July 16th-19th, 2007 McGill University, Montréal, Canada

1. Elliptic Flow Fluctuations in Heavy Ion Collisions AM July 16th-19th, 2007 McGill University, Montréal, Canada July 2007 Early Time Dynamics Montreal Paul Sorensen Brookhaven National Laboratory for the STAR Collaboration

2. introduction • motivation for this study • perfect fluid claims • data and model uncertainties • v2 fluctuations: possible access to initial geometry and reduction of data uncertainties • analysis strategy and correction to QM analysis • new results • non-flow  (with comparisons to models and fits to autocorrelations measurements) • v2 and v2 • relatioinship to cumulants v{2}, v{4}, v{6} • v2/v2 (with model comparisons) • relationship to preliminary PHOBOS results

3. perfect fluid

4. why perfect? zero mean-free-path limit ballistic expansion STAR Preliminary

5. why perfect? in a hydro model viscosity seems to reduce v2 but large v2 is observed in data small viscosity suggested by: 1) pretty good agreement with ideal hydro and 2) independence of v2 shape on system size

6. why perfect? Teaney QM2006 small viscosity suggested by: 1) pretty good agreement with ideal hydro and 2) independence of v2 shape on system size

7. model and data uncertainties typically the real reaction plane is not detected inter-particle correlations unrelated to the reaction plane (non-flow) can contribute to the observed v2 different methods will also deviate as a result of event-by-event v2 fluctuations. ambiguity arises in model calculations from initial conditions perfect fluid conclusion depends on v2 measurement and ambiguous comparison to ideal hydro my motivation to measure v2 fluctuations: eliminate source of data uncertainty find observable sensitive to initial conditions

8. qy qx j simulated q distribution flow vector distribution j is observed angle for event j after summing over tracksi J.-Y. Ollitrault nucl-ex/9711003; A.M. Poskanzer and S.A. Voloshin nucl-ex/9805001 • q-vector and v2 related by definition: v2 = cos(2i) = q2,x/√M • sum over particles is a random-walk  central-limit-theorem • width depends on • multiplicity: narrows due to failure of CLT at low M • non-flow: broadensn = cos(n(i- j)) (2-particle corr. nonflow) • v2 fluctuations: broadens

9. flow vector distribution from central limit theorem, q2 distribution is a 2-D Gaussian Ollitrault nucl-ex/9711003; Poskanzer & Voloshin nucl-ex/9805001 • note: QM results found with wrong multiplicity dependence for this term: • forced this fit parameter to zero • forced v2 to it’s maximum value • that data therefore represents upper limit on v2 fluctuations: derived under the accidental approximation of minimal non-flow experimentally x, y directions are unknown:  integrate over all  and study the length of the flow vector |q2| fold various assumed v2 distributions (ƒ) with the q2 distribution. function accounts fornon-flow , v2, and fluctuations v2

10. =-1 =0 =1 - - - {like-sign} - - + + + - {/2} {full} flow vector distribution STAR Preliminary • The width depends on how the track sample is selected. Differences are due to more or less non-flow in various samples: • less for like-sign (charge ordering) • more for small  (strong short range correlations)

11. =-1 =0 =1 - - - {like-sign} - - + + + - {/2} {full} non-flow term 2 STAR Preliminary differences in the width provide a lower limit on the amount of non-flow in the full event the total width provides an upper limit

12. non-flow term 2 STAR Preliminary differences in the width provide a lower limit on the amount of non-flow in the full event the total width provides an upper limit

13. v2 and v2 range of allowed v2 values specified upper limit on v2 fluctuations given STAR Preliminary

14. comparison to cumulant analysis Information determined from analysis of cumulants from fit to the q-distribution only values on curves are allowed: all parameters are correlated once one is determined, the others are specified

15. v2 and v2 new level of precision being approached still significant fluctuations after including minijets from the autocorrelations with fit to autocorrelations STAR Preliminary

16. comparison to geometric  fluctuations from finite bin widths have not been removed yet likely to reduce ratio below the model! STAR Preliminary

17. comparison to geometric  fluctuations from finite bin widths have not been removed yet likely to reduce ratio below the model! systematic uncertainties are still large and under investigation STAR Preliminary

18. relationship to PHOBOS results PHOBOS STAR Preliminary this is essentially an acceptance corrected q-distribution the underlying analysis turns out to be quite similar and susceptible to the same uncertainties i.e. the width of this distribution can be explained either by non-flow or fluctuations

19. conclusions • new analysis finds that case of zero v2 fluctuations cannot be excluded using the q-vector distributions • the non-flow term needs to be accurately determined (see T. Trainor) • analysis places stringent constraints on , v2, and v2: • when one parameter is specified, the others are fixed • presents a new challenge to models • measurement challenges standard Glauber models: • upper limit coincides with participant eccentricity fluctuations • accounting for correlations and finite bin widths will likely exclude most glauber models • glauber leaves little room for other sources of fluctuations and correlations • CGC based Monte Carlo may leave room for other fluctuations and correlations • non-flow term and fluctuations may follow expected dependence of CGC: • still well below hydro prediction (larger initial eccentricity)? • can CGC+QGP+hadronic explain , v2, and v2?

20. correction to previous analysis fraction of tracks with a partner = (n tracks from pair)/M is a constant*(M-1)= 2 *(M-1) 2 = 0.00047 g2 = 0.109 but this should be (M-1)2 the difference: how does the fraction of tracks with a partner depend on subevent multiplicity the consequences: since the multiplicity dependence of the non-flow term is the same as for fluctuations it becomes difficult to distinguish between the two

21. correlations and fluctuations