Event by Event Fluctuations

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Event by Event Fluctuations
CERN Heavy Ion Forum May 24 2006

• Gunther Roland
• MIT

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What can we learn from fluctuations?
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
ca 1990
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Nature of the Phase Transition
Search for critical phenomena induced near phase
transition
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Nature of the Phase Transition
ca 1998
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Nature of the Phase Transition
Temperature (MeV)
Quark-Gluon Plasma
200
Phase Boundary
Hadron Gas
Atomic Nuclei
0
Plot from M. Stephanov, Correlations 05
0
1
Matter Density µB (GeV)
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Nature of the Phase Transition

• Theoretical guidance is limited
• Experimental strategy
• Search in different observables, correlate
  observables
• Fine grained exploration of µB, T space

time
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Nature of the Phase Transition

• Theoretical guidance is limited
• Experimental strategy
• Search in different observables, correlate
  observables
• Fine grained exploration of µB, T space

Experiments only see final state particles
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Nature of the Phase Transition

• Theoretical guidance is limited
• Experimental strategy
• Search in different observables, correlate
  observables
• Fine grained exploration of µB, T space

lt(X - ltXgt)2gt
Enhanced Fluctuations near Critical Point
vs
Rajagopal, Shuryak, Stephanov
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Energy Regimes and Accelerators
RHIC
SPS
Fit by Becattini et al.
AGS
central AA
SPS
AGS
RHIC
Change from baryon- to meson dominated system
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First result on ltpTgt fluctuations (1999)

• pT - simple observable (supposedly...)
• High statistical precision
• spT/ltpTgtinclt 0.1
• Sensitive to many interesting scenarios
• Critical Point
• DCC production
• Droplet formation
• Any non-statistical, momentum-localized process

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First result on ltpTgt fluctuations (1999)

• pT - simple observable (supposedly...)
• High statistical precision
• spT/ltpTgtinclt 0.1
• Sensitive to many interesting scenarios
• Critical Point
• DCC production
• Droplet formation
• Any non-statistical, momentum-localized process

s2pT,dyn s2M(pT) - s2M(pT),mixed
Dynamical Fluctuations
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Excitation Function Momentum Spectra
Compilation by NA49 Plot from Claudia Hoehne,
QM05
filled symbol particle open symbol antiparticle
The Step
- Structure in energy dependence of ltmTgt -
Reminiscent of Van Hoves T vs e prediction
(1982) - Surprisingly difficult measurement ?
Decay corrections, PID acceptance
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Excitation Function Momentum Fluctuations
Compilation by STAR STAR PRC 72 044902 (2005)
SPS CERES
The Step
RHIC STAR
AGS?
Central AA
Monotonic energy dependence over measured
range No results near step region
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Nature of the Phase Transition
ltpTgt Fluctuations
STAR
SpT
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• Is strangeness enhanced in every event?
• Can we see signs of super-cooling below Tcrit?

K/p
T
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Event-by-event fit of K/p (NA49)
One Event
Event Ensemble
ltdE/dxgt
ltdE/dxgt
log(ptot GeV)
log(ptot GeV)


Slide from Christof Roland, Correlations 05, MIT
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PbPb, 17.2 GeV NA49, PRL 86 (2001) 1965

• Dynamical fluctuations are small ( lt 5)
• Compatible with resonance gas (Jeon, Koch
  nucl-th/9906074)
• Strangeness enhancement in every event
• Chemical freeze-out at same T in every event

PhD thesis Christof Roland, 2000
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Particle Ratios
Nature of the Phase Transition
The Horn
NA49 Phys.Rev.C66054902,2002 Plot from Claudia
Hoehne, QM05
Average K/p ratio
Non-monotonic behavior at AGS/SPS boundary
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Nature of the Phase Transition
NA49, Christof Roland, QM04
STAR, Supriya Das, VI Workshop 05
The Horn
AGS?
RHIC STAR Preliminary
SPS NA49 Preliminary
Strong increase at low energy Comparison between
experiments difficult
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Nature of the Phase Transition
NA49, Christof Roland, QM04
K/p Fluctuations
p/p Fluctuations
Proton/p fluctuations negative ? Correlated
production of protons and pions
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
Monotonic vs evolution of global
fluctuations Magnitude of fluctuations
moderate Scaling of relative fluctuations Increa
se in K/p fluctuations at low vs
Equilibrium evolution? Small latent
heat? Kinetic freeze-out far from critical
point? Connection to PT/CP?
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
ca 2000
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Properties of the Medium
Net Charge/?y Fluctuations ? Charge/DoF
Flucs change from 1-2 (QGP) to 4 (Pion
Gas) Fluctuations frozen b/c charge
conservation Diffusion vs Expansion
timescale
Ratio N/N-
Jeon, Koch PRL (2000) hep-ph/0003168 Asakawa,
Heinz, Mueller PRL (2000) hep-ph/0003169
Event-by-event distribution of net charge ratio
Note Similar for net baryon number
Connection to quark number
susceptibilities Connection to Critical point
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Properties of the Medium
Net Charge Fluctuations
PHENIX PRL 89 (2002)
STAR PRC 68 (2003)
130 GeV AuAu
Ratio
? lt 0.7, 0.1 GeV/c lt pT
Stochastic Fluctuations
Charge Conservation
P130 GeV AuAu
HIJING
Quark- Coalescence
Net Charge
Bialas, 2003
Resonance Gas
QGP
Centrality
Centrality
Fluctuations agree with stochastic distributions
of Hadrons
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Net Charge Fluctuations
Quark- Coalescence
Bialas, 2003
QGP
Little (no) vs dependence of charge fluctuations
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
Quark coalescence? Property of
Hadronization? Diffusion? Bound states?
Net charge fluctuations large ( hadron
gas) Small/no vs dependence
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Forward/backward multiplicity correlations
Use variance s2C
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Forward/backward multiplicity correlations
effective cluster size 2-2.5 for 200 GeV AuAu
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Clusters in AA (and pp) collisions
effective cluster size 2-2.5 for 200 GeV AuAu
Cluster in ??,?f space via 2-particle
correlations (pythia pp _at_200 GeV, ?lt3)
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UA5 Phys.Lett.B123361,1983
Keff
PN
546 GeV
Clusters in AuAu reminiscent of results from pp
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Measuring global charge fluctuations
Clustersize ?y2
Acc. Clustersize Rapidity gap
SPS
NA49
Acc. Clustersize lt Rapidity gap
RHIC
STAR
Acc. gt Clustersize ltlt Rapidity gap
LHC
CMS
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Beyond global charge fluctuations
STAR 200 GeV pp
Pythia, 200 GeV pp, all pT , all charges
Like sign
Split sample
2-D angular correlation function
Unlike sign
Tom Trainor et al (STAR)
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Charge Dependent Correlations
STAR 200 GeV pp
Like sign
longitudinal charge ordering
gaussian
flat
subtract
Unlike sign
Charge Dependent (CD) correlations like sign
- unlike sign
Tom Trainor et al (STAR)
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Difference of like-sign and unlike-sign
2-particle correlations
?f
pp
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Difference of like-sign and unlike-sign
2-particle correlations
?f
??
pp
AuAu
STAR nucl-ex/0406035
Evolution of cluster properties/charge
correlations
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Correlations and Fluctuations, revisited
Net-charge Fluctuations
Global scaling, even though underlying
correlations change
Text
Central AA
pp
centrality ?
Net-charge correlations (c.f. Balance Function)
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
Large multiplicity fluctuations Strong change in
underlying correlation structure
Particles produced in large clusters Understand
ing of hadronization essential Collision
dynamics reflected in correlation structure
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
Some remarks on future measurements
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NA49 Horn
Strangeness Fluctuations vs vs
NA49 (Christof Roland QM04)
NA49
preliminary
Fluctuations in K/pi ratio
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Strangeness Fluctuations vs vs
Opportunity with possible low-E run at RHIC STAR
with ToF/Si-VTX upgrade is ideal place
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v2 near mid-rapidity
PHOBOS 200 GeV Statistical errors only
PHOBOS 200 GeV h
Statistical errors only
AuAu
preliminary
CuCu preliminary
Geometrical initial state eccentricity from
Glauber model
Surprisingly large flow signal in CuCu!
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Realign the coordinate system to maximize
ellipsoidal shape (a principal axis
transformation)
Participant eccentricity (versus standard
eccentricity)
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Hydro- Limit
Eccentricity Fluctuations provide additional
correlation strength Nuclear Physics!? ?
Measure v2 fluctuations
CuCu
AuAu
CuCu PHOBOS QM 2005
Participant Eccentricity provides universal
scaling Approach to equilibrium?
Low Density Limit STAR, PRC 66 034904
(2002) Voloshin, Poskanzer, PLB 474 27
(2000) Heiselberg, Levy, PRC 59 2716, (1999)
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Denes Molnar, BNL workshop June 05
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Analogy Cosmic Microwave Background
Cosmic microwave background
COBE 1992
Penzias, Wilson 1964
WMAP
?T/T 10-5
ltTgt3K
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Summary

• Rich existing data set on fluctuations
• Energy independence of global pT, charge
  fluctuations
• Energy dependence in K/p, p/p fluctuations
• limited statistical significance
• Non-trivial structure/change in charge
  correlations
• Low-vs scan at RHIC could confirm and improve
  experimental results

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Excitation Function K/p Fluctuations
Normalized by dN/dy
RHIC
AGS?
SPS
Scaling by dN/dy or (dN/dy)1/2 does not work over
full energy range
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
Look at the medium using 2-particle correlations
(untriggered) at high(er) pT
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Properties of the Medium
2-particle momentum correlations
0-5
Shape of near-side parton-fragmentation peak
evolves with centrality
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Properties of the Medium
2-particle momentum correlations
Subtract fragmentation peak to look at medium
AuAu 200 GeV 20-30
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What can we learn from fluctuations?
Nature of the phase transition?
(How) Does matter thermalize?
How is entropy produced?
Properties of the medium?
How are hadrons made?
Medium modification of pT correlation
shape Possible medium modification due to
partonic recoil
Interaction of partons with bulk medium (flow
field) Extract bulk properties (e.g. viscosity)?
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(No Transcript)
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Net Charge, and K/p Fluctuations
Instead of measuring the variance of a yield
ratio,
Study the dynamical fluctuations
Side Note
ltptgt Fluctuations