1. HuaZhong Normal University IWND09, August 22~25, Shanghai 1 Event-by-Event Fluctuations of Net-Baryon Distribution and Higher Order Cumulants ZHOU You, LIU Feng Institute Of Particle Physics (IOPP) HuaZhong Normal University (HZNU)

2. HuaZhong Normal University IWND09, August 22~25, Shanghai 2 outline Motivation Some definitions and MC data Results of centrality dependence, transverse momentum dependence, rapidity dependence, & energy dependence, of fluctuations of Net-Baryon distribution and higher order cumulants Summary and Outlook

3. HuaZhong Normal University IWND09, August 22~25, Shanghai 3 motivation QCD Phase Diagram RHIC beam energy scan program : Locate the QCD critical point. Draw the QCD phase boundary. STAR Beam User Request Key measurements: (1)PID hadron spectra, ratios, v 2 … (2)Fluctuations: - Net-p Kurtosis - K/  -, … JY Chen for STAR -CPOD2009 ★ Mapping the QCD phase diagram ★ Searching the Critical Point Figure 1 CP

4. HuaZhong Normal University IWND09, August 22~25, Shanghai 4 is Correlation length motivation 2 nd Order Cumulant: 4 th Order Cumulant: M. A. Stephanov, PRL 102, 032301 (2009) at the Critical Point "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 " 4 th Order Cumulant is more sensitive than 2 nd Order Cumulant to study the CP baryon number fluctuation is a highlight in heavy ion physics and studying the event-by- event fluctuations of observable provide useful tools to research the critical point arXiv: 0606047 arXiv: 0805.0236 arXiv: 0809.0685 arXiv: 0903.2911 Phys. Rev. D 79, 074505 (2009) nayak (STAR Collaboration)@QM2009... is a measure of the range over which fluctuations in one region of space are correlated with those in another Sensitive to long range correlations Shows large non-monotonic behaviour as a function of T

5. HuaZhong Normal University IWND09, August 22~25, Shanghai 5 Figure 2 motivation M.Cheng et al. arXiv: 0811.1006 v3 [hep-lat] M.Cheng et al.Phys. Rev. D 79, 074505 (2009) in all cases the quadratic(2 nd order) fluctuations rise rapidly in the transition region and approach to SB limit where the quartic(4 th order) fluctuations show a maximum. the value for net-baryon is about 1.0 when T 200MeV ☞ ☞ The measurement of higher order cumulants of net-baryon distribution and its variations will provide the connection between experimental observable and Lattice Gauge Theory calculations. This maximum is most pronounced for the baryon number fluctuations. Figure 3

6. HuaZhong Normal University IWND09, August 22~25, Shanghai 6 analysis 2 nd Order Cumulant: 4 th Order Cumulant: is Standard deviation a measure of the symmetry of a distribution a measure of the peakedness of the distribution for a Gaussian distribution, the value of skewness and kurtosis is 0 MC data we used: RQMD v2.4: 9.2 GeV ~4M Events 12.3GeV ~1M Events 17.3GeV ~1M Events 20 GeV ~3M Events UrQMD v2.3: 9.2 GeV ~16M Events AMPT v2.11: 9.2 GeV(3mb) Default ~2M Events String Melting ~8M Events ☞ ☞ all for Au+Au collision ☞ ☞ ☞ ☞ ☞

7. HuaZhong Normal University IWND09, August 22~25, Shanghai 7 centrality dependence for Net-Baryon from peripheral to central collisions: Mean values, C 2 increase smoothly Skewness and Kurtosis: decreasing C 4 and R 4,2 decreases rapidly in central collision Au+Au 9.2GeV RQMD v2.4 0< p T <1.0 (GeV/c) |Y|<0.5 Figure 4

8. HuaZhong Normal University IWND09, August 22~25, Shanghai 8 transverse momentum dependence The results of different p T do not take effect distinctly although the value are not the same. p T distribution for net-baryon Figure 9 Figure 10 Net-Baryon

9. HuaZhong Normal University IWND09, August 22~25, Shanghai 9 rapidity dependence different rapidity also do not play an active role rapidity distribution Figure 13 Figure 12 ☞ ☞ rapidity window ① |Y|<0.5 ② |Y|<1.0 Net-Baryon

10. HuaZhong Normal University IWND09, August 22~25, Shanghai 10 rapidity dependence they all have similar trends although a diverge happened in central collision for C 4 、 R 4,2 Figure 14 Figure 15 ☞ ☞ rapidity region 0.5< |Y| <1.0 Net-Baryon 0< p T <1.0(GeV/c)

11. HuaZhong Normal University 11 IWND09, August. 22~25, Shanghai energy dependence of C 4 the right panel shows at 9.2, 12.3, 17.3, 20 GeV, C 4 exhibit unlike behaviour. But we can get non-monotonic behaviour at all time. Figure 5 Figure 6 Net-Baryon

12. HuaZhong Normal University 12 IWND09, August. 22~25, Shanghai energy dependence of K B the right panel shows at 9.2, 12.3, 17.3, 20 GeV, K B exhibit similar behaviour. the left panel shows energy dependence of K B, in central collision, the trend are seen the same Figure 7 Figure 8 Net-Baryon

13. HuaZhong Normal University 13 IWND09, August. 22~25, Shanghai MC model difference UrQMD for Net-Baryon other MC models are used to check our results Figure 16

14. HuaZhong Normal University IWND09, August 22~25, Shanghai 14 MC model difference AMPT for Net-Baryon we can find the trend of UrQMD and AMPT are similar to those of RQMD Figure 17

15. HuaZhong Normal University IWND09, August 22~25, Shanghai 15 We have presented a study of mean value, variance C 2, skewness, kurtosis(K B ), C 4 and R 4,2 of event- by-event net-baryon distribution. The trend of centrality dependence of different p T and Y window are similar Calculations from UrQMD and AMPT model also support our conclusion This work present baseline predictions of Net-Baryon distribution and higher order cumulants, it will help to understand the expectations from experiment results for the forthcoming RHIC Beam Energy Scan Program. Next to do: 1 Centrality dependence Net-Baryon distribution at high Energy 2 Net-Charge Kurtosis Summary and Outlook

16. HuaZhong Normal University IWND09, August 22~25, Shanghai 16 Thanks for your attention also thanks to the Organizer of IWND2009

17. HuaZhong Normal University IWND09, August 22~25, Shanghai 17 backup

18. HuaZhong Normal University IWND09, August 22~25, Shanghai 18 analysis how does the different cut effect the results of all observable transverse momentum dependence rapidity dependence ① ② T centrality dependence T central > T peripheral energy dependence T highEnergy > T lowEnergy observable T Critical Point LGT

19. HuaZhong Normal University IWND09, August 22~25, Shanghai 19 T h e q u a d r a t i c f l u c t u a t i o n s o f l i g h t a n d s t r a n g e q u a r k n u m b e r v e r s u s t e m p e r a t u r e ( u p p e r f i g u r e ) a n d t h e r a t i o o f s a n d u q u a r k f l u c t u a t i o n s o n l a t t i c e s o f s i z e × 4 a n d × 6, r e s p e c t i v e l y.

20. HuaZhong Normal University IWND09, August 22~25, Shanghai 20 transverse momentum dependence mean 、 C 2 、 skewness 、 K B have the similar trend C 4 and R 4,2 seems different in four P T regions 0.0 < P T <0.5 0.5 < P T <1.0 1.0 < P T <1.5 1.5 < P T <2.0 Figure 11 ☞ ☞ P T region 0.5<P T <1.0(GeV/c) Net-Baryon

21. HuaZhong Normal University The fluctuations of net-baryon number in a subsystem are of the order of the root of the average net- baryon number in this subsystem. arXiv:0903.2911v2 [hep-ph]