhi Qiu, Phys. Rew. C 84, 024911(2011) Shown a similar linear dependence of the elliptic flow v 2 on initial ellipticity ε 2. (Color online) v 2 vs. ε 2 , each centrality class contains 1000 MC-KLN events, grouped in eccentricity bins of sufficient width to have reasonable statistics in each bin.

Constraints from v 2 fluctuations for the initial state geometry of heavy-ion collisions R. Thorsten , ar. Xiv: 1401. 2069(2014) The initial state fluctuations ε 2 of models are close to momentum fluctuations v 2 of ATLAS. Centrality dependence of v 2 or ε 2 fluctuations in various scenarios to generate the initial state from the initial nucleon distributions.

Analysis Method One of the most important signals for the discovery of strongly coupled quark-gluon plasma (s. QGP) is the large elliptic flow parameter of produced particle in the A+A collisions. We employ the new issue of a parton and hadron cascade model PACIAE 2. 1 to calculate the charged particle probability density distribution of v 2 and ε 2 in Pb+Pb collisions at √s. NN=2. 76 Te. V. The calculated results are compared with the ATLAS data and the relation between v 2 and ε 2 are further investigated.

Analysis Method PACIAE model It is the parton and hadron cascade Model based on PYTHIA and is divided into four stages 1. The string fragmentation in PYTHIA is switched-off temporarily and the diquarks (anti-diquarks) are broken randomly into quarks (antiquarks), so the parton initial state is obtained. 2. The parton rescattering is proceeded until partonic freez-out. 3. Then the hadronization is followed. 4. At last the hadronic rescattering is proceeded until hadronic freez-out. Ben-Hao Sa , etal. Comput. Phys. Commun. , 183, 333 (2012).

Analysis Method Compared to PYTHIA, PACIAE model adds two processes.

Analysis Method PACIAE 2. 1 model The spatial overlap zone formed in non-center N-N coll. is almond-like The of the produced particle from string fragmentation In PYTHIA (PACIAE 2. 0) model But in PACIAE 2. 1 model The Fourier expansion of particle transverse momentum azimuthal distribution Ben-Hao Sa , et al. Comput. Phys. Commun. , 184, 1476 (2013). A. M. Poskanzer, et al. Phys. Rev. C 58, 1671 (1998). S. A. Voloshin, et al. Z. Phys. C 70, 665 (1996)

Analysis Method The eccentricity are calculated according to participating nucleon positions (r; Φr) relative to their center of mass in a single event Defined the stander, reaction-plane, and the participant eccentricities as follows: where G. -Y. Qin, et al. , Phys. Rev. C 82, 064903 (2011). D. Teaney, et al. , Phys. Rev. C 83, 064904 (2011). B. Alver, et al. , Phys. Rev. C 77, 014906 (2008).

Analysis Method The hydrodynamic have explored that the v 2 of final hadronic state is approximately proportional to the initial spatial eccentricity ε 2 The probability density distribution of relative fluctuation of v 2 should be equal to the corresponding ones of ε 2 ATLAS Colleb. , JHEP 10, 183 (2013); M. L. Miller, Ann. Re. V. Nucl. Part. Sci. 57, 205 (2007). H. -J. Drescher, Phys. Rev. C 65, 044905 (2006). G. -Y. Qin, Phys. Rev. C 82, 064903 (2010). H. Niemi, , Phys. Rev. C 87, 054901 (2013).

The Results of eccentricities • Distribution of ε 2 , ε 2, s , ε 2, rp , ε 2, part are all similar ; • Distribution of ε 2, s , ε 2, rp , ε 2, part are almost overlapped with each other. Fig. 1 Comparing the charged particle ε 2 probability density distribution calculated by different methods in different centrality bins with PACIAE.

The Results of comparison v 2 and ε 2 • Their distribution are all similarly ; • Distribution of v 2 are almost narrower than those of the ε 2 ; • Distribution of the v 2(c = 1) move Fig. 2 Comparing the charged particle ε 2 and v 2 probability density distribution calculated by the PACIAE model in different centrality bins. to the right relative to the v 2(c = 0. 5).

The Results of comparison v 2 and ε 2 Fig. 4 The charged particle <v 2> distribution calculated by our model , modelofresult the as a. Our function ε 2 , inshown Pb-Pbthat collisions elliptic flow v 2 of final hadronic state is approximately proportional to the initial spatial eccentricity ε 2. MC-KLN Zhi Qiu, Phys. Rew. C 84, 024911(2011)

The Results of comparisonδv 2 and ε 2 Fig. 5 Comparison between the δv 2 and ε 2 by PACIEA Model. The ε 2 fluctuations are somewhat similar to v 2 fluctuations calculated by PACIAE Model.

The Results of comparisonδv 2 and ε 2 Fig. 6 Theδε 2 in PACIAE Model compare with δv 2 of ATLAS in various centralities of Pb-Pb collisions at s. NN =2. 76 Te. V. The ATLAS v 2 fluctuationsin and the PACIAE ε 2 fluctuationsin are in good agreement.

The Results of comparisonδv 2 and ε 2 Fig. 7 The PACIAEδv 2 in comparison with the ATLAS data in various centrality. The ATLAS v 2 fluctuationsin and the PACIAE v 2 fluctuationsin are in good agreement.

Summary and Outlook • • We have investigated the charged particle v 2 and ε 2 in relativity heavy ion collision by PACIAE model. The ε 2 fluctuations approximately equal to v 2 fluctuations , which has been proved in PACIAE model. The results calculated with PACIAE 2. 1 model are consistent with the ATLAS experiment. The high order vn andεn fluctuations in relativity heavy ion collision should be studied further.

Thanks for your attention! 25