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D& #g$&$,  0lCYTD<4___PPT9 Motivation Neighboring angular-bin multiplicity correlation pattern in transport models Anisotropic correlation coefficientACC SummaryZ 2 GMG*CG4{8XH  0޽h ? 33___PPT10i.kh`?$+D=' = @B +n 0     (  B  <Df3o?"0@NNN?NjDjB  <Df3o?"0@NNN?NYY  BB C 1. MotivationC`   <6Q Some form of a quark-gluon plasma is formed at RHIC, and one of the evidences is the anisotropic collective flow behavior observed. <GCE   B(d3fjJ" `q The successful hydrodynamic description on the observed mass dependence of v2 at pt < 2GeV shows that observed dense matter behaves like a perfect fluid, and is referred as sQGP.$Mf   <`]N ,$  0 DExperimentally  Hydrodynamic model can still not quantitatively fit the observed mass dependence of v2 for Cu+Cu data. PRL98, 242302(2007) Pjf3,\p  < Y $ 0LD___PPT9& |Theoreticallly local thermal equilibrium is required. Viscosity=0 is hard to be understood. B#PMP8X  0ܯ I  HHowever $ 2RB  s *DV xV RB  s *D  H  0޽h ? 33___PPT10.pď$+j KDD' = @B D' = @BA?%,( < +O%,( < +D.' =%(D' =%(D~' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-}6B!slide(fromLeft)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+p+0+0 ++0+0 +( 0   P o (  B  <Df3o?"0@NNN?NjDjB  <Df3o?"0@NNN?NYY  BB C 1. MotivationC   <lÑ    <ƑP@7  z  6ʑ3fjJ"` The main experimental physical quantity v2  1 it only globally characterizes the possible direction and strength of anisotropic distribution. 2) The intrinsic interaction of final state particles is absent.)G33O33G33C-CC:CCCBCz(    , ;  >F  Z$ؑGH=IVK$MN= 6; ,$D 0 2-particle azimuthal corr.G33, B  s *DjJTC,$D 0Cl GS !  S G! ,$D 0e  <Lf3jJ"`G !  the average correlation of two particles separated by a certain angle, no matter where the two particles are in the whole azimuthal space.C{ ZB  s *D S c e  64f q ,$D 0 oHow the particles in different azimuthal directions interact with each other can not be drawn from them either.ppG HH  0޽h ? 33___PPT10.pď$+;[*DM' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*pD' =-g6B fade*<3<*p+8+0+0 +4 0 9t (  tB t <Df3o?"0@NNN?NjDjB t <Df3o?"0@NNN?NYY t BB |$2. Introduction of the corr. pattern%%C  t <   t 0 BA spatial-dependent neighboring correlation pattern is suggested: (CBGB  t C xA ?A3fjJ?"6@@NNN?N@ <   t 0C*  5 An  t 6@ Z,$  0 Nm: the sequence number of bins nm: the multiplicity in the mth angular binHO#Gf3Of3+Gf3?   t 6  'cWu Yuanfang, Lianshou Liu, Yingdan Wang, Yuting Bai and Hongbo Liao, Phys. Rev. E71, 017103(2005).dd f3!  t 6 ,$ 0 n It s a good observable for tracing the interaction among different azimuthal directions in relativistic heavy ion collision..~CgG"C 1 #t < q   l ) 6t),$D 0B 't NDjJ?"0@NNN?NB (t NDjJ?"0@NNN?NZZB )t NDjJ?"0@NNN?N  B *t NDjJ?"0@NNN?N  B ,t NDjJ?"0@NNN?Ncc .t TL> 31?"6@`NNN?N2 K1.8n<P2E33! /t  `HB 31?"6@`NNN?N5[ K2.8n<PE33 0t ThF 31?"6@`NNN?N2) KM.8n<PE33 1t TE 31?"6@`NNN?N'  N& & .8n<PG33el a  7ta ,$D 0B +t NDjJ?"0@NNN?NB -t NDjJ?"0@NNN?N66B 2t HDjJ?"0@NNN?N7 3t BHRa  d2&0 2G33 4t 6,WA  a0&0 2G33l %   9t%  ,$D 0y $t 0 `    A typical spatial distri. of two bin corr. is drawn. i.e.If the particles are produced independently, then = , Cm,m+1 vanishes.PusJ33433f39f3f3f3f3f3f3f3f3f3f3 f3F  ] 8t 04p%   Cy How the nearby particles correlate with each other in different directions of azimuthal space can be measured! Eus5us3 $"W H t 0޽h ? 33___PPT10.pď$+ "D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*7t%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*7tD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*7tD' =-g6B fade*<3<*7tD' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*6t%(D' =-6B'blinds(horizontal)*<3<*6tD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* tD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* tD' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*9t%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*9tD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*9tD' =-g6B fade*<3<*9tD2' =%(D' =%(D' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<* t%(D' =-6B%slide(fromBottom)*<3<* t+p+0+ t0 ++0+ t0 +  0   `  (  B  <Df3o?"0@NNN?NjDjB  <Df3o?"0@NNN?NYY  BpG |$2. Corr. pattern in transport models%%CY  c (Oy1f,k,kXX?"6@ NNN?N gTransport models:, C,  TW ?"6@ NNN?N   RQMD with hadron rescattering:Z!e33ae33 4    6, %   AMPT with string melting: RE33AE33  TLb ?"6@ NNN?NC  FH. Sorge, Phys. Rev. C52, 3291 (1995); Y. Lu et al. nucl-th/0602009 DG0E&f3&f3$?3   <HiA\ Ka hadron-based transport model; where v2 is smaller than the data at RHIC. 6L'AI$A"C   Tr ?"6@ NNN?NV   VZi-Wei Lin, Che Ming Ko, Bao-An Li, Bin Zhang and Subrata Pal, Phys. Rev. C72, 0649012W0V&f3$H;   0xx T   =a multi-phase transport model, where parton cascade + hadron rescattering are both included. This model can reproduce v2 (pt) data at RHIC.NAYAIA>%  EH  0޽h ? 33___PPT10i.pď$+D=' = @B + 0   p g (  J  C "A fig1,B  <Df3o?"0@NNN?NjDjB  <Df3o?"0@NNN?NYY  B0g {#2. Corr. pattern in transport model$$C"  <C1  j In Fig.(a)  Corr. patterns from two models are  cos2 like, opposite to the well-known cos2 like azimuthal distribution. 3333333333(*   % a $< 2<l  %a   %a,$D 0X    `0A3fjJ?"6@ `NNN?N%a@___PPT10 n___PPT9PH fcos2 like pattern in peripheral coll. flat in mid-central coll. -cos2 like pattern in near-central coll.140<110eDea"e. e  g B)8X`B   0DԔ @p@2   Bds q)b,$ 0 In Fig.(b)+Fig.(c) : two opposite trends dominate in peripheral and near-central collisions, which can be called as in-plane and out-of-plane corr. pattern respectively. In the mid-central collisions, the two trends turn to balance.P0 233 ,YH  0޽h ? 33  ___PPT10 .pď$+$D- ' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DC' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B#slide(fromRight)*<3<* D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<* D' =-g6B fade*<3<* +8+0+ 0 +c 0  ,y(  ,B , <Df3o?"0@NNN?NjDjB , <Df3o?"0@NNN?NYY , Bĉg {#2. Corr. pattern in transport model$$C\ , THʉ jJ?"6@ `NNN?N&N= 6What is the physical origin of the two opposite trendsH70 2&&33/& , BЉq 8What is the physical origin of the two opposite trends ?N90 2GG331G  ,  x 0W jJ??wiSO_GB2312"6@`NNN?N`y:;  ,  `Ӊdf3jJ?"6@ `NNN?N/8___PPT10F___PPT9(  2:& In-plane corr. pattern:8 2"c"  @  , BT݉<,$ 0 dIt is the same as in-plane flow, which is caused by anisotropic expansion in peripheral collisions.ee ,  `df3jJ?"6@ `NNN?Nq h  <:&Out-of-plane corr. pattern : V 2"C$33"   , < ?"6@ NNN?N q  the anisotropic expansion and the late hadronization are impossible to produce stronge correlations in out-of-plane directions. :D 33B ,'  +L , <D ?"6@ NNN?Ns qm  HOnly the initial source anisotropy is preferential in these directions. 0I 33Ga , 6 q,$ 0 A larger initial number of participant nucleons in the out-of-plane directions, which in turn generates stronger interaction in these directions.H , 0޽h ? 33"  ___PPT10 .pď$+%ID^ ' = @B D ' = @BA?%,( < +O%,( < +D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<* ,D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<* ,D' =-g6B fade*<3<* ,D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*,D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*,D' =-g6B fade*<3<*,+p+0+ ,0 ++0+,0 +P  0  0 (  0B 0 <Df3o?"0@NNN?NjDjB 0 <Df3o?"0@NNN?NYY 0 B  {#2. Corr. pattern in transport model$$C 0  ydjJf,k,kXX?"6@ `NNN?Nj~v0___PPT106___PPT9 :& Why the out-of-plane corr. patterns appear at near-central coll.?FD c  c  Bg  ")" 0 <$ ?"6@ NNN?N xIn peripheral collisions :4 GG 0 <<, ?"6@ NNN?Nc 0 ]  fIn near-central collisions :  G  0 </ ?"6@ NNN?N  The overlap zone is small, and so is the no. of participants; the diff. between two axes of overlap zone is large, and so is the difference of pressure gradient.G  0 N<<̙Af3jJ?"6@ NNN?Nq,$D 0 {The anisotropic expansion dominates the final observable,the effects of initial interaction in corr. patterns are hidden. 2| v33z33,.$  0 6IF q  b The overlap zone becomes large, and the diff. between two axes of overlap zone is small. ccG  0 ZR̙Af3jJ?"6@ NNN?Nf ql,$D 0 B The initial interactions are strong enough to show themselves up!8C v33g 33BH 0 0޽h ? 33___PPT10.pď$+ՈD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =-6B'blinds(horizontal)*<3<* 0D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =-6B'blinds(horizontal)*<3<* 0+p+0+ 00 ++0+ 00 +  0    (  B  <Df3o?"0@NNN?NjDjB  <Df3o?"0@NNN?NYY  Bf |$2. Corr. pattern in transport models%%C  0Tl I If there is hydrodynamic flow, the system should be well thermalized and reach thermal equilibrium. Then all other interaction before anisotropic expansion should be forgotten!J v}332AlCMG"9 u@  <lQ   The out-of-plane corr. pattern is observed as the result of initial interaction before anisotropic expansion, i.e, a larger initial number of participant nucleons in the out-of-plane directions. This is out of the hydrodynamic expectationQv}33v}33AnCAUEA.G>[  0k , ,$ 0 Measuring the corr. pattern by the data of RHIC and LHC is looking forward to 2P 2NG33E33$;H  0޽h ? 33___PPT10.pď$+%Db' = @B D' = @BA?%,( < +O%,( < +DT' =%(D' =%(D' =A@BB7BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*+8+0+0 +  0   +4P* (  4B 4 <Df3o?"0@NNN?NjDjB 4 <Df3o?"0@NNN?NYY 4 B<\ l&3. Anisotropic correlation coefficient*'&Ch 4 0ؖF @ 2) The main contribution in the expansion series comes from cos2(-r). 3) The coefficient u2 provides the preferential direction and strength of anisotropic correlation pattern. We specify it as anisotropic correlation coefficient (ACC). BG33g33o33G33GOVG;C4B8X 4 NA ?fA jJ?"`N  b 4 B4 *The correlation patterns are typical periodic function of azimuthal angle in periph.and central collisions, so it can be expanded by Fourier seriesV-C6:  <=J +4 0̴S i  $1) r is the direction of reaction plane, and is zero in model analysis, while in real exp. data analysis, it has to be determined event-by-event.nICG33CC;CC8XH 4 0޽h ? 33___PPT10i.pď$+D=' = @B + 0   P T(  TB T <Df3o?"0@NNN?NjDjB T <Df3o?"0@NNN?NYY T B̵  h"3. The rapidity dependence of ACC *#!C T 6̙f3jJ" ` q,$  0 ySo in finite rapidity range of current relativistic heavy ion exp., studying the corr. pattern and ACC is expectable. *zuEAQ%  T 0T֍"`* > 2A 8 qj   Tjx V  T C &Afig2-cqj T  T C $A label"oj   T 04_ l l (+1, +5][-5,-1); [-1 +1] are chosen ,which correspond to forward, backward and central rapidity region.@k 2<CG33C4 S  T NTލd3fjJ" ` @^  \ACC is independent of the choice of rapidity and similar to that in whole rapidity space.]]c H T 0޽h ? 33___PPT10.pď$+OND*' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(Dl' =A@BB BB0B@%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-6B#slide(fromRight)*<3<*T+8+0+T0 +C!  0 `XN(  XB X <Df3o?"0@NNN?NjjB X <Df3o?"0@NNN?NYY X B @ 4. Summary C X 0`? `|A spatially-dependent azimuthal multiplicity corr. pattern is suggested! There are two kinds of interactions at early stage of Au +Au collisions at "sNN =200GeV generated by the two models.l ysG33g33o33&G33> e&8X  X <Tɍf" `,$ 0 dThanks gMl :  X@,$D 0d  X 6   a. one is in-plane preferential --- which is expected from anisotropic expansion due to initial eccentricity in non-central collisions.JCGpCCe  X B@ 5:  b. another new one is out-of-plane preferential --- which may be resulted from larger initial number of participant nucleons in these direction.</GcCA X <p  <A  X 0% {  > 2A  X <0u  <A  X 0M ,$ 0 H The out-of-plane corr. pattern is observed as the result of initial interaction before anisotropic expansion. This is out of the hydrodynamic expectationdRyxSAtGC.G.= X <  e ,$ 0  Studying the corr. pattern of data of RHIC and LHC is looking forward to! i.e, ACC is independent of rapidity range, it is measurable in finite rapidity range of current relativistic heavy ion exp..hO yx yxGG33YG6AH X 0޽h ? 33!___PPT10.pď$+]D%' >= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*XD' =-g6B fade*<3<*XD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-s6Bcircle(in)*<3<*XD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-s6Bcircle(in)*<3<*XD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =-6B#slide(fromRight)*<3<* X++0+ X0 ++0+X0 ++0+X0 + 0  p\(  \X \ C     \ S  0   H 3._eQTy_'`sQT|pe.$ H \ 0޽h ? 3380___PPT10.xy: 0 `J(  `X ` C     ` S ٴ 0   Lv[͑yP[xd[hf(WRHIC:SNuNQGP vQ-NncKNN1\/f‰Km0RNTy_'`ƖSOAm. [ N AmSORf[!jWv^ N_}Yv;TTCu+Cupenc yr+R(W-N_xd-N [pencv~gkAmSORf[!j Wv'Y_Y0 t NAmSORf[ gNMRc 1\/f0R@\Wps^a_~b0RُHNNirtǏ z|~(WYdkve :\^0RpS0SYl g|n'`vAmSO(Wt Nv^ N}Yt0 vMR_N g_Y+Rv^ps^avNNel [N_N_}YvTRHICpenc\Ok0n H ` 0޽h ? 3380___PPT10.t 0 d(  dX d C     d S  0   6 AmSORf[!jWxvzvN;N[‰Kmϑ/fv_2, 000 [/fNteSO‰Kmϑ +g`|P[v Q\O(u NSs0 2-particle tv҉sQT/fN*N_ Nvirtϑ,~QN_YirtOo`,kYAu+Aù`̀sQTv m1YKN{|v,FO/f[/fvg*Nv$N|P[vs^GWsQTv~g, SsQ_vQv[MOn. 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