2. 1 Effect of Eccentricity Fluctuations and Nonflow on Elliptic Flow Methods Jean-Yves Ollitrault, Art Poskanzer, and Sergei Voloshin QM09

3. 2 Methods “Two-particle”: v 2 {2}: each particle with every other particle v 2 {subEP}: each particle with the EP of the other subevent v 2 {EP} “standard”: each particle with the EP of all the others v 2 {SP}: same, weighted with the length of the Q vector Many-particle: v 2 {4}: 4-particle - 2 * (2-particle) 2 v 2 {q}: distribution of the length of the Q vector v 2 {LYZ}: Lee-Yang Zeros multi-particle correlation review of azimuthal anisotropy: arXiv: 0809.2949

4. 3 Integrated v 2 STAR, J. Adams et al., PRC 72, 014904 (2005)

5. 4 correct for event plane resolution nonflow: correlations not associated with the reaction plane fluctuations: measure mean of some power of the distribution differences between methods: where want to generalize this to the other methods specify the plane, because theoreticians usually calculate in the reaction plane Nonflow and Fluctuations

6. 5 Methods Comparison (2005) STAR, J. Adams et al., PRC 72, 014904 (2005) 2-part. methods multi-part. methods To expand scale, plot ratio to Standard Method: “Because of nonflow and fluctuations the true v 2 lies between the lower band and the mean of the two bands.” std. method 5% low! systematic error: spread of methods

7. 6 Reaction, Participant, and Event Planes participant plane coordinate space momentum space

8. 7 event plane resolution root-mean-square mean PHOBOS Simulations PHOBOS+Heinz, PRC 77, 014906 (2008) various v distributions and mult

9. 8 Include Fluctuations in absence of fluctuations for full events, it is more complicated

10. 9 The  Equation for Subevents for full events, it is more complicated I 0,1 are modified Bessel functions resolution parameter only function of 

11. 10 PHOBOS+ with Equation Eq. Fluctuations!

12. 11 Analytic Correction for Fluctuations method similar to momentum conservation correction: N. Borghini, P.M. Dinh, J.-Y. Ollitrault, A.M. Poskanzer, and S.A. Voloshin, PRC 66, 014901 (2002)

13. 12 Analytic Correction for Nonflow nonflow

14. 13 Differences of Measured v 2 Values All differences proportional to Without additional assumptions can not separate nonflow and fluctuations

15. 14 v 2 Fluctuations from  part Fluctuations Assume width with same percent width as  part : 2D Gaussian fluctuations in reaction plane lead to Bessel-Gaussian fluctuations along the participant plane axis   is from standard deviation of nucleon MC Glauber of  part Bessel-Gaussian: Voloshin et al., Phys. Lett. B 659, 537 (2008)

16. 15 Assumptions Application to Data MC Glauber  participant less nonflow

17. 16 Data Corrected to published agreement for mean v 2 in participant plane corrected to PP

18. 17 Nonflow and Fluctuations with my assumptions and parameters:

19. 18 corrected to RP v 2 in the Reaction Plane in Gaussian fluctuation approximation: Voloshin, Poskanzer, Tang, and Wang, Phys. Lett. B 659, 537 (2008) a v 2 for theorists

20. 19 CGC Model Glauber CGC reaction plane Fluctuations from CGC Nonflow from partly weighted by

21. 20 Conclusions Understanding of effects of fluctuations and nonflow All corrections proportional to  tot 2 Can not separate  and  v without assumptions consistent from different measurements with  part fluctuations from MC Glauber  = 2  pp /N part and etaSub less Other assumption also work with slightly different results Important for measurements with respect to event plane: HBT, R AA, conical emission, etc. Better multi-particle correlations are needed because they do not need any correction

22. 21 Extra

23. 22 Project Chronology I asked Constantin Loizides of PHOBOS He said Ollitrault understood I asked Jean-Yves Sergei rederived it elegantly I asked, does it explain why v 2 {EP} is 5% low? I did numeric integrations Jean-Yves derived analytic equations I applied them to published STAR data I did numeric integrations to test equations Sergei did simulations to test equations