S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page1 Azimuthal correlations and anisotropic flow: trends and questions Sergei A. Voloshin 1.Definitions: What is flow and what is non-flow? Spatial asymmetry? Let us speak the same language! 2.Continuous worry: is it really collective? Has anything to do with the impact parameter orientation (real flow)? q -distributions. Measuring non-flow in AA and pp. 3.Non-flow and many particle correlations. Mixed harmonics analysis. 4.Many reasons for flow fluctuations. Fluctuations contribution to mixed harmonic analysis. 5.2-particle correlations at different angles to the Reaction Plane: High pt, azHBT, non-identical particles, balance functions. 6.Conclusions/Summary Not a review, Not a presentation of STAR results

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page2 Directed flowElliptic flow Anisotropic flow  correlations with respect to the reaction plane Term “flow” – not necessarily “hydro” flow – used only to emphasize the collective behavior  multiparticle azimuthal correlation. Anisotropic flow. Definitions: v’s “… v2 in pp collisions is almost 100% …” “… event anisotropy at high pt, elliptic flow at low pt…” The situation is not totally clear for 2-particle spectra. Discussed a little bit below. Fourier decomposition of single particle inclusive spectra Non-zero v4 – is it bad?

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page3 Anisotropic flow. Definitions:  ’s  Other similar/same quantities: Ollitrault:  s Heiselberg:  Sorge: A 2 Shuryak: s 2 And more recent ones: Those have clear meaning only for particles produced at the point x=y=0. The physics is (due to Sorge) that v 2 is proportional to any of them. Better to use the same definition to allow cross comparison (unless a new physics based relation established). (Low density limit (Heiselberg) is probably the best to check the meaning) Note: -- it is not at all trivial what should be used (if any) for higher harmonics (no simple form) -- s 2 parameter in the Blast Wave fit to v 2 (p t ) in general is a different parameter -- do not confuse initial and final state anisotropy

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page4 Such absorption corresponds to suppression for inclusive yield in central collisions about factor of 4-5 b/2R A V2V2 V4V4 Flow due to absorption. v 2, v 4 ; e 2, e 4 See also: nucl-th/ A. Drees, H. Feng, J. Jia would behave quite differently (sign, etc.) WS density, finite absorption Surface emission limit, hard sphere Not clear what should be used for  4

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page5 Looking for collectivity: q-distributions Two more: 1)q-distributions: 2)Q vector products Distribution in the magnitude of the flow vector Correlations due to flow: shift of the peak Non-flow contribution: widening of the distribution Used in the very first E877 analysis Better shape description  higher moments (cumulant orders)  new method of Ollitrault (?)

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page6 v 2 from q-distributions -- The results are very close to those from 4-particle correlation analysis. -- Difficult to trace the contribution of flow fluctuations. STAR, PRC 66 (2002)

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page7 Azimuthal correlation in pp collisions Goals (from “flow” point of view): 1.Check if non-flow estimates/measurements reported for Au+Au are consistent with measurements in pp. (One could expect the difference of the order of factor of <~2. Examples: Extra particles in jets  non-flow  ; B-to-B jet suppression -  ) 2.Use pp data to estimate non-flow effects in Au+Au in the regions where other methods do not work well (like high p t region; Kaon and Lambda ? ) Approach/method: 1.“Scalar product”. The basic quantity in this approach is Advantages: simpler to work with and much simpler to interpret. Subscript “2” is omitted in equations on a next few slides. Flow   non-flow

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page8  uQ*  in pp and AA collisions Non-flow looks exactly the same in pp and AA  Directly “correctible”.

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page9 pp vs. AA The plot above, showing the rise and fall of azimuthal correlations ( M ) can be explained only by flow: no any other known source of the azimuthal correlation is able to give such a dependence. The origin of such dependence: ~ M *  STAR Preliminary Most peripheral 5% central 0 pt 7 GeV M<~10 M>~500 STAR results are presented by A. Tang at this workshop

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page10 Mixed harmonics: how it works What to do when the reaction plane is known: (AMP, SV: PRC “method” paper) … and when it is not exactly known: Similar for v 4 via Borghini, Dinh, Ollitrault

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page11 Non-flow and mixed harmonics Compare to 5—6  reported. -- Totally relies on non-flow estimates for v2. -- Higher order cumulants do not help

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page12 Non-flow or Fluctuations? Correct if v is constant in the event sample Should be used even in a case of  =0 Several reasons for v to fluctuate in a centrality bin: 1)Variation in impact parameter in a given exp. centrality bin (taken out in STAR PRC flow paper) 2)Real flow fluctuations (due to fluctuations in initial conditions, in local particle density, or in the system evolution)

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page13 Fluctuations in eccentricity  fluctuations in v 2 x,y – coordinates of “wounded” nucleons v 2 ~   fluctuations in flow Calculations: R. Snellings and M. Miller

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page14 Compare to data R. Snellings Fluctuations in initial geometry could explain the entire difference between v 2 {2} and v 2 {4}

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page15 On the other hand, it is noticed that it will be interesting to study fluctuations in Flow fluctuations: mixed harmonics Calculations by R. Snellings. <cos(4  s ) used as e 4 The effect can be as large as factor of 3

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page16 Where we are – checking with “oldstuff” S.V. RHIC Winter Workshop, Berkeley, January     

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page17 2-particle correlations wrt RP x – azimuthal angle, transverse momentum, rapidity, etc. J. Bielcikova, P. Wurm, K. Filimonov S. Esumi, S.V. nucl-ex/ “a” == “trigger particle” CERES, nucl-ex/ Selection of one (or both) of particles in- or out- of the reaction plane “distorts” the RP determination Approach: - “remove” flow contribution - parameterize the shape of what is left - study RP orientation dependence of the parameters

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page18 STAR Results STAR preliminary Back-to-back suppression is larger in the out-of-plane direction K. Filimonov, STAR, DNP 2003 Complications: particles in the “trigger” pt region could have different origin and correspondingly different “flow”.

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page19 Approach: “Same” –”Opposite” Next step: compare differences for 2 different pseudorapidity windows used to count the associated particles  get numbers of “Same” and “Opposite” separately. Here one has to use one of the assumptions: - the eta distribution of associated particles in “opposite” direction is flat, or - it is the same as in pp collisions Work with differences: (# of associated particles in the SAME direction) - (# of associated particle in the OPPOSITE direction) Advantage: Flow contribution cancels out exactly. STAR, PRL 90 (2003)

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page20 Only sketch… central Out-of-plane In-plane Number of associated particles. “Same” – “Opposite” peripheral (!) Larger difference values correspond to either larger “same” or smaller “opposite”.

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page21 azHBT S.V. LBNL 1998 annual report # R20 RQMD v 2.3, RHIC

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page22 azHBT-2 IPES initial conditions, U. Heinz, P. Kolb PL B542 (2002) 216 Should we try very low k T at RHIC?

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page23 Non-identical particle correlations

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page24 Summary: trends, questions 1.Please avoid (unnecessary) introduction of new terms 2.Not clear what, if any, to use instead of e 2 for higher harmonics 3.How to get rid of non-flow effects at the level of 0.1% level (v n ) 4.How to disentangle non-flow and flow fluctuations effects 5.2-particle correlations with respect to the RP - future direction? 6. How to disentangle “jet” and “soft” flow at intermediate pt? 7.Is the azHBT sensitive to the in-plane expansion? 8.… 9.Plasma of constituent quarks? Thanks to STAR “flow group” for discusion