Experimental Results for Fluctuations And Correlations as a Signature of QCD Phase Transitions in Heavy Ion Collisions Gary Westfall Michigan State University,

Experimental Results for Experimental Results for Fluctuations And Correlations as a Fluctuations And Correlations as a

Signature of QCD Phase Signature of QCD Phase Transitions in Heavy Ion CollisionsTransitions in Heavy Ion Collisions

Experimental Results for Experimental Results for Fluctuations And Correlations as a Fluctuations And Correlations as a

Signature of QCD Phase Signature of QCD Phase Transitions in Heavy Ion CollisionsTransitions in Heavy Ion Collisions

Gary Westfall

Michigan State University, USA

Gary Westfall, Quark Matter 2008 1

Correlations and FluctuationsCorrelations and FluctuationsCorrelations and FluctuationsCorrelations and Fluctuations• Depend on previous talk for theoretical justification• Look for discontinuities or changes in experimental

results for correlations and fluctuations as a function of incident energy• K/π Fluctuations• Balance Function• Net Charge Fluctuations• Multiplicity Fluctuations - several approaches

• pt Correlations

• RHIC Energy Scan• SPS Program


KK//ππ Fluctuations FluctuationsKK//ππ Fluctuations Fluctuations


NA49Preliminary

See talk by Z. Ahammedin Session X

See talk by M.Rybczynski, Session X

KK//ππ Fluctuations FluctuationsKK//ππ Fluctuations Fluctuations



TorrieriQM06

KK//ππ Fluctuations FluctuationsScaling with Scaling with dNdN//dηdηKK//ππ Fluctuations Fluctuations

Scaling with Scaling with dNdN//dηdη



Au+Au statistical errorsCu+Cu statistical+systematic errors

Balance FunctionBalance FunctionBalance FunctionBalance Function• Charge fluctuations can be studied with several

different variables that can be expressed in terms of each other

• We choose to illustrate charge fluctuations using the balance function


B(Δη)=12

N+−(Δη)−N++(Δη)N+

+N−+(Δη)−N−−(Δη)

N−

⎧⎨⎩

⎫⎬⎭

e.g. N+−(Δη) is histogram of Δη =η2 −η1 for + with -

e.g. N+ is the number of positive particles

Bass, Danielewicz, Pratt PRL 85 2689 (2000)

Balance FunctionBalance FunctionBalance FunctionBalance Function


NA49Phys. Rev. C 76, 024914 2007

Balance functions forPb+Pb at sNN

½ =6.3 to 17.3 GeV

Balance functions forAu+Au at sNN

½ =20 to 200 GeV

Data

Shuffled

Au+Au 200 GeV

STAR, QM 02, QM 04

Balance FunctionBalance FunctionBalance FunctionBalance Function


NA49

NA49Phys. Rev. C 76, 024914 2007

W =100 ⋅ Δη

shuffled− Δη

data( )Δη

shuffled

Large W means narrow balance function

Net Charge Fluctuations at RHICNet Charge Fluctuations at RHICNet Charge Fluctuations at RHICNet Charge Fluctuations at RHIC

Gary Westfall, Quark Matter 2008 9See poster by M. Sharma

Net Charge Fluctuations at RHICNet Charge Fluctuations at RHICNet Charge Fluctuations at RHICNet Charge Fluctuations at RHIC

Gary Westfall, Quark Matter 2008 10See poster by M. Sharma

The slope in p+p, Cu+Cu and Au+Au depends on the correlation length: the shorter the correlation, the larger the slope

The distributions indicate that the correlation length is shorter for central collisions and for larger systems, in agreement with the observed reduction of

the width of the balance function

ν+−,dyn η ' < η

ν+−,dyn η ' <1

Net Charge Fluctuations at the SPSNet Charge Fluctuations at the SPSNet Charge Fluctuations at the SPSNet Charge Fluctuations at the SPS


NA49 PRC 70, 064903 (2004)

Multiplicity Fluctuations at the SPSMultiplicity Fluctuations at the SPSMultiplicity Fluctuations at the SPSMultiplicity Fluctuations at the SPS


ω =Var n( )

n=

n2 − n2

n

NA49, 0712.321 [nucl-ex] 2007

1% most centralScaled to 4π

Multiplicity Fluctuations at RHICMultiplicity Fluctuations at RHICMultiplicity Fluctuations at RHICMultiplicity Fluctuations at RHIC


C2 η1,η2( ) =ρ2 η1,η2( )−ρ1 η1( )ρ1 η2( )

C2 η1,η2( )ρ1

2 =αe−δη/ξ + β

PHENIX, PRC 76, 034903 (2007)

k δη( ) =1

2αξ / δη + β

Multiplicity Fluctuations at RHICMultiplicity Fluctuations at RHICMultiplicity Fluctuations at RHICMultiplicity Fluctuations at RHIC


PHENIX, PRC 76, 034903 (2007)See talk by K. Homma in Session X

αξ related to susceptibility of

density fluctuations

in the long-wavelength limit

non-monotonic behavior

observed a a function of

centrality (Npart : 90)

Forward/Backward Multiplicity CorrelationsForward/Backward Multiplicity CorrelationsForward/Backward Multiplicity CorrelationsForward/Backward Multiplicity Correlations


See talk by B. Srivistava Session XIXSee poster 220 by T. Tarnowsky

Energy Dependence of F/B Multiplicity FluctuationsEnergy Dependence of F/B Multiplicity FluctuationsEnergy Dependence of F/B Multiplicity FluctuationsEnergy Dependence of F/B Multiplicity Fluctuations


b =nfnb − nf nb

nf2 − nf

2 =Dbf

2

Dff2

Central Au+Au 0 – 10%

200 GeV62.4 GeV

Long range correlations are an indicator of multiple elementaryelastic collisions

Long range correlations decreases as the incident energy is decreasedSTAR preliminary

See talk by B. Srivistava Session XIXSee poster 220 by T. Tarnowsky

pptt Fluctuations Fluctuationspptt Fluctuations Fluctuations


Δpt ,i Δpt ,j =1

Nevent

Ck

Nk Nk −1( )k =1

Nevent

∑

Ck = pt ,i − pt( ) pt ,j − pt( )j =1,i ≠ j

Nk

∑i =1

Nk

∑

Σpt =Δpt ,i Δpt ,j

pt

Adamova et al., CERESMiskowiec for NA49, CPOD 2007

pptt Fluctuations Fluctuationspptt Fluctuations Fluctuations


Adamova et al., CERES

Calculate <Δpt,i,Δpt,j> for pairs within a given range of Δϕ and multiply by dN/dη

The region of 30° < Δϕ < 60° is free from effect such as HBT and jets and may be a fruitful region to search for discontinuities as a function of incident energy

RHIC Energy ScanRHIC Energy ScanRHIC Energy ScanRHIC Energy Scan• Energies as low as sNN

1/2 = 4.5 GeV (10 AGeV fixed target)


(GeV) (MeV)

Min Bias BBC Rate(Hz)

Days/Mevents

NumberOf Events

Number ofbeam days

4.6 570 5(5) 9(4.6) 5 45(23+2)

6.3 470 7(50) 4(0.5) 5 20(3+1)

7.6 410 13(150) 2(0.2) 5 10(1+1)

8.8 380 20(300) 1.5(<1) 5(>5) 7.5(1+1)

12 300 54(1000) 0.5(<1) 5(>50) 2.5(1+1)

18 220 >100(>1000) 0.25(<1) 5(>50) 1.5(1+1)

28 150 >100(>1000) 0.25(<1) 5(>50) 1.5(1+2)

sNN μB106

T. Satogota, RHIC

NA 49/61 Future ProgramNA 49/61 Future ProgramNA 49/61 Future ProgramNA 49/61 Future Program


M. Gazdzicki

Proposed Energy and Mass ScansProposed Energy and Mass ScansProposed Energy and Mass ScansProposed Energy and Mass Scans


Addition of TOF to STARAddition of TOF to STARAddition of TOF to STARAddition of TOF to STAR


• STAR will add TOF for Run 10

• The TOF will provide excellent particle identification for π, K, and p for a large fraction of the measured particles event-by-event

• Improved K/π fluctuation measurements

• Improved balance functions with identified π, K, and p

• See talk by G. Odyniec, session XXIV

P. Sorensen Charged pions and kaons0.2 < pt < 0.6 GeV/c

Conclusions 1Conclusions 1Conclusions 1Conclusions 1

• We have experimental results for correlations and fluctuations covering incident energies where one might expect effects from the QCD critical point and we have some hints in the

• However, the results are not conclusive• In particular, we have several different variables,

acceptances, and interpretations that need to be unified

• We need to measure correlation fluctuation variables over the broadest range in incident energy and system size


Conclusions 2Conclusions 2Conclusions 2Conclusions 2

• The SPS and RHIC scans will provide an excellent opportunity to study the QCD critical point• SPS system/energy scan will add a large number of

points in T/μB space in the search for the critical point

• We also look forward to correlations and fluctuations related to the QCD phase transition at GSI/FAIR


Extra SlidesExtra SlidesExtra SlidesExtra Slides


Balance Function with Identified PionsBalance Function with Identified PionsBalance Function with Identified PionsBalance Function with Identified Pions


Charged pion pairs0.2 < pt < 0.6 GeV/c

• The excellent particle identification for π, K, and p for a large fraction of the measured particles event-by-event will allow new kinds of event-by-event measurements such as the balance function with identified particles

Relation between Net Charge Relation between Net Charge Fluctuations and the Balance FunctionFluctuations and the Balance Function

Relation between Net Charge Relation between Net Charge Fluctuations and the Balance FunctionFluctuations and the Balance Function


Jeon and PrattPRC 65, 044902 (2002)

HBTHBTHBTHBT


HBTHBTHBTHBT


Documents

Experimental Results for Fluctuations And Correlations as a Signature of QCD Phase Transitions in Heavy Ion Collisions Gary Westfall Michigan State University,