Elliptic Flow Fluctuations and Non-flow correlations

1. Elliptic Flow Fluctuations and Non-flow correlations Paul Sorensen Brookhaven National Laboratory for the collaboration

2. introduction ambiguity arises in calculations from uncertainty in initial conditions perfect fluid conclusion depends on ambiguous comparison to ideal hydro motivation to measure v2 fluct.: find observable sensitive to initial conditions • Talk outline: • analysis procedures and changes since QM06 • non-flow 2 and v2 from the q-distribution • comparison to cumulants v{2}, v{4} • v2 of events with a “ridge” and/or a “jet”! See STAR Poster: Navneet Kumar Pruthi

3. qy qx simulated q distribution j j is observed angle for event j after summing over tracksi flow vector distribution 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 • non-flow: broadensn = cos(n(i- j)) (2-particle corr. nonflow) • v2 fluctuations: broadens

4. flow vector distribution from central limit theorem, q2 distribution is a 2-D Gaussian Ollitrault nucl-ex/9711003; Poskanzer & Voloshin nucl-ex/9805001 x, y directions are unknown:  integrate over all  and study the length of the flow vector |q2| fold v2 distributions ƒ(v2) with the q2 distribution to account forfluctuations v2 correction to QM06 analysis: those results were an upper limit dynamic width dominated by non-flow and/or fluctuations not determined independently

5. STAR Preliminary non-flow evident width depends on the track sample differences are due to more or less non-flow in various samples smaller 2 for like-sign (charge ordering) larger 2 for small  (strong short range correlations) also in 2-D correlations: can be fit with a  independent cos(2) term + non-flow structures See STAR Talk: Michael Daugherity STAR Preliminary N.B. relationship of measured 2 from 2 particle correlations and dynamic width is not trivial: depends on ZYAM and 2-component model (see backup slides)

6. the well constrained combinations of fit parameters are: the dynamic width is the difference between the above equations STAR Preliminary dynamic width from dN/dq fit see Miller, Snellings, nucl-ex/0312008 • includes systematic errors from comparisons to cumulants • minimum 2derived from differences between subevents [q*q] - [q+*q-]

7. 200 GeV Au+Au STAR Preliminary STAR Preliminary mean and width of ƒ(v2) analysis places an upper limit on flow fluctuations

8. STAR Preliminary comparison to models upper limit challenges models • confined quark MC: • treats confined constituent quarks as the participants • decreases eccentricity fluctuations • color glass MC: • includes effects of saturation • increases the mean eccentricity comparison to hydro (NexSPheRio): Hama et.al. arXiv:0711.4544 eccentricity fluctuations from CGC: Drescher, Nara. Phys.Rev.C76:041903,2007 extraction of Knudsen number: Vogel, Torrieri, Bleicher. nucl-th/0703031 fluctuating initial conditions: Broniowski, Bozek, Rybczynski. Phys.Rev.C76:054905,2007 first disagreement with standard and use of quark MC: Miller, Snellings. nucl-ex/0312008

9. Central Au+Au 200 GeV J. Putschke, QM2006 large  small  STAR Preliminary can we eliminate v2 = 0? is there any evidence for v2 changing event-to-event? • consider events containing two high-pT tracks (pT>2 GeV/c) • is the average v2(pT<2 GeV/c) still the same in this sample? • or when the high pT tracks are correlated at large ?or small ? • or when the tracks are uncorrelated? STAR Preliminary dN/dq for low pT tracks vs  for the high pT leading hadrons shape of the q-distribution for underlying event has non-trivial dependence on  and  of the leading and next-to-leading hadron

10. event classes? characteristics of the events yielding a “ridge pair” appear to be very different from those yielding a “jet pair” See STAR Poster: Navneet Kumar Pruthi “jet” “ridge” STAR Preliminary • the “ridge” is calculated by projecting ||>0.7 correlation to ||<0.7 • the “jet” is the remaining correlation at ||<0.7 after subtracting the “ridge” • inferred v2 for events associated with “ridge” pairs is large • inferred v2 for events associated with “jet” pairs is small • this conclusion is a direct consequence of the zero-yield at minimum assumption and the 3-component model: (v2 modulated background + ridge + jet)

11. event classes? events yielding a “ridge”-like pair have large v2 events yielding a “jet”-like pair have small v2 • possible interpretations: • interactions of a jet with the medium and medium response to a jet (radial flow coupling to a jet C.Pruneau, nucl-ex/0711.1991) • do initial state quantum fluctuations lead to: • instabilities and growth of strong color fields M. Strickland, hep-ph/0511212 • large q^ and small /s Majumder, Muller, Bass. Phys.Rev.Lett.99:042301,2007 • un-quenched jets can preferentially come from events fluctuating towards small q^ and large /s (small flow)? • strong fields lead to the ridge and large v2? • what about jets on the periphery? and tangential jets? momentum conservation effects?

12. summary • we find that the case of zero v2 fluctuations cannot be excluded with dN/dq without knowledge of non-flow, cluster flow, and non-poissonian multiplicity fluctuations • analysis places stringent constraints on 2, v2, and v2: • when one parameter is specified, the others are fixed • measurement challenges standard Monte-Carlo Glauber models: • upper limit is below standard nucleon MC Glauber • upper limit coincides with participating nucleon eccentricity fluctuations • nucleon MC Glauber: leaves no room for other sources of fluctuations & correlations • Is there any evidence that v2 fluctuates? Not from untriggered dN/dq but analysis of high pT triggered events seems to indicate non-zero v2.

13. the following is back-up material

14. total uncorrelated background correlated signal the statistical decomposition • decomposition into events that yielded: • uncorrelated high pT pairs • correlated and ridge-like high-pT pairs • correlated and jet-like high-pT pairs • each bin has a different signal to background ratio. • analyze the q-distribution of events contributing to each bin • algebraically solve for the q-distribution of signal and background separately

15. acceptance effects about 4% acceptance effects could mimic correlations unrelated to the event plane easy to quantify using simulations run through a TPC filter quantified systematics from CLT approximation

16. two-component model and ZYAM non-flow component v2 modulated background relationship to 2-particle corr.

17. more about 2-particle correlations simple case: v2=0.00 2should be the width of the q-distribution zyam b makes 2 too small vary b until 2+2v2 matches q width

18. more about 2-particle correlations add some fluctuations: v2=0.010 2should be smaller zyam b makes 2 too small vary b until 2+2v2 matches q width

19. more about 2-particle correlations add some fluctuations: v2=0.015 2should be smaller zyam b makes 2 too small vary b until 2+2v2 matches q width

20. more about 2-particle correlations add some fluctuations: v2=0.020 2should be smaller zyam b makes 2 too small vary b until 2+2v2 matches q width

21. more about 2-particle correlations add some fluctuations: v2=0.025 2should be smaller zyam b makes 2 too small vary b until 2+2v2 matches q width

22. more about 2-particle correlations add huge fluctuations: v2=0.045 2should be smaller zyam b makes 2 too small vary b until 2+2v2 matches q width v2{2} = 5.154e-02 v2{4} = 4.093e-02 <v2> = 6.083e-02 v2{2} = sqrt(<v2>^2 + sigv^2 + delta) = 5.202e-02 sigv/<v2> = 73.98%

23. more about 2-particle correlations add huge fluctuations: v2=0.045 2is now negative huge v2 and negative 2 the subtracted yield

24. what’s going on 2 observed in two-component model depends on jet-flow difference between simulated 2 and observed 2 depends on cluster flow there are still more variables that can come into play  highly probable that multiple solutions could match the STAR data

25. compared to autocorrelation 2D fit • difference between 2-D fit and projection over all autocorrelations •  introduces dependence on function used to fit the data !! words of caution about inter-analysis comparisons !! be careful

26. comparison to Estruct let’s see what happens if we take those values for 2

27. v2 and v2 caution! not necessarily a consistent picture yet with fit to autocorrelations STAR Preliminary

28. 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

29. confined quark monte carlo models of the initial conditions are not trivial

30. introduction • motivation for this study • use v2 fluctuations to try to access information about initial geometry: distinguish between models of initial conditions • reduce systematic errors on v2 • results from 200 GeV Au+Au collisions • analysis procedures and change in QM06 conclusions • non-flow 2 and v2 from the q-distribution • comparison to cumulants v{2}, v{4} • v2 of events with a “ridge” and/or a “jet”! See STAR Poster: Navneet Kumar Pruthi