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We are very grateful to Zhixu Liu and Jiaxin Du for offering us the data

Anisotropic flow, Azimuthal Balance Function, and Two-charged-particle Azimuthal Correlations in RQMD and AMPT. Yanping Huang and Yuanfang Wu. IOPP, Central China Normal University, Wuhan, China. Introduction 2. Behaviors of these three measurements in RQMD and AMPT

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We are very grateful to Zhixu Liu and Jiaxin Du for offering us the data

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  1. Anisotropic flow, Azimuthal Balance Function,and Two-charged-particle Azimuthal Correlationsin RQMD and AMPT Yanping Huang and Yuanfang Wu IOPP, Central China Normal University, Wuhan, China • Introduction • 2. Behaviors of these three measurements • in RQMD and AMPT • 3. Conclusions and Suggestions We are very grateful to Zhixu Liu and Jiaxin Du for offering us the data samples of RQMD and AMPT.

  2. 1. Introduction ► Anisotropic collective flow is caused by initial spatially-anisotropic participant zone and interactions in non-central nucleus-nucleus collisions, ψR is azimuthal angle of reaction plane defined on an event-by-event base. The observed large flow at RHIC has been argued as an indicator of early thermal equilibrium. Its flavor dependence is supposed to be highly relevant to interpretation of strongly interacting QGP. J. Adams, et al, (STAR Coll.), Nucl. Phys. A 757, 102(2005); K. Adcox, et al, (PHENIX Coll.), Nucl. Phys. A 757, 184(2005). Miklos Gyulassy, Larry McLerran, Nucl. Phys. A 750, 30-63(2005). B. M\"uller, Annu. Rev. Nucl. and Part. Phys.,1(2006). QM’06

  3. 1. Introduction (cont.) ►Azimuthal charge balance function ☺Another independent constraint on the temperature and the amount of transverse flow at the freeze-out. ☺It is expected from thethermal modelthat the higher temperature and thesmallerelliptic flow, the wider the azimuthal balance function. __ T f = 90 MeV, β=0.6 - - T f = 165 MeV β=0.5 P. Bozek, Phys. Lett. B 609, 247(2005). It is interesting to see how azimuthal charge balance function behaves in the dynamical models RQMD and AMPT. QM’06

  4. 1. Introduction (cont.) ► Two-charge-particle azimuthal corr. L. Foa, Phys. Reports 22(1975). nab(δφ): is the number of pairs of charged a and b particles satisfying the criteria that their relative angle equals δφ. nab: is the total number of the same kind of pairs for all possible separated angles. K. Adcox, et al., (PHENIX Coll.), PRL 89, 212301(2002) ► Why we choose these three measurements ? ☻They are all anisotropic trans. momentum dis. related. ☻The behaviors of these three measurements in RQMD and AMPT will help us in understanding the underlying dynamics. ☻ Both two-charge-particle azimuthal corr. and azimuthal charge balance func. are reaction plane irrelevant and therefore easily to measure. QM’06

  5. 1. Introduction (cont.) ► Models Au-Au collisions at √s NN=200GeV RQMD (v2.4): A MC generator of Relativistic Quantum Molecular Dynamics ( hadron ), Without hadron rescattering, v2 = 0; With hadron rescattering, v2 > 0, but smaller than the data. H. Sorge, Phys. Rev. C52, 3291 (1995). See Feng Liu’s talk in the same session. AMPT: A MC generator of AMulti-Phase Transport Model (parton + hadron) Default AMPT, v2 > 0,but still smaller than data; AMPT with string melting, where parton transportation, hadron rescattering and quark coalescence at hadronization are implemented in the model. This model reproduces v2 (pt) data at RHIC. Zi-Wei Lin, Che Ming Ko, Bao-An Li, Bin Zhang and Subrata Pal, Phys. Rev. {\bf C72}, 064901 (2005). QM’06

  6. 2. Behaviors of three measurements in models ► v2 of all, positive and negative charged particles RQMD without rescattering: no v2 at all. RQMD with rescattering: same middle values of vc2 , v-2, v+2. AMPT with string melting: same big values of vc2 , v-2, v+2 v2 is the biggest for mid-central coll. and is smaller for central and very peripheral collisions. QM’06

  7. 2. Behaviors of three measurements in models ► Ccc, C ++ ,C– and C+- in RQMD Rescattering on: ☺ Small angular corr. appear! ☺ The diff. among them are small but visible. ☺ Large angular corr. remains. Rescattering off: ☺ No small angular corr. ☺ Large angular corr. due to momentum conservation. QM’06

  8. 2. Behaviors of three measurements in models ► Centrality dependence of Ccc, C ++ ,C-- ,C+-, in RQMD Rescattering off: Momentum conservation leads to the observed large angular correlations, especially for the most peripheral collisions. Rescattering on: The small angular corr. are the strongest for the mid-central coll. , small for most central coll. and even smaller for the most peripheral coll. This centrality dependence is the same as v2 . QM’06

  9. 2. Behaviors of three measurements in models ► Ccc, C ++ ,C-- ,C+- in AMPTwith string melting In AMPT, small angular corr. becomes stronger than large angular corr. Difference among Ccc, C ++ , C-- , and C+- are very small. ► Centrality dependence of Ccc, C ++ ,C-- ,C+- in AMPT Small angle corr. have the same centrality dependence as flow. QM’06

  10. 2. Behaviors of three measurements in models ► Two-charge-particle corr. from PHENIX Coll. Data show: ●A anisotropic corr. pattern is symmetric about ∆φ=900; ●This anisotropy increase with impact parameter and pt. Models show: ► The small angle corr. is related to anisotropy of pt distribution ►The same symmetry structure in AMPT with string melting. ► The same centrality dependency in both RQMD and AMPT K. Adcox, et al, Phys. Rev. Lett. 89, 212301(2002) QM’06

  11. 2. Behaviors of three measurements in models ► Azimuthal charge balance function in RQMD RQMD w/o RQMD w No centrality dependence. This means that the corr. caused by momentum cons. are cancelled in the measurement. The more central coll., the narrower BF, which are diff. from centrality dependence of v2 . QM’06

  12. 2. Behaviors of three measurements in models ► Azimuthal charge balance function in AMPT __ T f = 90 MeV, β=0.6 - - T f = 165 MeV β=0.5 This is different from the expectations from the thermal model, where the smaller elliptic flow, the wider azimuthal balance function. In more central coll., the BF is narrower In more periph. coll., the BF is wider. QM’06

  13. 3. Conclusions and suggestions The behaviors of anisotropic flow, azimuthal charge balance function, and two-charge-particle azimuthal corr. in RQMD and AMPT are compared. ● The large angular corr. are due to the constraint of momentum conservation. ● The small angular corr. mainly come from anisotropic transverse momentum distribution caused by hadron level rescattering and/or parton level transportation. ● The centrality dependence of the small angular corr. is the same as the centrality dependence of v2 in both AMPT and RQMD. ● To measure the two-charge-particle azimuthal corr. at STAR detector, where TPC covers the whole azimuthal angle. QM’06

  14. 3. Conclusions and suggestions ● From the behavior of two-charge-particle azimuthal corr., we see that azimuthal charge balance function (ACBF) well cancel the contributions caused by the constraint of momentum conservation. ● ACBF changes monotonically with centrality in both RQMD and AMPT models. This is different from the centrality dependence of v2 and what expected from thermal model. ● It is interesting to see how the B( ∆φ) behave in current heavy ion collisions. ● These three measurements are all sensitive to the anisotropic transverse momentum distributions. 谢 谢 / thank you ！ QM’06

  15. Appendix AMPT default QM’06

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