ATLAS dipolar flow vn ATLAS eventbyevent Jiangyong Jia
ATLAS dipolar flow vn ATLAS event-by-event Jiangyong Jia for the ATLAS Collaboration https: //atlas. web. cern. ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2012 -114/ Quark Matter 2012 Aug 13 th- Aug 18 th
2 Motivation Detailed study of v 1 -v 6 also 1208. 1874
3 Motivation Singles Foreground Acceptance Pairs
4 Motivation Singles Foreground Acceptance Pairs
5 Motivation Rich event-by-event patterns for both vn and Φn! Singles Foreground Acceptance Pairs
6 Motivation Rich event-by-event patterns for both vn and Φn! For results on Φn correlations, see Foreground Acceptance S. Mohapatra parallel 7 D Fri.
Motivation Unfold for final multiplicity effects (mainly). The key is response function: Foreground Acceptance 7
ATLAS detector η<0 η>0 Inner detector Tracks |η|<2. 5 n n Tracks in Inner Detector(ID) divided into subevents with flexible η ranges! Pb+Pb data from fall 2010 (48 M events) 8
Obtaining single particle distribution n Ideal detector: n Correct for acceptance & efficiency: Efficiency weight applied track by track as function of p. T and η 9
Flow vector distribution & smearing Observed Eb. E flow vector distribution: Smeared around the true flow vector: 10
Determining response function n η<0 η>0 Estimated by the correlation between “symmetric” subevents n 2 D response function is a 2 D Gaussian! n Response function obtained by integrating out azimuth angle 11
Bayesian unfolding algorithm as implemented in the Roo. Unfold n True (“cause” c or vn) vs measured distribution (“effect” e or vnobs) Denote response function n Unfolding matrix M is determined via iterative procedure Prior, c 0, can be chosen as input vnobs distribution or it can be chosen to be closer to the truth by a simple rescaling according to the EP vn Number of iterations Niter adjusted according to sample statistics and binning. 12
Basic unfolding performance: v 2, 20 -25% n 13 V 2 converge within a few % for Niter=8, small improvements for larger Niter.
Dependence on prior: v 4 20 -25% n n Despite different initial distribution, v 4 all converged for Niter=64 Wide prior converges from above, narrow prior converges from below! Constraining the residual non-convergence 14
Compare to unfolding for half-ID: 20 -25% n Agrees within a few % in most cases, can be larger in the tails reflects the non-convergence of half-ID (since width of its response function is √ 2 wider) v 2 v 3 Residual non-convergence of half-ID v 4 15
16 v 2 -v 4 probability distributions v 2 n n v 3 v 4 p(vn) distributions with shape uncertainty only Overlaid with Gaussian function adjust to the same mean (curves)
17 Unfolding in different p. T ranges: 20 -25% v 2 n v 3 v 4 Distributions for higher p. T bin is broader, but they all have ~same reduced shape unfolding is robust. Hydrodynamic response ~ independent of p. T.
Centrality (Npart) dependence of relative widths n=2 Dotted lines indicate Gaussian limit 0. 523 n v 2: Gaussian in 0 -2% centrality, reach 0. 34± 0. 02 for 20 -30% 18
Centrality (Npart) dependence of relative widths n=2 n=3 n n n=4 v 2: Gaussian in 0 -2% centrality, reach 0. 34± 0. 02 for 20 -30% v 3 -v 4: ~Gaussian for full centrality range. 19
Compare to vn n Verified!! Expectations: n=2 20 EP results 20 n=3 n=4
Measuring the hydrodynamic response: v 2 n 21 Check: Rescale εn distribution to the mean of data 0 -1% 5 -10% 30 -35% 40 -45% For Glauber and CGC mckln 3. 46 20 -25% 55 -60% Both models fail describing p(v 2) across the full centrality range
Glauber or MC-KLN? Glauber MC-KLN R. Snellings QM 2011 Same as the dashed lines from right figure… n n MC-KLN works better in more central collisions Glauber better in more peripheral collisions 22
23 How about v 3? and v 4? n n 0 -1% 5 -10% 30 -35% 40 -45% 20 -25% 55 -60% Good agreement except in peripheral collisions, but this could be trivial, since all Gaussian functions have same reduced shape. Similar observation for v 4 Non-linear responses
Summary n n 24 We measured event-by-event probability distribution of v 2 -v 4 in various centrality: p(vn). Distributions are Gaussian for v 2 in central collisions, and for v 3 and v 4 in all centrality ranges. n Also supported by the values of ratio n The reduced shape has no p. T dependence hydro response indep of p. T Event plane vn is consistent with n p(v 2) is inconsistent with p(ε 2) from Glauber &MC-KLN model. n n Provides direct constraints on the hydrodynamic response to initial geometry fluctuations.
25 Back up
Non-flow from short range correlations? 26 η<0 η>0 n n Use to estimate . is Gaussian!! Nonflow small or number of sources responsible for short-range correlations multiplicity and they are not correlated between the subevents. n n n to True for resonance decays, Bose-Einstein correlation, and single jets? Non-flow effects is included in response function and unfolded away? Influence of non-flow to 2 PC is different from single unfolding, and for different gaps. But consistent results are observed (see next).
27 Method 2—unfolding Eb. E two-particle correlation n Eb. E pair correlation between two symmetric subevents n Define observed vn from correlation analysis as: n n η<0 η>0 Term “Bn” is essential! it captures some statistical fluctuations. The 2 PC response function obtained trivially from
Compare with 2 PC unfolding: 20 -25% n vnobs, 2 PC is broader than vnobs, but converges to the same answer n Residual non-convergence mainly due to 2 PC unfolding 28
Compare single & 2 PC unfolding with η gaps 29
Response function for single and 2 PC n broader than approach each other at for large vn. for small vn. 30
Basic unfolding performance: v 4, 20 -25% n More iterations in peripheral collisions and for v 3 and v 4 n n bulk region is converged, both unfolded and refolded, for Niter = 32, but the tails still exhibit some small changes up to Niter = 64. Statistical error approaches √N for 64<Niter<128 (thanks to large sample stat. ). n The differences are always less than 5% between Niter 64 and 128 31
Dependence on prior: v 2 20 -25% n Converge for Niter=8 32
Dependence on prior: v 2 20 -25% n Converge for Niter=8 33
v 4 comparison with eccentricity 0 -1% 5 -10% 30 -35% 40 -45% Non-linear responses 20 -25% 55 -60% 34
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