# Presentation: 376445

##  Three Particle Correlations

- N. N.  Ajitanand
- Nuclear Chemistry, SUNY Stony Brook
- 27 May 2008
- AGS-RHIC Workshop 2008

-  Three Particle Correlations

## Outline 

- Outline

- Formation of the QGP medium
- Probing the QGP medium
- Medium modification of jets
- Experimental 3-particle studies
- Conclusions and Outlook

## Energy density required for QGP formation 

***Energy density required for QGP formation ***

*** ******Necessary to create  ******ε****** > 0.6 – 1.0 GeV/fm******3 ****** in heavy ion collisions***

## Achieved Energy Density is Well Above the

***Achieved Energy Density is Well Above the***
*** ******Predicted Value for the Phase Transition***

***200 GeV Au+Au  Collisions studies at RHIC!***

## Conclusion : Strongly Interacting State of   matter produced in 200 GeV Au + Au  

*Quark scaling of v2 indicates *
*flow sets in at the partonic stage*

-  hydro-like flow observed

**Conclusion : Strongly Interacting State of   matter produced in 200 GeV Au + Au  **
**called   sQGP**

## Jets are a natural probe of the Medium

_**Jets are a natural probe of the Medium**_

**In relatvistic heavy ion collisions hard parton-parton processes occur early**

**Scattered partons propagate through the medium radiating gluons and interacting with partons of the medium**

**Finally partons fragment, (possibly) outside the medium**

## Associated low pT particle

- Jet Study via 2-particle azimuthal  Correlations

- High pT particle

**Correlation Function**

- N(pT)

## It is necessary to decompose the correlation function to obtain 

**It is **_**necessary**_** to decompose the correlation function to obtain **
**the Jet Function!**

**H(v2)**
**Obtain **
**using BBC Reaction Plane**
**Large ****η**** gap minimizes non-flow effects**

***  ******Correlation***

*** ******Jet***

**vary a0 till condition is satisfied**

***Ajitanand et.al. ******Phys. Rev. C 72, 011902 (2005)***** **** **

## Simulation Test of Jet Recovery using ZYAM

**Simulation Test of Jet Recovery using ZYAM**

**Di-jet faithfully recovered**

**Normal Jet Shape**

**abnormal Jet Shape**

**Line : Input Jet Correlation Squares : Extracted Jet  Correlation**

**Caution : Jet recovery very sensitive to v2  **
**Need to assess error in v2 estimation very carefully**

**Open symbols : v2 **
**Closed symbols : 0.95 v2**** **

## 200 GeV Au+Au  : Hadron Jet Shapes

**200 GeV Au+Au  : Hadron Jet Shapes**

**Jet-pair distributions resulting from decomposition show**
**significant modification**

**PRL 97, 052301 (2006)**

**200 GeV Au+Au**
**1<pT<2.5**
**vs**
**2.5<pT<4.0**

## Medium  modification of jets : Expectations

**Medium  modification of jets : Expectations**

**Mach-cone in HIC first introduced in 1970s by Hofmann, Stöcker, Heinz, Scheid and Greiner.**
**Away-side structure in 2-particle correlations renewed interest.**
**Conical emission**** is a possible explanation for shape:**
**Mach-cone shock waves**
**Čerenkov gluon radiation**
**Other explanations suggested:**
**Large angle gluon radiation**
**Defected jets**
**deflected by radial flow**
**path-length dependent energy loss**

## Conical Emission

**Conical Emission**

**Mach-cone**:
- Shock waves excited by a supersonic parton.
- Can be produced in different theories:
**Hydrodynamics**
- H. Stöcker et al. (Nucl.Phys.A750:121,2005)
- J. Casalderra-Solana et. al. (Nucl.Phys.A774:577,2006)
- T. Renk & J. Ruppert (Phys.Rev.C73:011901,(2006))
**Colored plasma**
- J. Ruppert & B. Müller (Phys.Lett.B618:123,2005)
**AdS/CFT**
- S. Gubser, S. Pufu, A. Yarom.  (arXiv:0706.4307v1, 2007)
**Čerenkov Gluon Radiation**:
- Radiation of gluons by a superluminal parton.
- I.M. Dremin (Nucl. Phys. A750: 233, 2006)
- V. Koch et. al. (Phys. ReV. Lett. 96, 172302, 2006)
- A. Majumdar Hard Probes 2006
- Parton Cascade
- G. L. Ma et. al. (Phys. Lett. B647, 122, 2007)

**Notes:**
add references

## Mach-Cone

- Mach angle depends on speed of sound in medium
- T dependent
- Angle independent of associated pT.

- PNJL Model

**Mikherjee, Mustafa, Ray**
**Phys. Rev. D75 (2007) 094015 **

## Mach-Cone and Flow

**Renk, Ruppert, **
**Phys. Rev. C76, 014908 (2007)**

**Renk, Ruppert,**
**Phys. Lett. B646 19 (2007)**

- Rapidity distribution and longitudinal flow affects the observed angle and width.
- Transverse flow affects shape of 3-particle correlation.
- signal at ~1 GeV/c ~9x larger if flow and shockwave aligned than if perpendicular.

## Hydrodynamic Mach-Cone

**Hydrodynamic Mach-Cone**

- Energy radiated from the parton is deposited in collective hydrodynamic modes.
- Strength of the correlation dependent on source term which is not fundamentally derived.
- Similar to jet creating a sonic boom in air.

- Cloud formed by a plane
-  breaking the sound barrier.

**Betz QM08**

## Colored Modes

**Colored Modes**

- QCD analog of charged particle in plasma from QED.
- Mach-cone is longitudinal modes excited in quantum plasma by a supersonic parton.
- Colored sound.
- Černkov gluon radiation is the transverse mode excited by superluminal parton in the plasma.

**J. Ruppert & B. Müller, **
**Phys. Lett. B618 (2005) 123**

- Parallel

- Perpendicular

- Current Density

## Ads/CFT

**Ads/CFT**

- Mach cone with strong diffusion wake from heavy quarks.
- Mach cone with no diffusion wake for quarkonium.
- No need to add a source term.
- Done in infinitely massive limit.

- Poynting Vector

- shock-wave

- diffusion wake

- Bullet at 2.45cs

**Gubser, Pufu, Yarom **
**arXiv:0706.4307v1 (2007)**

## Čerenkov Gluon Radiation

**Čerenkov Gluon Radiation**

- Gluons radiated by superluminal partons.
- Angle is dependent on emitted momentum.

**Koch, Majumder, Wang**
**PRL 96 172302 (2006)**

- Čerenkov angle vs
- emitted particle momentum

- p (GeV/c)

## Experimental 3-particle Studies from STAR and PHENIX

## STAR 3- Particle Cumulant Analysis 

**STAR 3- Particle Cumulant Analysis **

- Measure 1-, 2-, and 3-Particle Densities

- 3-particle densities = superpositions of ***truly*** correlated 3-particles, and combinatorial components.

**Cumulant technique**:

- Simple Definition  Model Independent.

**PROs**

**CONs**

- Not positive definite Interpretation perhaps difficult.

**Pruneau, nucl-ex/0608002**

## Measurement of 3-Particle Cumulant

- Clear evidence for ***finite 3-Part Correlations***
- Observation of flow like and jet like structures.
- Evidence for v2v2v4 contributions

## STAR 3- Particle Azimuthal Correlation Analysis

**STAR 3- Particle Azimuthal Correlation Analysis**

- Jet+Flow Subtraction :

- Intuitive in concept Simple interpretation in principle.

- Model Dependent v2 and normalization factors systematics

** ****Ulery  QM08**

**PROs**

**CONs**

## Azimuthal 3-Particle Correlations

**Azimuthal 3-Particle Correlations**

## STAR Results

**STAR Results**

*pp*

- d+Au

- Cu+Cu 0-10%

- Au+Au 50-80%

- Au+Au 10-30%

- Au+Au 0-12%

##     ZDC 0-12% Au+Au shows significant peaks in off-diagonal projection at: 
	1.38 ± 0.02 (stat.) ± 0.06 (sys.) radians

-     ZDC 0-12% Au+Au shows significant peaks in off-diagonal projection at:
- 	**1.38 ± 0.02 (stat.) ± 0.06 (sys.)** radians

**STAR Projections and Angle**

## STAR Associated PT Dependence

**STAR Associated P****T**** Dependence**

- No significant pT dependence of observed emission angle.
- Consistent with Mach-cone
- Inconsistent with simple Čerenkov radiation

- 0.5<pTAssoc<0.75

- 1<pTAssoc<1.5

- 2<pTAssoc<3

## STAR Summary/Conclusions

**Cumulant Method**
**Unambiguous evidence for three particle correlations**.
- Clear indication of away-side elongated peak.
- No evidence for Cone signal given flow backgrounds
**Jet-Flow Background Method**
**Model Dependent Analysis**
- Cone amplitude sensitive to magnitude v2 and details of the model.** **
**Observe Structures Consistent with Conical emission** in central collisions

## PHENIX  3-particle Analysis

**PHENIX  3-particle Analysis**

- Polar coordinate system relative to trigger particle direction.
- Natural coordinate system if jets are back-to-back in both  and .
- * is angle from trigger.
- * the angle between the two associated particles projected onto plane defined by trigger.
- 2.5<pTTrig<4 GeV/c
- 1<pTAssoc<2.5 GeV/c

- Near Side

- Away Side

- Au+Au 10-20 %

**Ajitanand QM08,HP06, IWCF’06**

## Simulations

**Simulations**

-     Simulations with  PHENIX acceptance.

- Simulated
- Deflected jet

- *

- *

- Azimuthal Sections

## PHENIX SIM

**Test of Harmonic removal**

** ****Jet+Harmonic**

**ZYAM gives good Jet Recovery**

** ****Input Jet**** **

** ****Harmonic removed**** **

**Jet Correlation = Total Correlation – a0*(Harmonic Correlation)**
**“****ao”  is adjusted till ****Jet Correlation surface**** goes to zero at its minimum (ZYAM )**

## True 3P correlations successfully recovered 

**True 3P correlations successfully recovered **

** ****(2+1) correlations obtained taking 2P in event 1 and 1P from event 2  **
**For data relative amounts of soft-soft and hard-soft correlations set by relative strengths of observed 2P correlations**

**True 3P Correlations absent **

**True 3P Correlations present**

**Test of (2+1) removal **

**(2+1) processes successfully removed **

## PHENIX Preliminary

**3-particle Correlations without harmonic removal**

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

- Data

- Most central  shows jet dominated landscape with strong away side modification

- 10-20 %

- 0-5 %

- 5-10 %

- 20-40 %

- 40-60 %

- 60-90 %

## Total 3-particle Jet Correlation 

**Total 3-particle Jet Correlation**

**Strong away side modification in both total and true 3P Jet Correlations**

**Radial section**** **

**True 3-particle Jet Correlation**

- Jet Correlations

## Data

- _Data_

- Simulated
- Deflected jet

**The data validates the presence of a  Mach Cone away-side jet but does not rule out contributions from other topologies.**

**Total 3P jet correlations**

**True 3P jet correlations**

- Azimuthal Sections

## 0-5 %

**0-5 %**

**5-10 %**

**10-20 %**

**20-40 %**

**40-60 %**

**60-90 %**

**200 GeV Au+Au Run 7 PHENIX *****Preliminary***

**Run 7  3-particle Correlations  (~ 5 times Run 4 statistics)  **

**Analysis in progress**

## Conclusions

**Conclusions**

- Broadened and double-peaked away-side structure in 2-particle correlations.
- Can be explained by conical emission or other physics mechanisms.
- Mach-cone
- Čerenkov gluon radion
- PHENIX
- shape consistent with Mach-cone simulation.
- STAR
- Evidence of conical emission of correlated hadrons at an observed angle of 1.38 radians
- pT independence of the angle suggests Mach-cone emission
- With the aid of theoretical models the extracted angle my provide information on the speed of sound of the medium and the equation of state.

## Outlook

**Outlook**

- New data and detectors will allow for:
- Higher statistics will allow for systematic studies of both trigger (RP aligned) and associated pT
- Helped by increased jet production at LHC
- Jet reconstruction may reveal Mach cone in favorable cases
- Identified particle results:
- Mach-cone emission should have a mass dependence in correlation strength
- Full azimuthal TOF detectors ALICE and STAR (upgrade) will provide good PID for these analyses.
- Possible change in angle between SPS, RHIC, and LHC.
- Different initial temperatures
- Many theoretical investigations have been carried out.
- More work is needed to understand what the data tells us about cs and EOS.