ATLAS measurement of reaction-plane correlations in Pb-Pb collisions at √sNN =2.76 TeV Jiangyong Jia for the ATLAS Collaboration Conference Note at: https://cdsweb.cern.ch/record/1451882 v1-v6 measurements, see arXiv: 1203.3087 and talk by S. Mohapatra Tuesday, plenary 2B Hard Probe 2012 May 27th- June 1st

Motivation Alver, Roland etc ~400 nucleons ~20000 particles Initial geometry has multiple shape components due to fluctuations. They are transferred by flow into momentum space with global phases Φn. Additional information can be inferred from correlations of Φn!

How to measure the reaction plane correlations Two-plane correlations in , k = least common multiple of n & m Dictated by invariance under and any global rotation arXiv:1104.4740

How to measure the reaction plane correlations Two-plane correlations in , k = least common multiple of n & m Dictated by invariance under and any global rotation arXiv:1104.4740 Measure correlation between EP, followed by a simple resolution correction. Observed correlator Desired correlator arXiv: 1105.3928 PHENIX but no corrections for reso. Resolution for individual planes

Two-plane correlators Sensitivity limit is set by the raw signal (n<=6) and the values of Res{} List of two-plane correlators:

Two-plane correlators Sensitivity limit is set by the raw signal (n<=6) and the values of Res{} List of two-plane correlators: Introduce notation Can generalize into multi-plane correlations Variable: satisfying arXiv:1104.4740 arXiv:1203.5095 1205.3585

Three-plane correlators “2-3-5” “2-4-6” “2-3-4” Constructed as linear combination of two-plane correlators, for example: These correlators has decent resolution Reflects correlation of two Φn relative to the third angle

Expectations from Glauber Model Plane directions in configuration space Expected to be strongly modified by medium evolution in the final state arXiv:1011.1853, 1203.5095 1205.3585

ATLAS detectors for Event Plane: Ψn 9 |η|<4.9 ECal+FCal Divide into subevents with flexible η ranges!

ATLAS detectors for Event Plane: Ψn 10 |η|<4.9 ECal+FCal Tracks |η|<2.5 Inner detector Divide into subevents with flexible η ranges!

Obtaining the event plane correlations So just combine into one measurement A & C are symmetric so only 3 combined measurements: Type 1,2,3 Gap is required to remove autocorrelation, more important for Res. Event-mixing to check acceptance effect (planes taken from different events)

Observed two-plane correlation signal 4(Ψ2-Ψ4) 6(Ψ2-Ψ3) 6(Ψ2-Ψ6) 10(Ψ2-Ψ5) 12(Ψ3-Ψ4) 6(Ψ3-Ψ6) Significant correlations beyond detector systematics

Correlation between Φ2 and Φ3: “2-3” corr Observed correlation Combined Res Corrected result Small observed signal, good resolution small corrected signal (<0.02)

Compare with ALICE Overall magnitudes are similar, but our data show slight increase towards peripheral collisions.

Correlation between Φ2 and Φ4: “2-4” corr Coefficients decrease slowly with j, imply a narrow correlation. Φ2 and Φ4 correlation due to average geometry? Note: lowest-order coefficient is the projection of v4 onto Ψ2 plane e.g. arXiv:1205.5761

Correlation of Φ2 or Φ3 with Φ6 Φ2 and Φ3 weakly correlated, but both strongly correlated with Φ6. They show opposite centrality dependence Φ2 Φ6 correlation may due to average geometry, but Φ3 Φ6 correlation? v6 dominated by non-linear contribution: v23, v32 ? Different from Glauber model Teaney and Yan

Φ3 vs Φ4 and Φ2 vs Φ5 correlations are weak (< few %)

Observed three-plane correlation signal Significant correlations signals observed

Three-plane correlation results Rich centrality dependence patterns are observed

Deriving the sine and cosine product Comment on the bottom right panel

Summary We measured correlations between two and three reaction planes Significant correlations are observed for Correlation is very small but nonzero for Correlation is negative for Some correlators qualitatively similar to Glauber model, others do not Non-linear response of the medium to initial fluctuations i.e. correlations can be generated dynamically via hydrodynamic evolution? This measurement provides new constraints for models. arXiv:1104.0650

Cross-checks: two-plane correlations Despite different acceptance and detector technology (EM energy vs charged tracks), results are consistent

Cross-checks: three-plane correlations

arXiv:1205.5761

From observed to final signal:cos (2Φ2+3Φ3-5Φ5) Raw signal Combined reso Corrected signal Do each of the three types of combination separately and then combine The three types are consistent!

Selection of correlation observables Can generalize into multi-plane correlations Sensitivity limit is set by the resolution Res{} χn, thus Res{}, decreases fast with n Decrease slower with j, especially if χn is large Introduce notation arXiv: 1205.3585