Transcript Document

Event-by-event Fluctuation & Phase Transition
OUTLINE
critical
point
• Motivation
• Fluctuation measures:
• <pT> fluctuation
Tapan K. Nayak
CERN & VECC
Strangeness in Quark Matter
UCLA
March 28, 2006
• Multiplicity fluctuation
• Particle ratio, strangeness
• Balance functions
• Net charge fluctuation
• Moments of net charge
• DCC
• Long range correlations
• Near term activities
• at RHIC
• at LHC
• Summary
Event-by-event fluctuation and phase transition
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QCD phase diagram
Stephanov, Rajagopal & Shuryak PRL 81 (1998)
Early universe
quark-gluon plasma
Temperature
Tc
critical point ?
hadron gas
colour
superconductor
nucleon gas
nuclei
CFL
vacuum
r0
• Phase transition/Latent heat
 Supercooling
 QGP droplet formation
 <pT>, Multiplicity fluctuations
 Baryon-strangeness correlations
 Moments of strangeness, baryon
number and net charge distributions
- (recent calculations by EjiriKarsch-Redlich, Gavai-Gupta
and Koch-Majumdar-Randrup)
• Location of the critical point
 detailed study of particle ratio and
fluctuations
Neutron stars
baryon density
At the CRITICAL POINT:
singularities in thermodynamical observables
• Chiral symmetry restoration
 formation of DCC
 charge-neutral fluctuations
=> LARGE EbyE FLUCTUATIONS
Event-by-event fluctuation and phase transition
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Lattice predictions
Points for discussion:
• Location of the Critical point
• Theoretical expectations
Karsch et al.
Gavai, Gupta hep-lat/0412035
Fodor, Katz JHEP 0404 (2004) 050
CRITICAL END POINT
• Fluctuation measures
• Fluctuation sources (statistical+dynamic)
geometrical:
 impact parameter
 number of participants
 detector Acceptance (y, pT)
 energy, momentum, charge conservation
 anisotropic flow
 Bose-Einstein correlation
 resonance decays
 jets and mini-jets
 formation of DCC
 color collective phenomena ….

• Role of strangeness
• Dedicated measurements?
Lattice calculations have not yet
converged on the location of Critical
Point. The best guess so far: around
c.m. energy of 5-20 GeV/nucleon.
From lattice: TC ~ 170 15 MeV
eC ~ 0.7-1.5 GeV/fm3
Event-by-event fluctuation and phase transition
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Central Pb+Pb
√s = 17.2 GeV
<pT> fluctuations
• <pT> of emitted particles is related to
the temperature of the system. EbyE
fluctuations of <pT> is sensitive to
temperature fluctuations predicted for
QCD phase transition.
• non-statistical (dynamical) part of
the <pT> fluctuation provides valuable
information regarding:
• critical point of phase transition
• droplet formation
• Formation of DCC
charged hadrons
y>4.0
NA49, Phys Lett B459 (1999) 679
Event-by-event
<pT> compared to
stochastic
reference (mixed
events)
data
mixed
events
STAR: Phys. Rev. C 72 (2005) 044902
• Can be measured experimentally
with high precision.
The following are used to construct
various fluctuation measures:
• pT of particle
• Mean pT of the event (<pT>)
• Mean of the <pT> distribution
Event-by-event fluctuation and phase transition
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<pT> fluctuations: centrality dependence
FpT 
CERES
H. Sako QM04
 pT
p
T
K. Perl PRC 70 (2004) 034902
,incl.
NA49
δpt,i  pt,i  pt ;
p
T
,incl.

 pT 
nucl-ex/0403037
Phys. Rev. C 72 (2005) 044902
STAR
pT2  pT
p
2 FpT
pT
N
T
M. Tannenbaum
J. Mitchell
2
Different observables
are sensitive to
different processes.
STAR sees a smooth
dependence on
collision centrality
whereas NA49 and
PHENIX see larger
fluctuations in midcentral collisions.
STAR attributes this
difference due to
effects of acceptance
and elliptic flow
(Pruneau QM05,
Voloshin Bergen05)
PHENIX
PRL 93 (04) 092301
Event-by-event fluctuation and phase transition
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<pT> fluctuations:
energy dependence
C. Pruneau QM05
<pT> fluctuations in (hf) bins
STAR: nucl-ex/0509030
Adamova et al., Nucl. Phys. A727, 97
(2003)
200 GeV
fluctuations
correlations
No Energy dependence of <pT> fluctuations
is seen from CERES & STAR data.
This study is also useful for studying
contributions from (mini)jets to fluctuations.
Event-by-event fluctuation and phase transition
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Multiplicity fluctuations
NA49: M. Rybczynski, QM2004
PRC 65 (2002) 054912
Charged
particles
Photons
Gaussians for narrow bins in centrality
Photons
w= /<N>
2
Charged
Particles
WA98: Fine bins in centrality
that fluctuation from Npart is
Photonsso
minimal.
Centrality dependence of
multiplicity fluctuations do not
show evidence of nonstatistical contribution.
However recent NA49
analysis of scaled variance
show non-statistical
fluctuations at mid-central
collisions.
Fine bins in centrality
Event-by-event fluctuation and phase transition
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Particle ratio & fluctuations
<K->/<p>
<K+>/<p+>
Particle Ratio:
<K/p has an increasing
trend with energy,
whereas a horn structure
seen in <K+/ p+>.
2data - 2mix = 2dynamic
J. Phys. G30 (2004) S1381
dyn
M. Gazdzicki QM04
C. Roland (NA49)
SQM2004
Fluctuation in Ratio:
• K/p fluctuations are
large at low beam
energy & decrease with
increasing energy.
• p/p fluctuations are
negative, indicating a
strong contribution from
resonance decays.
Event-by-event fluctuation and phase transition
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K/p fluctuation in STAR
  rms/mean
dyn = sqrt(data2 – mixed2)
Supriya Das: SQM’06 Symposium
 dyn,K p 
N K N K  1
NK
2

Np Np  1
Np
2
2
N K Np
NK
Np
Fluctuation in K/p decreases with increasing energy till the top SPS energy
and remains flat above it. The amount of fluctuation decreases with increasing
centrality and is similar for 62 GeV as well as 200GeV AuAu collisions.
Event-by-event fluctuation and phase transition
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Balance functions
Z=0
• Bass-Danielewicz-Pratt, PRL 85, 2000
• D. Drijard et al, NP B(155), 1979
Opposite charged particles are
created at the same location of
space–time.
Charge–anticharge particles
created earlier (early stage
hadronization) get further
separated in rapidity.
Particle pairs that were
created later (late stage
hadronization) are correlated
at small Δy.
The Balance Function
quantifies the degree of this
separation and relates it with
the time of hadronization.
Early Hadronization
 Large h
Late Hadronization
 Small h
1 N (y)  N (y) N (y)  N (y) 
B(y)   


2
N
N

Event-by-event fluctuation and phase transition
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Balance functions: centrality & energy dependence
Gary Westfall: STAR
Panos Christakoglou: NA49
Panos Christakoglou
STAR: Au+Au@ √sNN = 130 GeV PRL 90 (2003)
NA49: Pb+Pb@ √sNN = 17.2 GeV PRC 71 (2005)
STAR data
NA49 data
NA49 shuffling
STAR shuffling
simulation
NA49 data
 h shuffling  h
W 

h shuffling

STAR data
central
peripheral
DATA show a strong centrality
dependence of balance function width.
data

 100%


W is a normalized measure of the
time of hadronization with respect
to uncorrelated data sample.
This is consistent with delayed
hadronization at RHIC compared to
SPS energies.
Event-by-event fluctuation and phase transition
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Balance functions for identified particles
Bass-Danielewicz-Pratt, PRL 85, 2000
and Gary Westfall, J.Phys.G30, S345-S349 (2004)
Heavier particles are characterized
by narrower bf distributions:
2T

m
• The balance function width for pions
get narrower with increasing centrality,
remains constant for kaons.
• HIJING reproduces results for kaons,
but not for pions.
STAR Preliminary
• The ratio of widths of pions to kaons is
consistent with delayed hadronization
picture.
pions
y
y
pions
 1.3-1.4
1.31
y
Panos Christakoglou in ALICE PPR
p
kaons
kaons
ALICE
simulation
showing BF
widths of
p,K,p
K
p
Mass (GeV)
Event-by-event fluctuation and phase transition
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Net charge fluctuations
confined:
few d.o.f.
• Prediction: A drastic decrease in the EbyE
fluctuations of net charge in local phase space
regions in the deconfined QGP phase compared
to that of the confined case hadronic gas.
QGP:4 and pion gas: 1-2
Jeon, Koch: PRL (2000) 2076
Asakawa, Heinz & Muller: PRL (2000) 2072
deconfined:
many d.o.f.
Charged multiplicity: nch = n+ + n–
Net charge:
Q = n + - n–
Charge ratio:
R = n + / n-
(1) v(Q)  Var(Q)/<nch>
(for stochastic emission, v(Q) = 1)
(2) v(R)  Var(R) * <nch>
(for stochastic emission, v(R) = 4)
(3) (Q)
• Evolution of fluctuation
Shuryak & Stephanov: PR C63 (2001) 064903
Heiselberg & Jackson: PR C63 (2001) 064904
Mohanty, Alam & TN: PR C67 (2003) 024904
4 dynamic
 ,dyn      ,stat
(5) Moments of Net charge
distributions
Event-by-event fluctuation and phase transition
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Net charge fluctuation: energy dependence
J. Mitchell, QM’04
STAR: Au+Au
Preliminary
nucl-ex/0401016
 ,dyn      ,stat
peripheral
 dyn

central
C. Pruneau
QM05
• Net charge fluctuations measured by PHENIX &
NA49 are consistent with independent emission.
STAR: 5% Central Au+Au
PHENIX |h|<0.35, f=p/2
CERES 2.0< h <2.9
• Net charge fluctuations measured by STAR are
close to the quark coalescence model of Bialas.
• Fluctuations are larger at SPS compared to RHIC,
but remain constant over a large range of energy.
Event-by-event fluctuation and phase transition
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Moments of net charge distributions
Calculation of Non-linear susceptibilities (higher order
derivatives of pressure with respect to chemical potentials):
Lattice calculations
•Ejiri, Karsch and Redlich: hep-ph/0510126
•Gavai, Gupta: hep-lat/0510044
4th moment
2nd moment
6th moment
(similar to kurtosis)
•Net charge
•Isospin
•Strangeness
=> Interesting structure close to T=TC
Is it possible to make precise measurement of
higher moments of net charge?
• bins in centrality
• bins in pT
Event-by-event fluctuation and phase transition
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Q(net charge) distributions
Q distributions for AuAu 200GeV at 4
different centralities and 6 bins in pT
MEAN of Q distributions
<Q>
low pT
high pT
<Q>/Npart
Q (net charge)
Moments of Q distributions have been analyzed.
<Q>/Npart is independent of centrality.
Event-by-event fluctuation and phase transition
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Variance and kurtosis of net charge distributions
(Q) with pT binned
AuAu 200GeV
Kurtosis
(4th moment)
Centrality & pT
 (Q) is low at low pT ad increases with
increase of pT. Could be an effect of more
resonance production at low pT.

First analysis of the 4th moment of net
charge distribution is performed. Detailed
comparison in terms of lattice calculations
is expected soon.
Event-by-event fluctuation and phase transition
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Formation of DCC
Bjorken, Kowalski & Taylor SLAC-pub-6109 (1993)
Review: Mohanty & Serreau Phy Rep 414 (2005)
Large fluctuations in number of
photons and charged particles
Methods of Analysis:
• Gamma-Charge correlation
• Discrete Wavelet analysis
• Power spectrum analysis
• ‘Robust’ variables
• Event shape analysis
• Sliding window method (SWM)
=> WA98 and NA49 have put upper limit
on DCC production at 3x10-3 level.
=> DCC production also shows up in other
forms including strangeness correlations.
Aggarwal, Sood, Viyogi
nucl-ex/0602019
WA98
PMD &
SPMD
PRC 67 (2003) 044901
Recent simulation for
RHIC show better
sensitivity for DCC by
using SWM with photon
and charged multiplicity:
Event-by-event fluctuation and phase transition
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Long-range multiplicity correlations
Correlation strength:
=> Study of correlations among
particles produced in different rapidity
regions.
=> The long-range correlations are
expected to be much stronger in p-A
and A-A, compared to p-p at the same
energy.
b
 N f N b    N f  N b 
 N    Nf 
2
f
2
Terence J Tarnowsky
Nuclear Dynamics,
San Diego March 2006
STAR Preliminary
•
STAR: forward region of 0.8<h<1.0
& backward of -1.0<h<-0.8.
•
Increase in correlation strength
observed for central collisions
compared to peripheral for AuAu
collisions at 200GeV.

Dbf2
D 2ff
Search for critical point at RHIC
• The QCD phase boundary is worthy of study,
including that of the tri-critical point.
• STAR experiment with the inclusion of TOF
will be the ideal place for this study.
• PHENIX will be able to carry out an extensive
program for the search of critical point.
AGS SPS
RHIC
• RHIC has an unique capability to scan the full
range from the top AGS to top RHIC energy.
• The idea is to have an energy scan from c.m.
energy of 4.6GeV to 30GeV in suitable steps
corresponding to baryon chemical potentials of
150MeV to 550MeV.
QCD Critical Point
• Fluctuation study especially with strangeness
plays a major role in the search for critical
point.
Energy Density
Event-by-event fluctuation and phase transition
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EbyE fluctuation in ALICE
Slope parameter
<pT> pions
With the large multiplicity of several tens of thousands
expected in each collision at LHC energies, EbyE
analyses of several quantities become possible. This
allows for a statistically significant global as well as
detailed microscopic measures of various quantities.
EbyE measures in ALICE:
simulation for Pb+Pb at 5.5TeV
<pT> kaons
<pT> protons
http://aliceinfo.cern.ch/
ALICE-PPR
EbyE HBT radii
Event#1
K/p
Event#2
p/p
Event#3
Event-by-event fluctuation and phase transition
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• Fluctuations of thermodynamic quantities
are fundamental to the study of phase
transition – including quark-hadron phase
transition.
• Lattice calculations suggest fluctuation
patterns in strangeness, baryon number &
net charge even at small chemical
potentials - increasing towards the critical
point.
• Exploratory study using many fluctuation
measures continues - interpretation of
results become complex because of
several competing processes which
contribute.
• Indication of large fluctuation patterns
around SPS energies.
fluctuation in the quantity
What’s done so far :
Thermodynamic quantity /
Summary
Fluctuation behavior???
Critical point???
Energy Density
What’s coming up:
• Fluctuation study will play a
major role in the search for the
critical point at RHIC.
• ALICE: detailed EbyE physics
and fluctuation to understand the
physics of bulk matter as well as
high-pT particles and jets.
• Future GSI facilities: CBM
Event-by-event fluctuation and phase transition
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