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W. Holzmann

Journal Club. Methods of Flow Measurements. W. Holzmann. Outline. Introduction (Why are flow measurements important?). (Selected) Methods of flow measurements: - Reaction Plane Method - Two Particle Correlation Method - (Cumulant Method) - Lee-Yang Zero Method.

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W. Holzmann

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  1. Journal Club Methods of Flow Measurements W. Holzmann

  2. Outline • Introduction (Why are flow measurements important?) • (Selected) Methods of flow measurements: - Reaction Plane Method - Two Particle Correlation Method - (Cumulant Method) - Lee-Yang Zero Method • Recent examples of elliptic flow measurements • Summary

  3. Ne W. Scheid, H. Muller, and W. Greiner, PRL 32, 741 (1974) H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980) • Kolb+Heinz nucl-th/0305084, energy density fractional contours Probing Nuclear Matter Properties via Collective Flow

  4. Focus of This Presentation: Elliptic Flow coordinate-space-anisotropy  momentum-space-anisotropy y py px x Elliptic flow strength mostly determined by EOS and initial eccentricity

  5. Reaction Plane Method Obtain estimate of Reaction Plane: The Event Plane STAR

  6. The issue of Resolution! Flow if non-flow is small! Obtain resolution from sub-events: For two subevents w/ equal multiplicity and resolution: Approximate formula, better use fit to subevent distribution

  7. Resolution from Correlation between Subevents only flow! non-flow! J-Y. Ollitrault, Nucl Phys A590 561 (1995)

  8. Resolution from Correlation between Subevents in Phenix Very good fits to subevent distribution: non-flow very small!

  9. What about acceptance? Remove biases from acceptance correlations by making distribution of event planes isotropic: Flatening of Event Plane Distribution Strategy: Many ways( see Poskanzer & Voloshin: PRC 58 1671 (1997)), for example: Recentering of Xn and Yn Fit event plane distribution to Fourrier expansion and shift event-by-event This is done in PHENIX

  10. First Application of the Azimuthal Correlation Technique at RHIC Two Particle Correlation Method Wang et al., PRC 44, 1091 (1991) Lacey et al. PRL 70, 1224 (1993)

  11. Hydro or Transport With large Opacity HIJING Flow leads to strong anisotropy – no asymmetry Jets lead to strong anisotropy and an asymmetry Information Content of Two Particle Correlation Function • The anisotropy of the correlation function can reflect • both flow and Jet contribution • The Asymmetry provides crucial Jet Information

  12. V2 From Assorted Correlations If away-side jet correlation is small p2(assor.) (pT) p2(assor.) = v2(pT) x v2’’ pT

  13. PHENIX PRELIMINARY V2 From Assorted Correlations - Phenix Example Year-1 Phnx v2 measurement and 62.4 GeV data were analyzed with two particle correlations

  14. Is there a bias introduced by the finite Phenix acceptance? General Analytic Proof acceptance/efficiency function probability distr. for particle detection

  15.  Correlations If Flow predominate Multiparticle correlations can be used to reduce non-flow contributions (N. Borghini et al, PRC. C63 (2001) 054906) V2 From Cumulants

  16. PPG047 Comparison of V2 From Different Methods In 62.4 GeV Au+Au Collisions at RHIC, Reaction Plane and Two Particle Correlation Methods give same answer.

  17. An Alternative Approach: Lee-Yang Zeroes • Removes non-flow correlations from flow measurement, important additional tool for v2 study • Directly investigates large order behavior of cumulant expansion (no costly computational evaluation of cumulants of specific order n)

  18. The Lee-Yang Zero Procedure in a Nutshell R. S. Bhalerao, N. Borghini, J.-Y. Ollitrault , Nucl. Phys. A727 (2003) 373 Calculate Q() the projection of the flow vector on arbitrary angle , can be done for fixed , but in practice use several  values and average define generating function for large number of values of z=ir, w/ r real and positive and plot mod(G(z)) as a function of r. The integrated flow estimate: w j01=2.405 the 1st root of the Bessel function J0(x) and r0 the value of r at the first minimum of G(ir). Compute vn: Vn = M vn In practice, makes more numerical sense to use |G(ir)|2

  19. A working example: Look at int. v2 w/ L.-Y. Zeroes in ATLAS Use 50 events with fixed 5% v2 from Andrzej’s production at: /usatlas/scratch/olszewsk/data/hijing/flow/ Use all charged tracks (XKalman) w/ unit weights, No track quality cuts, upper pT cut = 4900 MeV.

  20. A First Look at int. v2 w/ L.-Y. Zeroes in ATLAS Input v2 faithfully recovered within statistical errors!

  21. R: measure of size of system How do you know you are looking at Flow? Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009

  22. Eccentricity scaling of the data v2 scales with eccentricity and across system size

  23. Can we make an estimate of cs? • We can make an estimate of cs from elliptic flow measurements Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009 Definition of v2 in model typically 2 times larger than with usual definition M. Issah WWND 2005

  24. Estimate of cs? Equation of state: relation between pressure and energy density v2/ecc for <pT> ~ 0.5 GeV/c cs ~ 0.35 ±0.5 (cs2 ~ 0.12), soft EOS F. Karsch, hep-lat/0601013 M. Issah WWND 2005

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