Charged Particle Fluctuation in Heavy Ion Physics

1. Charged Particle Fluctuation in Heavy Ion Physics ZHOU You, WU Kejun & LIU Feng Institute Of Particle Physics (IOPP) HuaZhong Normal University (HZNU) QNP09, Sept. 21~26 Beijing

2. discuss the properties and the behaviors of outline • Motivation • Results and Discussion • Summary and Outlook new measurements of higher order cumulants Skewness ,Kurtosis QNP09, Sept. 21~26 Beijing

3. motivation Figure 1 CP QCD Phase Diagram RHIC beam energy scan program : • Locate the QCD critical point. • Draw the QCD phase boundary. STAR Beam User Request Key measurements: PID hadron spectra, ratios, v2 … Fluctuations: - Kurtosis - K/ - <pT>, charged particle … ★ Mapping the QCD phase diagram ★ Searching the Critical Point

4. motivation Fluctuationsof Conserved Quantities • Electric Charge • Baryon Number • Strangeness • ... Phys.Rev. Lett. 85, 2076 (2000) Phys.Rev. Lett. 89, 082301 (2002) Phys. Rev. C66, 024904 (2002) Phys. Rev. C68, 044905 (2003) Phys. Rev. C68, 034902 (2003) Phys. Rev. C71, 051901(R) (2005) Phys. Rev. C79, 024904 (2009) ... The event-by-event fluctuations of conserved charges, like electric charge, baryon numberand strangeness, are generally considered to be sensitive indicators for the existence of a critical point . If at non-vanishing chemical potential a critical point exists in the QCD phase diagram, this will be signaled by divergent fluctuations. Charged particle fluctuations should also enable a direct measurement of the degree of thermalization reached in heavy ion collisions.

5. analysis • Monte Carlo data we used: • RQMD v2.4:(Relativistic Quantum Molecular Dynamics) • Relativistic Quantum Molecular Dynamics (RQMD) is a semiclassical microscopic model which combines classical propagation with stochastic interactions. • 7.7 GeV ~1M Events • 9.2 GeV~4M Events • 12.3GeV ~1M Events • 17.3GeV~1M Events • 20 GeV~3M Events • 27 GeV ~1M Events • AMPT v2.11: (A Multi-Phase Transport) • AMPT is a Monte Carlo transport model for heavy ion collisions at relativistic energies. It uses the Heavy Ion Jet Interaction Generator (HIJING) for generating the initial conditions, the Zhang's Parton Cascade (ZPC) for modeling the partonic scatterings, and A Relativistic Transport (ART) model for treating hadronic scatterings. • 9.2 GeV(3mb) • Default ~2M Events • String Melting ~8M Events ☞ all for Au+Au collision 5

6. charged particle ratio fluctuation Experimental Value (central Au+Au collisions at ) (STAR)Phys. Rev. C 68, 044905 (2003) (PHENIX)Phys. Rev. Lett. 89 082301(2002) • D-measure Q is net charge Nch is the total number of charged particles Predictions QGP phase Hadron phase Phys. Rev. Lett. 85, 2076 (2000) D-measure in a quark gluon plasma is expected to be significantly smaller (by a factor 3–4) than in hadronic gas. The experimental values from STAR and PHENIX equal to about 3, which are much larger than expected D value in QGP and closed to the predicted D value in Hadron phase. But it is not possible to draw a firm conclusion concerning the existence or nonexistence of a deconfined phase during the collisions from these results since, incomplete thermalization could lead to larger fluctuations than expected for a QGP.

7. charged particle ratio fluctuation Figure 2 Y cut Figure 4 Figure 3 • D-measure pT cut |Y|<0.5 centrality dependence pT cut doesn’t take effect DQquantity depend on theacceptance large acceptance leads to small DQ

8. Φmeasure M. Gaz´dzicki et al. Z. Phys. C 54, 127(1992) • Φmeasure S. Mro´wczyn´ski, Phys. Rev. C 66, 024904 (2002) centrality dependence Figure 5 Φ is free of the effect of charge conservation In "background" model Φ measure is ‘blind’ to the impact parameter variation as long as the ‘physics’ does not change with the collision centrality. Phys. Rev. C 66, 024904 (2002) Results from different Monte Carlo models proved that Φ is weakly depend on the collision centrality. Φ is insensitive to the collision centrality and sensitive to the dynamics. Phys. Rev. C 66, 024904 (2002)

9. Φmeasure Figure 6 Y cut pT cut Figure 7 Φ measure weakly depends on pT Φmeasure depends on the rapidity Φmeasure depends on the acceptance

10. measure accommodates for situation with non-symmetric charge distribution and varying global multiplicity. It is insensitive to the distribution of the independent particle sources. It measures both the dynamical and statistical fluctuation. M. Gaz´dzicki et al. Z. Phys. C 54, 127(1992) S. Mro´wczyn´ski, Phys. Rev.C 66, 024904 (2002) Γ measure Figure 9 pT cut Y cut Figure 10 Figure 8 also depend on the acceptance

11. S. Mro´wczyn´ski, Phys. Rev.C 66, 024904 (2002) pT cut Y cut J. Adams et al.(STAR Collaboration), Phys. Rev. C 68, 044905 (2003) B.I.Abelev et al.(STAR Collaboration),Phys. Rev.C 79, 024906 (2009) dynamical charge fluctuation • Dynamical Charge Fluctuation Figure 11 Figure 12 V+-,dyn is a hopeful observable, it almost doesn't depend on the acceptance

12. The observed monotonic reduction of the magnitude of ν+−,dyn arises from the progressive dilution of the charge conservation effect when the number of charged particle multiplicity is increased. We observed that the dynamical charge fluctuations are nonvanishing at all energies and exhibit a modest dependence on beam energy beam energy dependence centrality dependence Figure 14 Figure 13 Figure 15 dynamical charge fluctuation

13. is Correlation length higher order cumulants fluctuation M. A. Stephanov, PRL 102, 032301 (2009) "non-Gaussian moments (cumulants) of fluctuations of experimental observable are very sensitive to the proximity of the critical point, as measured by the magnitude of the correlation length" at the Critical Point 2nd Order Cumulant: 3rdOrder Cumulant: 4thOrder Cumulant: a measure of the range over fluctuations in one region of space are correlated with those in another • Sensitive to long range correlations • Show large non-monotonic behaviour as a function of T higher order cumulant is more sensitive than 2ndorder cumulant to study the CP

14. higher order cumulants fluctuation RQMD v2.4 centrality dependence standard definitions ☞ <NQ> ☞ Figure 17 ☞ a measure of the symmetry of a distribution ☞ • from peripheral to central collisions: • Mean values <NB>, C2 increase smoothly • Skewness , Kurtosis: decreasing a measure of the peakedness of the distribution

15. transverse momentum dependence RQMD v2.4 Figure 20 Figure 23 ☞ pT window ① 0 < pT < 0.5 ② 0 < pT < 1.0 ③ 0 < pT < 1.5 skewness and kurtosis almost don't dependent on acceptance

16. rapidity dependence RQMD v2.4 Figure 22 Figure 21 Figure 23 ☞ rapidity window ① |Y| < 0.5 ② |Y| < 1.0 ③ |Y| < 1.5 different rapidity windows don’t affect Skewness and Kurtosis

17. Only smooth trend of skewness and kurtosis can be found from RQMD model. This will provides baseline predictions to the higher order cumulants of net-charge distribution. ★ Figure 24 Figure 25 beam energy dependence RQMD v2.4 We studied the beam erergy dependence of skewness and kurtosis in order to find the diverage which is indicated the existence of critical point. ★

18. summary and outlook • We have presented a study of various observable of charge particle fluctuation. DQ、ΦQ、ΓQdependon the experimental acceptance. —V+-,dyn is a hopeful observable, it has a weak dependence on the acceptance. • Also we studied the higher order cumulants, Skewness, Kurtosis(KQ)of net-charge distribution. —Skewness and Kurtosis(KQ) almost don't depend on the acceptance, both of them are promising observables in experiments. • This work presents baseline predictions ofcharged particle fluctuation and higher order cumulants of net-charge distribution, it will help us to understand the expectations from experimental results for the forthcoming RHIC Beam Energy ScanProgram. • Next to do: 1 Centrality dependence of Net-Chargefluctuation at high Energy 2 Hadronlization and rescattering effect on the Net-Charge fluctuation (using modified AMPT model)

19. Thanks for your attention !

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21. higher order cumulants the value for net-charge is between 1 to 2 when T< 200MeV which consist with HRG. It is closed to SB limit when T >200MeV Figure 17 M.Cheng et al. arXiv: 0811.1006 v3 [hep-lat] M.Cheng et al.Phys. Rev. D 79, 074505 (2009) Figure 18 The quadratic(2ndorder) and quartic(4thorder) show a large fluctuation around 200MeV, this fluctuation are predicted as a signal of the existence of a critical point in all cases the quadratic(2ndorder) fluctuations rise rapidly in the transition region and approach to SB limit where the quartic(4thorder) fluctuations show a maximum.

22. (PHENIX) normalized variance fluctuation • Normalized Variance Figure 6 Figure 7 the same trend compared to D certainly

23. beam energy dependence large fluctuationsfor C4 and R4,2 turn to monotonic behaviour

24. Two versions of AMPT Model AMPT: A Multiphase transport model