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

2. 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!

3. 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:

4. 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:
Measure correlation between EP, followed by a simple resolution correction.
Observed correlator
Desired correlator
arXiv:
PHENIX but no corrections for reso.
Resolution for individual planes

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

6. 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:
arXiv:

7. 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

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

9. ATLAS detectors for Event Plane: Ψn9
|η|<4.9
ECal+FCal
Divide into subevents with flexible η ranges!

10. ATLAS detectors for Event Plane: Ψn10
|η|<4.9
ECal+FCal
Tracks |η|<2.5
Inner detector
Divide into subevents with flexible η ranges!

11. 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)

12. 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

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

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

15. 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:

16. 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

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

18. Observed three-plane correlation signal
Significant correlations signals observed

19. Three-plane correlation results
Rich centrality dependence patterns are observed

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

21. 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:

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

23. Cross-checks: three-plane correlations

24. arXiv:

25. 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!

26. 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: