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first measurements of event-by-event Elliptic Flow Fluctuations

STAR. first measurements of event-by-event Elliptic Flow Fluctuations. Paul Sorensen Brookhaven National Laboratory for the STAR Collaboration. motivation for this study 1) increase accuracy of  v 2  2) gain sensitivity to initial conditions (CGC?) 1 and 2 are needed for estimates

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first measurements of event-by-event Elliptic Flow Fluctuations

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  1. STAR first measurements of event-by-eventElliptic Flow Fluctuations Paul Sorensen Brookhaven National Laboratory for the STAR Collaboration

  2. Elliptic Flow Fluctuations — Quark Matter 2006 motivation for this study 1) increase accuracy of v2 2) gain sensitivity to initial conditions (CGC?) 1 and 2 are needed for estimates of viscosity • introduction • v2 uncertainties and eccentricity part fluctuations • analysis method: • flow vector distribution • sanity checks • results: the rms and mean (v2 and v2) outline

  3. Elliptic Flow Fluctuations — Quark Matter 2006 true reaction plane unknown: only estimated particle correlations unrelated to the reaction plane (non-flow) contribute to the observed v2 n-particle (n>2) correlations reduce the non-flow contributions but methods also deviate if v2 fluctuates elliptic flow

  4. Elliptic Flow Fluctuations — Quark Matter 2006 • monte-carlo models indicate large fluctuations of the initial eccentricity: • v2 fluctuations are also likely to be large • the major axis fluctuates to x’: • part is relevant to the observed v2 R. Snellings & M. Miller; nucl-ex/0312008 S. Manly (PHOBOS), nucl-ex/0510031 S. Manly, nucl-ex/0510031; R. Bholerao, J.-Y. Ollitrault, nucl-th/0607009; S. Voloshin, nucl-th/0606022 initial eccentricity

  5. Elliptic Flow Fluctuations — Quark Matter 2006 qy qx j simulated q distribution 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 • multiplicity: narrows due to failure of CLT at low M • non-flow: broadens gn = cos(n(i- j)) (2-part. correlations) • v2 fluctuations: broadens analysis method: flow vector dist.

  6. Elliptic Flow Fluctuations — Quark Matter 2006 from central limit theorem, q2 distribution is a 2-D Gaussian Ollitrault nucl-ex/9711003; Poskanzer & Voloshin nucl-ex/9805001 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 now accounts fornon-flow, v2, and fluctuations (v2) analysis method: flow vector length

  7. Elliptic Flow Fluctuations — Quark Matter 2006 • why isn’t it easy: •  non-flow (g2) broadens the distribution •  fluctuations (v2) also broaden the distribution • how do we distinguish between v2 and g2: • the width changes have a different dependence on the number of tracks: broadening from v2 scales with √M • analyze the same events sometimes use all tracks, sometimes fewer tracks • fit multiple distributions simultaneously: provides multiple equations to solve for the 2 unknowns 2/ndf = 1760/651 2/ndf = 705/651 2/ndf = 670/650 M=350, 250 Au+Au 200 GeV 20%-30% central v2 = (6.05 ± 0.2)% v2 = (2.36 ± 0.3)% g2 = (4 ± 5)% dN/dq2 v2 fixed at 0.0 g2 fixed at 0.0 all parameters free q2 analyzing the multiplicity dependence

  8. Elliptic Flow Fluctuations — Quark Matter 2006 simulated dN/dq q • Sanity checks: • fit to simulated data: do we get back what we put in? Test passed for all input values • fit data from combined centrality bins: does v2 increase as it should? Test passed • sensitivity to assumed shape of v2 distribution? we used a gaussian and a function that describes the part distribution: only small deviations in mean or rms <15% • fit using 2, 3, or 5 different multiplicities? some differences on range of allowed g2 values systematic studies

  9. STAR Preliminary centrality dependence of r.m.s. and mean (v2 and v2) for 200 GeV Au+Au collisions

  10. Elliptic Flow Fluctuations — Quark Matter 2006 r.m.s. width of the v2 distribution is 36% of the mean within errors independent of centrality width and mean

  11. Elliptic Flow Fluctuations — Quark Matter 2006 mean v2 lies between 2- and 4-particle cumulant v2 For discussion of fluctuations and cumulants see R. Snellings nucl-ex/0312008 and talk by S. Voloshin consistency with other methods

  12. Elliptic Flow Fluctuations — Quark Matter 2006 v2 from fit and from v2{2}2-v22 are consistent For discussion of fluctuations and cumulants see R. Snellings nucl-ex/0312008 and talk by S. Voloshin consistency with other methods

  13. Elliptic Flow Fluctuations — Quark Matter 2006 v2{4} agrees with q-fit results: non-flow does not have to be invoked difference between v2{2} and v2{4} apparently dominated by fluctuations For discussion of fluctuations and cumulants see R. Snellings nucl-ex/0312008 and talk by S. Voloshin consistency with other methods

  14. Elliptic Flow Fluctuations — Quark Matter 2006 v2/part scales with dN/dy1/3: fluctuation of this quantity consistent with data hydro with fluctuating initial conditions suggests sensitivity to EOS For v2/part scaling, see talks by A. Tang and S. Voloshin: QM2006 model comparisons

  15. Elliptic Flow Fluctuations — Quark Matter 2006 standard eccentricity is excluded by data model comparisons

  16. Elliptic Flow Fluctuations — Quark Matter 2006 • using the multiplicity dependence of the |q| distribution we’ve measured v2 fluctuations (v2) • uncertainty on v2 reduced • v2/v2 (rms/mean) is approximately 36% independent of centrality • agreement with NeXSPheRIO using a QGP EOS • also consistent with phenomenological scaling v2=0.034*part*(dN/dy)1/3 • new probe for early stages of HI collisions • explore pseudorapidity dependence (v21v22 - v21v21) to reveal dynamics beyond geometry • explore sensitivity to CGC • explore sensitivity to EOS (sys. errors on theory?) • explore sensitivity to critical point fluctuations summary

  17. supporting material fits to simulations derivations other?

  18. Elliptic Flow Fluctuations — Quark Matter 2006

  19. Elliptic Flow Fluctuations — Quark Matter 2006

  20. Elliptic Flow Fluctuations — Quark Matter 2006

  21. Elliptic Flow Fluctuations — Quark Matter 2006 0%-5% not gaussian for central or peripheral for central it’s well described by: v*exp[-0.5((v-v0)/v)2] I use this shape in my fit function glauber results

  22. Elliptic Flow Fluctuations — Quark Matter 2006 Fit results 0%-5%:  chisquare/ndf = 539.9/574 probability = 84% EDM=0.00159004 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 <v2> -4.88725e-08 2.65831e-04 2.65831e-04 -3.44983e+01 2 delta_v2 1.96408e-02 1.20468e-04 0.00000e+00 -6.21924e+00 3 g2 -6.09831e-03 3.23056e-03 -0.00000e+00 2.57024e+01 4 area 5.23554e+03 constant 5 v4 6.91200e-04 constant new result previous r.m.s. = 0.0128 (0.0151) mean = 0.0246 (0.0235) median = 0.0231 mode = 0.0196 fit results

  23. Elliptic Flow Fluctuations — Quark Matter 2006 dN/dv2 10%-20% 5%-10% 0%-5% v2 Positive definite by construction similar results with the largest deviations in the central bin as expected dN/dv2 matches dN/dpart distribution includes impact parameter fluctuations (we should remove that component) new result 0%-5% previous change r.m.s. = 0.0128 0.0151 -15% mean = 0.0246 0.0235 +5% median = 0.0231 mode = 0.0196 new result 5%-10% previous change r.m.s. = 0.0164 0.0181 -9% mean = 0.0347 0.0339 +2% median = 0.0334 mode = 0.0305 new result 10%-20% previous change r.m.s. = 0.0206 0.0216 -5% mean = 0.0487 0.0481 +1% median = 0.0475 mode = 0.0453 v2 distributions

  24. Elliptic Flow Fluctuations — Quark Matter 2006 • part and v2 should be corrected for impact parameter fluctuations • part correction comes directly from fixing b from glauber • v2 corrected using v2corr =b*∂v2/∂b impact parameter fluctuations

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