# Presentation: 004084

## 3-particle correlations: methods and results

*Marco van Leeuwen, LBL*

## Introduction

- Introduced to measure di-jets in Au+Au
- Disappearance at high-pT
- Enhancement, broadening at low, intermediate pT
- Other sources of correlations
- Flow
- Resonance decays

**2-particle azimuthal correlations in p+p, Au+Au**

**3-particle correlations**

- Relatively new activity
- Can remove two-body decays
- Flow still important

- 

- trigger

- associated

**Focus of this talk: Introduce/discuss methods**

- Present activity focuses on intermediate pT
- (mach cone vs deflected jets)
- Prospects for other measurements exist

- but will confront with data

## 2-particle correlations at intermediate pT

- 2-particle correlations at intermediate pT

**Status at QM05:**** **N.Grau, J.Jia, J. Ulery, M. Horner et al

- STAR Preliminary

- PHENIX

- Is there a ’dip’ at the away-side?

- Strong away-side broadening seen at low pT,assoc

**Need to establish jet-related origin...**

- Also note: systematic uncertainties should not be disregarded

**2.5 < p****T,trigger**** < 4.0 GeV**
**1.0 < p****T,assoc**** < 2.5 GeV**

- So far only shown for intermediate pT,trigger and low pT,assoc

- Conical emission: Mach cone? Cherenkov? Other mechanisms?

## New 2-particle results

**2.5 < p****T,trigger****< 4 GeV**

**6 < p****T,trigger****< 10 GeV**

**STAR preliminary**

**STAR preliminary**

**1 < p****T,assoc**** < 2.5 GeV**

- Poster, M. Horner

- Systematic study of intermediate pT,assoc under way

**Broadening persists to higher p****T,trigger****, but not ‘dip’**

- What happens to the away-side at intermediate pT?

## What is happening at intermediate pT?

- What is it?
- Conical emission (mach cone, cherenkov)
- kT-like effect/push from radial flow
- Problem with background/flow normalisation?

- Mach cone calculations materialising
- T. Renk and J. Ruppert, hep-ph/0509036, hep-ph/0605330

- ... but also: coalescence/recombination?

**2-particle correlations**
- Possible systematics
- pT,trigger, pT,assoc and centrality dependence
- Particle type dependence

- And detailed, honest theory evaluations/predictions

- Or give up...

**3-particle correlations**
- New avenue
- Sensitive to event-by-event structure
- Challenge: signals small, backgrounds large

## Toy model I

- Backgroundlevel

**Simple ansatz to illustrate 2- and 3-particle structures**

- Note:
- All events have one trigger
- All events are the same, no impact parameter fluctuations
- No flow

- 1D generation in 

- ‘Cone’ case

- All events same distribution:

- ‘kT’ case (deflected jets)

- Two classes of events:

- Normalisation chosen to have the same 2-particle structure

## Raw signal Ino background

- z-scale

- 1

*N**trig*

*d**2**N*

*d*12 *d*13

- 12

- 13

- 1

- 3

- 2

- Cone case

- kT case

- 12 ≈13

- (,)

- (,)

- ,  correlations can identify conical vs deflected jet emission

- In the absence of backgrounds...

- i.e. high pT,trigger and pT,assoc in Au+Au

## Toy model I, raw data

- kT case

- Cone case

- Dominant structure:
- Combinations of jet-pairs with random third particle

**Background level**

## Background terms

- +

- =

- Dominant structure in raw plots is the 2-particle structure folded with random third particles, 12

- Need to subtract 2x1 combinatorics

- First assoc particle not correlated
-  1(2) 2(1,3)

- Second assoc particle not correlated
-  1(3) 2(1,2)

- There is one more term, see later

## Toy model I, raw data

- kT case

- Cone case

- So there is a difference:
- Cone case: on-diagonal and off-diagonal are the same
- kT case: difference between on- and off-diagonal

- Difference is small:
- Need well-controlled background subtraction

## Background normalisation

- Absolute normalisation (average at                 )     Cumulant
- Phenomenological normalisation (e.g: scale background to have dips at 0)

- Signal 2

- Background 1 1
- (or mixed events)

- 3(1,2,3) – 1(1)2(2,3) – 1(2)2(1,3) – 1(3)2(1,2) + 21 1 1

## Background subtracted results

- Cone case

*k**T** *case

**ZYAM/Purdue normalisation**

**Cumulant normalisation**

- Signal seen in both schemes. Both schemes distinguish between conical emission and kT effect

- 4-peak structure for conicalemission
- 2-peak for kT-smearing

- Valleys and peaks due to different normalisation

- 4-peak/2-peak difference also visible

- Caveat: soft-soft term ignored (see next slides)

**Valley-peak strength similar: ****0.2 in both cases**

## Toy Model II

- Idea: include more dynamics

- Generate full set of , , pT from:
- Toy jet
- Simple jet spectrum
- Fragmentation from FF
- Toy cone
- Similar pT - distribution, but angle spread out to 1±0.15 radian
- Background
- Thermal spectrum, T=300 MeV

- Jet and cone distributed flat in 

- Example cone at (,)=(0,0)

- Example cone at (,)=(0,1)

- So far, only ‘cone version’ implemented

- Generation in ,  allows to study other variables

- Note: apparent depletion at =0due to fixed pT-cut

## Raw 3-particle correlation

- Qualitatively similar to Toy model I

- New feature: diagonal stripes from soft-soft

- z-scale

## Soft-soft correlations

- Jet-structure with uncorrelated triggerthermal component in model
- Resonance decays
- Flow

- Not present in model

- Possible sources scale differently with ratio fake triggers/real triggers

- No clear-cut way to subtract only unwanted terms (a la ZYAM):

- Cumulant 1 2(2,3)

- Mixed events

- Soft-soft contributions:
-   correlations of assoc particles,   no relation to the trigger

-   Use (approximate) cumulant normalisation       for both method: 1(1) 2(2,3)

- Note: cumulant scaled with Nevent/Ntrigger for per-trigger normalisation

## Result from Toy Model II

- ZYAM/Purdue method

- Results with different background normalisations very similar

- Extract signal robustly

- Cumulant method

## Flow in three-particle correlations

- J. Ulery, RHIC/AGS meeting

- Flow is dominant term in raw correlation

- Dominant terms are again 2x1and drop out to high precision

- Exercise for the reader

- Leading remaining term: v2 v2 v4

- Can be explicitly subtracted

## Experimental results: STAR

- Central Au+Au 0-12% triggered

- J. Ulery, parallel II Monday

- Data corrected for flowand 2x1 correlations

- Off-diagonal peaks indicate conical emission

- Additional structure along diagonal
- (no off-diagonal equivalent!)

- Also note:
- On-diagonal and off-diagonal peaks not same height

- First evidence of conical emission?

**Possibly**
- Need careful systematic checks (see Jason’s talk)

- If there is conical emission, it is not the only thingJet remnants along diagonal?

- 3 < pT,trigger < 4 GeV
- 1 < pT,assoc < 2 GeV

- Like to see cumulant analysis as systematic check

- ZYAM/Purdue normalisation

- Δ2

- v2 v2 v4 term subtracted

## Polar co-ordinates

- Trigger

- Associated

- Method being developed in PHENIX

- Motivation: cone ‘lives’ at constant 

- Caveat: cone not necessarilyback-to-back with trigger in 3-space

- Talk N. Ajitanand, parallel II Monday

- Combinatorialbackground

- Cone simulation

- Deflected Jet simulation

- More strength at  =0 for deflected

- =180° swamped?

## Experimental results: PHENIX

- Uncorrected, no v2 subtraction

- = 0

- Cent: 0-5%

**PHENIX *****Preliminary***

**PHENIX Acceptance**

- See N.N. Ajitanand’s talk

- 3 < pT,trigger < 4 GeV
- 1 < pT,assoc < 2 GeV

- Need careful comparison to expectations

- And/or 2x1, flow subtraction

## Summary/conclusion

- Methods promising
- Two-particle contributions overwhelming: need to subtract
- Background normalisation:
- Cumulant is unambiguous
- But may want to tune for specific observables
- Soft-soft normalisation most difficult
- First results show signs of conical emission ... but also something else

- Cross-checks/alternative approaches welcome:
- Cumulant method
- Other co-ordinates (polar angle, possibly )

## Outlook

- Possible future applications of three-particle correlations

- Explore  structure
- of away-side jet

- 12-23 correlations
- (cut on 23?)

- Different systematics, possiblyalso useful for conical emission

- Explore near-side ridgeevent-by-event

- 12-13 correlations
- (with cuts on 12, 13)

- Total 6 co-ordinates ()1, ()2 and ()3

**Make useful combinations. Need to cut on others**

- So far only speculation. Needs study

**3-particle correlations provide new angle on variety of questions**

- versus

- 

- Thanks to: F. Wang, J. Ulery, S. Voloshin, C.Pruneau, N. Ajitanand

## Extra slides

## Change from QM

- Mesh pattern removed.
- Increased statistics by about a factor of 1.5.
- Analysis improvements.
- Qualitatively similar structure.
- Not much signal at 1 radian from π, but interesting structure maybe present beyond 1 along the off diagonal in both.

- φ2=φ2-φtrig

- Au+Au 0-10%

- Δ1

- Δ2

**Slide taken from J. Ulery, RHIC/AGS User’s Meeting**

## Quantitatively...

- Large systematic fluctuation due to mesh.
- Mesh effect did not completely cancel out in differences between different areas; this was not taken in the systematics.

- φ2=φ2-φtrig

- Au+Au 0-10%

- Δ1

- Δ2

- center – deflected =
-    0.3 ± 0.3 (stat) ± 0.4 (syst)
- center – cone =
-    2.6 ± 0.3 (stat) ± 0.8 (syst)

- center – deflected =
-    -0.04 ± 0.06 (stat) ± 0.09 (syst)
- center – cone =
-    0.13± 0.06 (stat) ± 0.05 (syst)

**Slide taken from J. Ulery, RHIC/AGS User’s Meeting**