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Event-by-event fluctuation and phase transition 1
OUTLINE
• Motivation• Fluctuation measures:
• <pT> fluctuation• 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
Tapan K. Nayak
CERN & VECC
Strangeness in Quark MatterUCLA
March 28, 2006
Event-by-event Fluctuation & Phase Transition
critical point
Event-by-event fluctuation and phase transition 2
QCD phase diagramStephanov, Rajagopal & Shuryak PRL 81 (1998)
At the CRITICAL POINT:singularities in thermodynamical observables
=> LARGE EbyE FLUCTUATIONS
Tc
0baryon density
Temperature
Neutron stars
Early universe
nucleinucleon gas
hadron gascolour
superconductor
quark-gluon plasma
critical point ?
vacuum
CFL
• 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 Ejiri-Karsch-Redlich, Gavai-Gupta and Koch-Majumdar-Randrup)
• Location of the critical point detailed study of particle ratio and fluctuations
• Chiral symmetry restoration formation of DCC charge-neutral fluctuations
Event-by-event fluctuation and phase transition 3
Lattice predictionsKarsch et al.Gavai, Gupta hep-lat/0412035Fodor, Katz JHEP 0404 (2004) 050
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.
CRITICAL END POINT
From lattice: TC ~ 170 15 MeVC ~ 0.7-1.5 GeV/fm3
• Location of the Critical point
• Theoretical expectations
• 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?
Points for discussion:
Event-by-event fluctuation and phase transition 4
• <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
• Can be measured experimentally with high precision.
Event-by-event <pT> compared to stochastic reference (mixed events)
NA49, Phys Lett B459 (1999) 679
Central Pb+Pb√s = 17.2 GeV
data
mixedevents
charged hadronsy>4.0 <pT> fluctuations
STAR: Phys. Rev. C 72 (2005) 044902
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 5
PHENIX
CERESNA49
H. Sako QM04
M. TannenbaumJ. Mitchell
K. Perl
STAR
<pT> fluctuations: centrality dependence
.,inclp
pp
T
T
TF
σΦ
≈
22., TTinclp pp
T−=σ
;tt,it,i ppäp −=
><=Σ
N
F
pTT
T
p
T
pp
2σ
Different observables are sensitive to different processes.
STAR sees a smooth dependence on collision centrality whereas NA49 and PHENIX see larger fluctuations in mid-central collisions. STAR attributes this difference due to effects of acceptance and elliptic flow (Pruneau QM05, Voloshin Bergen05)
PRL 93 (04) 092301
PRC 70 (2004) 034902
nucl-ex/0403037
Phys. Rev. C 72 (2005) 044902
Event-by-event fluctuation and phase transition 6
<pT> fluctuations: energy dependence
C. Pruneau QM05
Adamova et al., Nucl. Phys. A727, 97 (2003)
No Energy dependence of <pT> fluctuations is seen from CERES & STAR data.
fluctuations correlations200 GeV
STAR: nucl-ex/0509030
<pT> fluctuations in () bins
This study is also useful for studying contributions from (mini)jets to fluctuations.
Event-by-event fluctuation and phase transition 7
Multiplicity fluctuations
PhotonsCharged Particles
Photons
Photons Charged particles
Gaussians for narrow bins in centrality
= σ2/ < N >
PRC 65 (2002) 054912
WA98: Fine bins in centrality so that fluctuation from Npart is minimal.Centrality dependence of multiplicity fluctuations do not show evidence of non-statistical contribution.However recent NA49 analysis of scaled variance show non-statistical fluctuations at mid-central collisions.
NA49: M. Rybczynski, QM2004
Fine bins in centrality
Event-by-event fluctuation and phase transition 8
<K->/<>Particle Ratio: <K/ has an increasing trend with energy, whereas a horn structure seen in <K+/ +>.
C. Roland (NA49)SQM2004
Fluctuation in Ratio: • K/ fluctuations are large at low beam energy & decrease with increasing energy.
• p/ fluctuations are negative, indicating a strong contribution from resonance decays.
J. Phys. G30 (2004) S1381 M. Gazdzicki QM04
σdata - σ
mix = σdynamic
σ dyn
Particle ratio & fluctuations<K+>/<+>
Event-by-event fluctuation and phase transition 9
K/ fluctuation in STAR
σrms/mean
σdyn = sqrt(σdata2 – σmixed
2)νdyn,Kπ =
NK NK −1( )
NK2 +
Nπ Nπ −1( )
Nπ2 − 2
NKNπNK Nπ
Supriya Das: SQM’06 Symposium
Fluctuation in K/ 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 10
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.
• Bass-Danielewicz-Pratt, PRL 85, 2000• D. Drijard et al, NP B(155), 1979
Balance functions
Early Hadronization Large
Late Hadronization Small
€
B(Δy) =12
N+− (Δy) −N++(Δy)N+
+N−+(Δy) −N−− (Δy)
N−
⎧ ⎨ ⎩
⎫ ⎬ ⎭
Z=0
Event-by-event fluctuation and phase transition 11
DATA show a strong centrality dependence of balance function width.
STAR: Au+Au@ √sNN = 130 GeV PRL 90 (2003)NA49: Pb+Pb@ √sNN = 17.2 GeV PRC 71 (2005)
Gary Westfall: STARPanos Christakoglou: NA49
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.
Balance functions: centrality & energy dependencePanos Christakoglou
central peripheral
NA49 shuffling
NA49 data
STAR shuffling
STAR data
STAR data
NA49 data
simulation
%100⋅⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
Δ
Δ−Δ=
shuffling
datashufflingW
Event-by-event fluctuation and phase transition 12
m
T2≈σ
Balance functions for identified particlesBass-Danielewicz-Pratt, PRL 85, 2000
Heavier particles are characterized by narrower bf distributions:
1.3-1.4
• The balance function width for pions get narrower with increasing centrality, remains constant for kaons.
• HIJING reproduces results for kaons, but not for pions.
• The ratio of widths of pions to kaons is consistent with delayed hadronization picture.
STAR Preliminary
and Gary Westfall, J.Phys.G30, S345-S349 (2004)
Mass (GeV)
ALICE simulation showing BF widths of ,K,p
K
p
Panos Christakoglou in ALICE PPRyΔ
pions
kaons
Event-by-event fluctuation and phase transition 13
confined:few d.o.f.
deconfined:many 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
• Evolution of fluctuation Shuryak & Stephanov: PR C63 (2001) 064903
Heiselberg & Jackson: PR C63 (2001) 064904 Mohanty, Alam & TN: PR C67 (2003) 024904
Net charge fluctuations
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) Φ(Q) νdynamic
• Moments of Net charge distributions
€
ν +−,dyn = ν +− −ν +−,stat
Event-by-event fluctuation and phase transition 14
Net charge fluctuation: energy dependence
J. Mitchell, QM’04
%νdyn
PHENIX ||<0.35, Δ=/2CERES 2.0< <2.9
STAR: 5% Central Au+Au
C. PruneauQM05
• Net charge fluctuations measured by PHENIX & NA49 are consistent with independent emission.
• 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.
STAR: Au+Au
€
ν +−,dyn = ν +− −ν +−,stat
nucl-ex/0401016
Preliminary
centralperipheral
Event-by-event fluctuation and phase transition 15
Moments of net charge distributions Lattice calculations
(similar to kurtosis)
•Ejiri, Karsch and Redlich: hep-ph/0510126•Gavai, Gupta: hep-lat/0510044
•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
Calculation of Non-linear susceptibilities (higher order derivatives of pressure with respect to chemical potentials):
2nd moment
4th moment
6th moment
Event-by-event fluctuation and phase transition 16
Q(net charge) distributionsMEAN of Q distributions
<Q>/Npart
<Q>
Q (net charge)
Q distributions for AuAu 200GeV at 4 different centralities and 6 bins in pT
low pT
high pT
<Q>/Npart is independent of centrality.Moments of Q distributions have been analyzed.
Event-by-event fluctuation and phase transition 17
Variance and kurtosis of net charge distributions
AuAu 200GeVν(Q) with pT binned
ν(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.
Centrality & pT
Kurtosis (4th moment)
Event-by-event fluctuation and phase transition 18
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.
Formation of DCCBjorken, Kowalski & Taylor SLAC-pub-6109 (1993)Review: Mohanty & Serreau Phy Rep 414 (2005)
WA98PMD & SPMD
PRC 67 (2003) 044901
Recent simulation for RHIC show better sensitivity for DCC by using SWM with photon and charged multiplicity:
Aggarwal, Sood, Viyoginucl-ex/0602019
2
2
22ff
bf
ff
bfbf
D
D
NN
NNNNb =
><−><
>><<−><=
Long-range multiplicity correlations
=> 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.
Terence J TarnowskyNuclear Dynamics, San Diego March 2006
STAR Preliminary
• STAR: forward region of 0.8<<1.0 & backward of -1.0<<-0.8.
• Increase in correlation strength observed for central collisions compared to peripheral for AuAu collisions at 200GeV.
Correlation strength:
Event-by-event fluctuation and phase transition 20
Search for critical point at RHIC
Ph
ysic
s m
easu
re
AGS SPS RHIC
QCD Critical Point
Energy Density
• 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.
• 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.
• Fluctuation study especially with strangeness plays a major role in the search for critical point.
Event-by-event fluctuation and phase transition 21
EbyE fluctuation in ALICE
Slope parameter <pT> pions <pT> kaons <pT> protons
K/ p/
Event#1 Event#2
Event#3
EbyE HBT radii
EbyE measures in ALICE: simulation for Pb+Pb at 5.5TeV
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.
http://aliceinfo.cern.ch/
ALICE-PPR
Event-by-event fluctuation and phase transition 22
Summary
Th
erm
odyn
amic
qu
anti
ty /
flu
ctu
atio
n in
the
qu
anti
ty
Energy Density
Fluctuation behavior???
Critical point???
What’s done so far : • 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.
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