July 16th-19th, 2007 McGill University AM 1 July 16th-19th, 2007 McGill University, Montréal, Canada July 2007 Early Time Dynamics Montreal AM for the STAR Collaboration

July 16th-19th, 2007 McGill University AM 2 introduction motivation for this study perfect fluid claims data and model uncertainties v 2 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)  v 2  and  v2 relatioinship to cumulants v{2}, v{4}, v{6}  v2 /  v 2  (with model comparisons) relationship to preliminary PHOBOS results

July 16th-19th, 2007 McGill University AM 3 perfect fluid

July 16th-19th, 2007 McGill University AM 4 why perfect? ballistic expansion zero mean-free-path limit STAR Preliminary

July 16th-19th, 2007 McGill University AM 5 why perfect? small viscosity suggested by:1) pretty good agreement with ideal hydro and 2) independence of v 2 shape on system size in a hydro model viscosity seems to reduce v 2 but large v 2 is observed in data

July 16th-19th, 2007 McGill University AM 6 why perfect? Teaney QM2006 small viscosity suggested by:1) pretty good agreement with ideal hydro and 2) independence of v 2 shape on system size

July 16th-19th, 2007 McGill University AM 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 v 2 different methods will also deviate as a result of event-by-event v 2 fluctuations. ambiguity arises in model calculations from initial conditions perfect fluid conclusion depends on v 2 measurement and ambiguous comparison to ideal hydro my motivation to measure v 2 fluctuations: eliminate source of data uncertainty find observable sensitive to initial conditions

July 16th-19th, 2007 McGill University AM 8 flow vector distribution q-vector and v 2 related by definition: v 2 =  cos(2  i )  =  q 2,x  /√M sum over particles is a random-walk  central-limit-theorem width depends on multiplicity:narrowsdue to failure of CLT at low M non-flow: broadens  n =  cos(n(  i-  j ))  (2-particle corr. nonflow) v 2 fluctuations:broadens J.-Y. Ollitrault nucl-ex/ ; A.M. Poskanzer and S.A. Voloshin nucl-ex/ simulated q distribution  j  j is observed angle for event j after summing over tracks i qxqx qyqy

July 16th-19th, 2007 McGill University AM 9 flow vector distribution length of the flow vector |q 2 | experimentally x, y directions are unknown:  integrate over all  and study the length of the flow vector |q 2 | from central limit theorem, q 2 distribution is a 2-D Gaussian fold various assumed v 2 distributions (ƒ) with the q 2 distribution. non-flow ,  v 2 , and fluctuations  v2 function accounts for non-flow ,  v 2 , and fluctuations  v2 Ollitrault nucl-ex/ ; Poskanzer & Voloshin nucl-ex/ 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 v 2 fluctuations: derived under the accidental approximation of minimal non-flow

July 16th-19th, 2007 McGill University AM 10 flow vector distribution  =-1  =0  =1 {  /2} {full} {like-sign} 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) STAR Preliminary

July 16th-19th, 2007 McGill University AM 11 non-flow term  2  =-1  =0  =1 {  /2} {full} {like-sign} 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 STAR Preliminary

July 16th-19th, 2007 McGill University AM 12 non-flow term  2 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 STAR Preliminary

July 16th-19th, 2007 McGill University AM 13  v 2  and  v2 STAR Preliminary range of allowed  v 2  values specified upper limit on v 2 fluctuations given

July 16th-19th, 2007 McGill University AM 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

July 16th-19th, 2007 McGill University AM 15  v 2  and  v2 STAR Preliminary new level of precision being approached still significant fluctuations after including minijets from the autocorrelations with fit to autocorrelations

July 16th-19th, 2007 McGill University AM 16 comparison to geometric   fluctuations from finite bin widths have not been removed yet likely to reduce ratio below the model! STAR Preliminary

July 16th-19th, 2007 McGill University AM 17 comparison to geometric   fluctuations from finite bin widths have not been removed yet likely to reduce ratio below the model! STAR Preliminary systematic uncertainties are still large and under investigation

July 16th-19th, 2007 McGill University AM 18 relationship to PHOBOS results 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 PHOBOS STAR Preliminary

July 16th-19th, 2007 McGill University AM 19 conclusions new analysis finds that case of zero v 2 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  v 2  :  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  v 2  ?

July 16th-19th, 2007 McGill University AM 20 correction to previous analysis 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 fraction of tracks with a partner = (n tracks from pair)/M is a constant*(M-1)=  2 *(M-1)  2 = g 2 = 0.109

July 16th-19th, 2007 McGill University AM 21 correlations and fluctuations