Elliptic Flow Fluctuations and Non-flow correlations Paul Sorensen Brookhaven National Laboratory Thank you to the Tata Institute for Fundamental Research and the organizers

introduction motivation to measure v2 fluctuations: ambiguity arises in calculations from uncertainty in initial conditions perfect fluid conclusion depends on ambiguous comparison to ideal hydro motivation to measure v2 fluctuations: find an observable sensitive to initial conditions analysis of the distribution of the length of the flow vector non-flow 2 and v2 from the q-distribution comparison to cumulants v{2}, v{4} relationship to 2 particle correlations v2 of events with a “ridge” and/or a “jet”! See STAR Poster at QM08: Navneet Kumar Pruthi

flow vector distribution qx qy simulated q distribution j j is observed angle for event j after summing over tracks i 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

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 for fluctuations v2 correction to QM06 analysis: those results were an upper limit dynamic width dominated by non-flow and/or fluctuations  not determined independently

See STAR Talk at QM08: Michael Daugherity non-flow evident STAR Preliminary 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 at QM08: Michael Daugherity STAR Preliminary

dynamic width from dN/dq fit STAR Preliminary the well constrained combinations of fit parameters are: the dynamic width is the difference between the above equations see Miller, Snellings, nucl-ex/0312008 Caution! relationship of measured 2 from 2 particle correlations and dynamic width is not trivial: depends on ZYAM and 2-component model (see following slides) includes systematic errors from comparisons to cumulants minimum 2 derived from differences between subevents [q*q] - [q+*q-]

relationship to 2-particle corr. two-component model and ZYAM* v2 modulated background non-flow component *ZYAM: assumption that there’s zero yield at the minumum of the correlation function above quantities are related to the width of the q-distribution

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

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

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

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

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

more about 2-particle correlations add huge fluctuations: v2=0.045 2 should 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%

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

compared to correlation 2D fit difference between 2-D fit and projection over all correlations  introduces dependence on uncontrolled assumptions !! words of caution about inter-analysis comparisons !! be careful

with fit to autocorrelations v2 and v2 consistency of this picture requires a contribution of non-poissonian fluctuations that breaks ZYAM with fit to autocorrelations STAR Preliminary

comparison to geometric  result is not unique: only the width dyn2 = 2+2v22 is uniquely determined multiple models may find consistency with the data systematic uncertainties are still under investigation STAR Preliminary

comparison to models upper limit using 2>0 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 STAR Preliminary 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

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? large  small  STAR Preliminary Central Au+Au 200 GeV J. Putschke, QM2006 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

See STAR Poster: Navneet Kumar Pruthi event classes? characteristics of the events yielding a “ridge pair” appear to be very different from those yielding a “jet pair” “jet” See STAR Poster: Navneet Kumar Pruthi “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)

event classes? possible interpretations: 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) is this evidence that 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?

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.

the following is back-up material

mean and width of ƒ(v2) assuming 2>0; analysis places an upper limit on flow fluctuations STAR Preliminary 200 GeV Au+Au STAR Preliminary

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 total uncorrelated background correlated signal 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

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

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 data

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

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

See STAR Poster: Navneet Kumar Pruthi 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