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Event-by-Event Fluctuations of Net-Baryon D istribution and H igher O rder C umulants

Event-by-Event Fluctuations of Net-Baryon D istribution and H igher O rder C umulants. ZHOU You , LIU Feng Institute Of Particle Physics (IOPP) HuaZhong Normal University (HZNU). o utline. Motivation S ome definition s and MC data R esults of centrality dependence ,

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Event-by-Event Fluctuations of Net-Baryon D istribution and H igher O rder C umulants

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  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) IWND09, August 22~25, Shanghai

  2. outline • Motivation • Some definitionsand 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 IWND09, August 22~25, Shanghai

  3. Figure 1 CP 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: PID hadron spectra, ratios, v2 … Fluctuations: - Net-p Kurtosis - K/ - <pT>, <N> …JY Chen for STAR -CPOD2009 ★ Mapping the QCD phase diagram ★ Searching the Critical Point IWND09, August 22~25, Shanghai

  4. motivation 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 ... 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: is Correlation length 4thOrder Cumulant: 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 4th Order Cumulant is more sensitive than 2nd Order Cumulant to study the CP IWND09, August 22~25, Shanghai

  5. Figure 3 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(2nd order) fluctuations rise rapidly in the transition region and approach to SB limit where the quartic(4th order) fluctuations show a maximum. This maximum is most pronounced for the baryon number fluctuations. the value for net-baryon is about 1.0 when T< 200MeV which consist with HRG. It is closed to SB limit 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. IWND09, August 22~25, Shanghai

  6. analysis 2nd Order Cumulant: • 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 is Standard deviation ☞ 4thOrder Cumulant: ☞ 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 ☞ IWND09, August 22~25, Shanghai

  7. Au+Au 9.2GeV Figure 4 centrality dependence for Net-Baryon RQMD v2.4 0< pT <1.0 (GeV/c) |Y|<0.5 • from peripheral to central collisions: • Mean values <NB>, C2increase smoothly • Skewness and Kurtosis: decreasing • C4 andR4,2 decreases rapidly in central collision IWND09, August 22~25, Shanghai

  8. Figure 9 Figure 10 transverse momentum dependence Net-Baryon pT distribution for net-baryon • The results of different pTdo not take effect distinctly although the value are not the same. IWND09, August 22~25, Shanghai

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

  10. Figure 14 0.5< |Y| <1.0 Figure 15 rapidity dependence Net-Baryon ☞ rapidity region 0< pT <1.0(GeV/c) they all have similar trends although a diverge happened in central collision for C4、R4,2 IWND09, August 22~25, Shanghai

  11. Figure 6 Figure 5 energy dependence of C4 Net-Baryon the right panel shows at 9.2, 12.3, 17.3, 20 GeV, C4exhibit unlike behaviour. But we can get non-monotonic behaviour at all time. IWND09, August. 22~25, Shanghai

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

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

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

  15. Summary and Outlook • We have presented a study of mean value<NB>,varianceC2, skewness, kurtosis(KB),C4andR4,2 of event-by-event net-baryon distribution. The trend of centrality dependence of different pT 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 ScanProgram. • Next to do: 1 Centrality dependence Net-Baryon distribution at high Energy 2 Net-Charge Kurtosis IWND09, August 22~25, Shanghai

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

  17. backup IWND09, August 22~25, Shanghai

  18. centrality dependence energy dependence how does the different cut effect the results of all observable T ThighEnergy > TlowEnergy Tcentral > Tperipheral observable rapidity dependence transverse momentum dependence analysis ① T Critical Point observable LGT ② IWND09, August 22~25, Shanghai

  19. The quadratic fluctuations of light and strange quarknumber versus temperature (upper figure) and the ratio ofs and u quark fluctuations on lattices of size× 4 and×6,respectively. • The quadratic fluctuations of light and strange quarknumber versus temperature (upper figure) and the ratio ofs and u quark fluctuations on lattices of size× 4 and×6,respectively. IWND09, August 22~25, Shanghai

  20. 0.5<PT<1.0(GeV/c) Figure 11 transverse momentum dependence Net-Baryon ☞ PTregion 0.0 < PT<0.5 0.5 < PT <1.0 1.0 < PT <1.5 1.5 < PT <2.0 mean、C2、skewness、KBhave the similar trend C4and R4,2seems different in four PTregions IWND09, August 22~25, Shanghai

  21. arXiv:0903.2911v2 [hep-ph] 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.

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