event-by-event fluctuation and phase transition 1 outline motivation fluctuation measures:...

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


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


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:


• <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


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


<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.


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


<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+>/<+>


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.


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


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


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


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


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


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


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.


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)


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:


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.


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


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

event-by-event fluctuation and phase transition 1 outline motivation fluctuation measures:...

Documents

event mean

qcd phase transition

fluctuations star

location of critical

various fluctuation

temperature fluctuations

critical end point

larger fluctuations