Eventbyevent flow and initial geometry from LHC Soumya

Event-by-event flow and initial geometry from LHC Soumya Mohapatra Jet Quenching Workshop, BNL 16 th April 2013

Importance of fluctuations § Initial spatial fluctuations of nucleons lead to higher moments of deformations in the fireball, each with its own orientation. Alver, Roland (ar. Xiv: 1003. 0194) 1. Odd harmonics present 2. vn is a distribution, can be characterized by mean and width 3. Each harmonic has a separate phase (phases may be correlated) Large acceptance of the LHC experiments coupled with the increased multiplicity has allowed for great precision is studying the nature of these fluctuations Understanding the initial geometry is critical for understanding jetsuppression 2

OUTLINE § Multi-particle correlation measurements • Cumulants, 2 PC, LYZ § Event by Event vn measurements § Event-plane correlations Emphasis on § Removing non-flow § Comparison between experiments and methods § Theory interpretation 3

Gaussian model of flow fluctuations ar. Xiv: 0708. 0800 ar. Xiv: 0809. 2949 For pure fluctuations vn. RP=0 4

Multi-particle correlations Sensitive to mean geometry and fluctuations Mean geometry only 5 ar. Xiv: 0708. 0800 0809. 2949 Limit when vn. RP>>δn (i. e. Average geometry dominates over fluctuations) Expected for v 2 in mid-central events Limit when vn. RP->0 (Pure fluctuations) Expected to hold for v 2 in central events and for higher order harmonics in all centralities Lee-Yang Zeros : Multi-particle correlations involving all particles in the event. suppresses non-flow Two particle correlations: similar to vn{2}, but often done with dh gap to suppress non-flow. Measures <vn 2> Event Plane (EP) Method : Returns a value in between <vn> and <vn 2>

v 2 from multi-particle correlations v 2{2} probably over-estimates <v 22> Due to non-flow v 2{EP} probably under-estimates <v 22> Good consistency between LYZ and 4 -particle cumulants : Reliable handle on average geometry! ar. Xiv: 1204. 1409 6

Comparison across experiments ATLAS-CONF-2012 -118 Good agreement among experiments for cumulants and even v 2{EP} 7

p. T dependence of Eb. E fluctuations ar. Xiv: 1205. 5761 Ratio of fluctuations in v 2 to mean v 2 is relatively independent of p. T Note that v 2{EP} changes by an order of magnitude over this p. T range but ratio is remarkably stable Hydro response factorizes of function of p. T and initial geometry! 8

Higher order cumulants for v 2 § Higher order cumulants such as vn{6}, vn{8} all measure vn. RP § vn. RP is less susceptible to non-flow and so are vn{4}, vn{6}, vn{8}. § ALICE results show consistency among them § Note these measurements are done in 1% bins (Good!) 9

Cumulant results v 3 ar. Xiv: 1105. 3865 § Relatively weak centrality dependence as compared to v 2 § Sizable v 3{4} is seen ~50% of v 3{2} • Implies mean geometry effects for v 3 ! § v 3{4} /v 3{2}=0. 5 => v 3 RP/δ 3 =0. 8 10

v 3{4} and average geometry 11

Event by Event flow measurements Track distribution in three central events Corresponding twoparticle correlations The large acceptance of the ATLAS/ALICE detectors and large multiplicity at LHC makes Eb. E vn measurements possible for the first time. 12

v 2 -v 3 probability distributions v 2 v 3 distributions are consistent with pure Gaussian fluctuations deviations in the tail (increases central->midcentral), Also see caveat in slide 11 For v 2 pure Gaussian fits only work for most central (2%) events 13

v 2 probability distributions via 2 PC A. Timmins, Hot Quarks 2012 ALICE Eb. E v 2 measurements obtained via 2 PC followed by unfolding. v 2 described by Bessel-Gaussian distribution: Contribution from mean geometry+fluctuations. 14

Relative fluctuations of v 2 Can obtain mean, σ from Eb. E distributions And calculate σ/mean Black points are fluctuations estimated from cumulant method : 15

Relative fluctuations of v 3 16 16

Comparison to cumulant results 17 A. Timmins Hot Quarks 2012 Extracted v 2{2}, v 2{4} and sigma from Eb. E distributions are consistent with cumulant measurements

Non-flow bias on fluctuation measurements 18 § Non-flow effects can bias the cumulant and Eb. E results § For cumulant the main effect is to enhance vn{2} • Can use vn{2} with Δη gap as substitute § vn{4} and higher cumulants relatively unaffected by non-flow § Can estimate non-flow from MC (ALICE Eb. E Measurements) • Not data driven § For Eb. E vn measurement the unfolding procedure can be used to remove non-flow (ATLAS Measurements) • Data driven procedure

Non-flow effects : ATLAS Eb. E § Non-flow effects are mostly uncorrelated between sub-events § They are removed during unfolding § HIJING+Flow afterburner test demonstrates this § Get response function by dividing tracks with η>0 and η<0 into sub-events § Get response function by randomly dividing tracks into sub-events § Do unfolding with both response functions and compare to input vn distribution Unfolded/True Events ar. Xiv: 1304. 1471 19

Comparison to initial geometry: v 2 For Glauber and CGC mckln Rescale εn distribution to the mean of data 0 -1% 30 -35% 5 -10% 40 -45% 20 -25% 55 -60% Both models fail describing p(v 2) across the full centrality range 20

Comparison to IP-Glasma model 21 ar. Xiv: 1301. 5893 Talk tomorrow by Bjorn Schenke 1209. 6330 (Gale, Jeon, Schenke, Tribedi, Venugopalan)

Correlation between phases of harmonic flow 22 n Complementary observables to vn n Correlation can exist in the initial geometry and also generated during hydro evolution n The correlation can be quantified via a set of correlators ar. Xiv: 1205. 3585 ar. Xiv: 1203. 5095 n This can be generalized into multi-plane correlations Glauber ar. Xiv: 1208. 1200

Event plane correlations Initial geometry + hydrodynamic ATLAS-CONF-2012 -049 ar. Xiv: 1208. 1200 Heinz & Qui geometry only Eb. E hydro qualitatively reproduces features in the data 23

Compare with Eb. E hydro calculation: 3 -plane 24 Initial geometry + hydrodynamic ATLAS-CONF-2012 -049 ar. Xiv: 1208. 1200 Heinz & Qui geometry only Npart Eb. E hydro qualitatively reproduces features in the data

Summary § Cumulants provide overview into nature of fluctuations • v 2{2} used to probe average geometry+fluctuations. • v 2 {4}=v 2 {6}=v 2 {8}=v 2 RP and LYZ probe average geometry. • Dependence of vn on p. T and initial geometry factorizes. § EBE measurements of v 2, v 3 and v 4 distributions done by ATLAS and ALICE(v 2). • • Eb. E measurement handles non-flow. Does not assume a particular form of the Eb. E distributions. Distributions look Bessel-Gaussian like (deviations in the tail). Distributions for v 2, v 3 and v 4 well reproduced by IP-Glasma+MUSIC, but not by Glauber. § EP Corrs give further insight into initial geometry as well as hydroevolution • Can differentiate hydro-effects from initial geometry effects. • Also gives information on initial geometry. 25