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
Gary Westfall, Quark Matter 2008 2
KK//ππ Fluctuations FluctuationsKK//ππ Fluctuations Fluctuations
Gary Westfall, Quark Matter 2008 3
NA49Preliminary
See talk by Z. Ahammedin Session X
See talk by M.Rybczynski, Session X
KK//ππ Fluctuations FluctuationsKK//ππ Fluctuations Fluctuations
Gary Westfall, Quark Matter 2008 4
See talk by Z. Ahammedin Session X
TorrieriQM06
KK//ππ Fluctuations FluctuationsScaling with Scaling with dNdN//dηdηKK//ππ Fluctuations Fluctuations
Scaling with Scaling with dNdN//dηdη
Gary Westfall, Quark Matter 2008 5
See talk by Z. Ahammedin Session X
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
Gary Westfall, Quark Matter 2008 6
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
Gary Westfall, Quark Matter 2008 7
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
Gary Westfall, Quark Matter 2008 8
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
Gary Westfall, Quark Matter 2008 11
NA49 PRC 70, 064903 (2004)
Multiplicity Fluctuations at the SPSMultiplicity Fluctuations at the SPSMultiplicity Fluctuations at the SPSMultiplicity Fluctuations at the SPS
Gary Westfall, Quark Matter 2008 12
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
Gary Westfall, Quark Matter 2008 13
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
Gary Westfall, Quark Matter 2008 14
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
Gary Westfall, Quark Matter 2008 15
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
Gary Westfall, Quark Matter 2008 16
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
Gary Westfall, Quark Matter 2008 17
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
Gary Westfall, Quark Matter 2008 18
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)
Gary Westfall, Quark Matter 2008 19
(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
Gary Westfall, Quark Matter 2008 20
M. Gazdzicki
Proposed Energy and Mass ScansProposed Energy and Mass ScansProposed Energy and Mass ScansProposed Energy and Mass Scans
Gary Westfall, Quark Matter 2008 21
Addition of TOF to STARAddition of TOF to STARAddition of TOF to STARAddition of TOF to STAR
Gary Westfall, Quark Matter 2008 22
• 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
Gary Westfall, Quark Matter 2008 23
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
Gary Westfall, Quark Matter 2008 24
Extra SlidesExtra SlidesExtra SlidesExtra Slides
Gary Westfall, Quark Matter 2008 25
Balance Function with Identified PionsBalance Function with Identified PionsBalance Function with Identified PionsBalance Function with Identified Pions
Gary Westfall, Quark Matter 2008 26
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
Gary Westfall, Quark Matter 2008 27
Jeon and PrattPRC 65, 044902 (2002)
HBTHBTHBTHBT
Gary Westfall, Quark Matter 2008 28
HBTHBTHBTHBT
Gary Westfall, Quark Matter 2008 29
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