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

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:

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

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

5 Methods Comparison (2005) STAR, J. Adams et al., PRC 72, (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

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

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

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

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

10 PHOBOS+ with Equation Eq. Fluctuations!

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, (2002)

12 Analytic Correction for Nonflow nonflow

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

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)

15 Assumptions Application to Data MC Glauber  participant less nonflow

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

17 Nonflow and Fluctuations with my assumptions and parameters:

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

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

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

21 Extra

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