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QCD Phase Diagram, Phase Transition and Fluctuations. Bedanga Mohanty Physics group, VECC, Kolkata. STAR Preliminary. First observation of anti-hypertriton Relevant to physics of neutron star. QM09 : J. Chen. Heavy Ion Collisions. Experimentally possible. Explore the QCD phase diagram.

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qcd phase diagram phase transition and fluctuations
QCD Phase Diagram, Phase Transition and Fluctuations

Bedanga Mohanty

Physics group, VECC, Kolkata

heavy ion collisions

STAR Preliminary

First observation of anti-hypertriton

Relevant to physics of neutron star

QM09 : J. Chen

Heavy Ion Collisions

Experimentally possible

Explore the QCD phase diagram

J. D. Bjorken Physical Review D 27 (1983) 140

Supported by theory

USA-NSAC 2007 Long-range Plan

F. Karsch, Prog. Theor. Phys. Suppl. 153, 106 (2004)

phase structure


Z3 breaking

B = 0

B > 0

Chiral symmetry


K. Rajagopal and F. Wilczek, Handbook of QCD

E. Laerman, O. Philipsen Ann. Rev. Nucl. Part. Sci. 53, 163, 2003

Phase Structure
at qm2009

Higher Moments of Charge Fluctuations in QCD at High Temperature -- C. Miao

Non-Gaussian Fluctuations Near the QCD Critical Point -- M. Stephanov

Signals of the QCD Critical Point in Hydrodynamic Evolution -- C. Nonaka

Critical opalescence - T. Kuihiro

Experimental study of the spontaneous strong parity violation -- S. Voloshin

Search for the Critical Point of Strongly Interacting Matter in NA49 -- K. Grebieszkow

Fluctuations of Conserved Quantities Using Higher Order Moments in STAR Experiment -- T. Nayak

Search for QCD critical point .. kurtosis of net proton in STAR experiment - B. Mohanty

Probing the QCD Phase Diagram with Chiral Effective Models -- C. Sasaki

p/ fluctuations in Au+Au collisions- G. Westfall

The Quarkyonic Phase Transition and the FPP-NJL Model in Large and Finite Nc

-- L. McLerran

p/ fluctuations in Au+Au collisions- J. Tian

SPS low-energy scan / FAIR prospects -- C. Hoehne

Critical Points in the QCD Phase Diagram with Two Flavors of Quarks -- J. Kapusta

The NA61/SHINE Experiment at the CERN SPS

- A. Laszlo

Bulk properties at 9.2 GeV in STAR - L. Kumar

Parity violation in Hot QCD -- D. Kharzeev

CBM at FAIR - J. M. Heuser

At QM2009

Finite temperature latice QCD : Present status -- P. Petreczky

QCD Transition Temperature: Approaching the Continuum on the Lattice -- Z. Fodor

Fixed Scale Approach to the Equation of State on the Lattice -- Kazuyuki Kanaya

The Chiral Critical Surface of QCD -- O. Philipsen

Critical Point in Finite Density Lattice QCD by Canonical Approach -- Shinji Ejiri

The Lattice QCD Equation of State and implications for Hydrodynamic Modeling of Heavy Ion Collisions -- R. Soltz

Continuum limit of Gloun plasma - S. Gupta

QCD critical point using canonical ensemble - A. Li

part 1
Part - 1

Lattice QCD results at B ~ 0

Experimental results on fluctuations and charge correlations

Before these, few things to keep in mind regarding

Lattice results …

lattice qcd

a : Lattice spacing

N : Sites in imaginary time

T : Temperature

Reality = continuum limit

Smaller “a”, larger Ntat fixed T


aNt ~ 1/T

Spatial volume also important

QM09 :

P4 : S. Ejiri

Naik and P4 : R. Soltz


Lattice Action

Smaller Nt - distortions due to cutoff effects

EOS computation cost ~ a-11

P. Hegde et al, Eur. Phys. C55, 423 (2008)

Different approach by

QM09 : K. Kanaya

“T integral method”

T varied by Nt at fixed “a”


Temperature change : Usually fix Ntvary “a” (g : lattice gauge coupling)

T. Umeda et al., arXiv : 0809.2842


Setting quark masses

Lines of constant Physics - m/m = const

Number of quark flavours : 2+1 flavour with mu = md and ms

Lattice QCD

(A) Quantum statistical ensemble in thermal equilibrium

Simulate : Z = Tr exp(-H/T)

order of phase transition for b 0

1st order :

Peak height ~ V

Peak width ~ 1/V

Cross over :

Peak height ~ const.

Peak width ~ const.

2nd order :

Peak height ~ V

T grows with 6/g2, g : gauge coupling

No significant volume dependence (8 times difference in volumes)

Phase transition at high T and  = 0 is a cross over

Lattice results on electroweak transition in standard model is an analytic cross-over for large Higgs mass

K. Kajantie et al., PRL 77, 2887-2890,2006

Order of Phase Transition for B ~ 0

Physical quark masses

Continuum limit

Simulations along Lines of Constant Physics

mK/m = 3.689; fK/m = 1.185

Staggered fermionic action

Y. Aoki et al., Nature443:675-678,2006

Relevant to LHC and current RHIC regimes

transition temperature


TC ~ 175 (2)(4)

- 192 (7)(4) MeV

- 185 - 195 MeV

Chiral and deconfinement

same T or different T ?

Transition Temperature

Point of sharpest change in temperature dependence chiral susceptibility, the strange quark number susceptibility and the renormalized Polyakov-loop

QM09 : Z. Fodor

R. Soltz

Possible sources of differences : (a) Ambiguity in locating Tc for


(b) Physical observable used to

set the scale (r0, fK);

(c ) Preferred renormalization of

chiral susceptibilities

(d) Use Wilson fermions

transition temperature1
Transition Temperature

V. G. Bornyakov et al, POS Lat2005, 157 (2005)

Y. Maezawa et al, hep-lat/0702005

C. Bernard et al, Phys. Rev. D 71, 034504 (2005)

M. Cheng et al, Phys. Rev. D 74, 054507 (2006)

Y. Aoki et al, Phys. Lett. B 643, 46 (2006); 0903.4155

  • Consequence for heavy-ion phenomenology
  • both at LHC and RHIC:
  • ~ T4; Results in ~ 60% in difference energy density at TC

F. Karsch : Lattice 2007

lattice equation of state

Velocity of sound

Important for heavy ion phenomenology

(T 1/cs2const

QM08 :S. Gupta

M. Cheng et al., Phys. Rev. D 77, 014511 (2008)


Agreement with perturbation theory

Consistent with Stefan-Boltzmann limit

G. Endrodi et al., PoS LAT2007:228,2007

Lattice : Equation Of State

gparton ~ 47.5

 ~ g (2/30)

g ~ 3


P. Petreczky

R. Soltz

15% deviation from Ideal gas at 4TC

Calculations with larger spatial volumes ?

fluctuation deconfinement transition

(DpT)2/pT2 ~ (DT)2/T2 = 1/Cv

(DN)2/<N> ~ 1/

Fluctuations in particle ratios

-- Sensitive to particle numbers

at chemical FO not kinetic FO

-- Volume effects may cancel

S. Jeon, V. Koch, PRL 83, 5435 (1999)

Fluctuation in conserved quantities : net charge,

net baryon number, net strangeness

-- Related to corresponding susceptibilities

-- Given strong longitudinal expansion, fluctuations

in QGP may be preserved during hadronisation

-- Conservation laws limit their dissipation

S. Jeon, V. Koch, PRL 85, 2076 (2000)

M. Asakawa, U. W. Heinz, B. Muller

PRL 85, 2072 (2000)

Fluctuation : Deconfinement Transition

For a thermodynamic system

Fluctuation in experimental observables

related to thermodynamic quantities

<(DE)2> ~ T2Cv(T)

M. Stephanov et al., PRD 60, 114028 (1999)

~ Naively

L. Stodolsky, PRL 75,1044 (1995)

S. Mrowczynski, PLB 430, 9 (1998)

General approach

Second moment of event-by-event

distributions of multiplicity,

mean pT, ET after removing

non-dynamical fluctuations.

fluctuation measures
Fluctuation Measures

Dominantly looking at second moment, constructions motivated

for removing non-dynamical fluctuations

ratio fluctuation results
Ratio Fluctuation Results


STAR : arXiv : 0901.1795



QM09 : G. Westfall

QM09 : J. Tian

QM09 : V. Konchakovski

conserved quantity fluctuation results
Conserved Quantity Fluctuation Results

Mostly fluctuation in net-charge has been studied




experimental possible deconfinement observables
Experimental : Possible Deconfinement Observables

QM09 : Y. Xu

PHENIX : direct photon arXiv:0804.4168

Tinitial > TC (Lattice)

initial > C (Lattice)

Observables from SPS indicating possible phase transition was discussed

in C. Hoehne Plenary Talk


Why we do not see fluctuations reflecting QGP to hadronic phase transition -

One possibility is dissipation of fluctuations

Is Relaxation > hadronic

This leads to the issue of acceptance needed to

measure the primordial fluctuations

ymin > ycoll (mean change in rapidity due to collisions)

~ (diffusion coefficient) free (mean free time)

M.A. Aziz et al, PRC 70, 034905 (2004)

E.V. Shuryak et al, PRC 63, 064903 (2001)

B. Mohanty et al, PRC 67, 024904 (2003)

What is the expectation for a cross-over phase transition ?

chiral magnetic effect

If one observes a difference between NL and NR clear indication of parity violations

But how do we experimentally distinguish L.H and R.H quarks (we detect hadrons)

Polarization in magnetic field ?

For finite volume : Charge difference in upper and lower hemisphere

Chiral Magnetic Effect

Topological structure of QCD vacuum -- Parity violations in strong interactions

Assume quark are mass less : (Helicity/Chirality)

R.H quarks & anti-quarks : s and p same direction

L.H. quarks & anti-quarks : s and p opposite direction

Mass less quarks can change chirality by interacting with gluons. Axial Ward Identity relates chirality to properties (topology) of gluon fields.

D.E. Kharzeev et al, NPA 803, 227 (2008)

u : Positive charge

d : negative charge

N L,R : total number of Left/Right handed q+qbar

of a particular flavour

QM09 : D. Kharzeev

chiral magnetic effect1

Parity even

Physical background

QM09 : S. Voloshin

Charge asymmetry observed in STAR experiment. Investigations so far indicate they could only be consistent with parity violation effects in strong interactions.

De-confined phase needed

Chirally symmetric phase needed

K. Fukushima et al, PRD 78, 074033 (2008)


Chiral Magnetic Effect

Topological structure of QCD vacuum -- Parity violations in strong interactions.

Heavy ion collisions :

Possibly we have produced a de-confined quark-gluon matter.

Large magnetic field in the direction of angular momentum.

Charge separation can take place along this direction.

Angular momentum is perpendicular to reaction plane.

Look for charge asymmetries.

S. Voloshin

PRC 70, 057901 (2004)

part 2
Part - 2

T. Andrews.

Phil. Trans. Royal Soc., 159:575, 1869

QCD Critical Point

Thermodynamic quantities ~ correlation length

Critical exponents, are universal, depend on degrees of freedom in the theory and their symmetry, no dependence on details of interactions.

Different physical systems == same universality class

T > TC T~TC T < TC

Critical Opalescence as observed in CO2 liquid-gas transition

For example :

Liquid-Gas system critical point and QCD critical point

Same universality class : Z2

Long range correlations, density fluctuations

first order phase transition b 0

Canonical ensemble used

M = 770 MeV

Nf = 2

P4-improved staggered quark action

First order phase transition for T/Tc < 0.83 and q/T > 2.3

Existence of critical point suggested

First Order Phase Transition (B > 0)

QM09 : S. Ejiri

PRD 78, 074507 (2008)

μ∗q /T is the chemical potential that gives a minimum of the effective potential

critical points linear model with quarks
Critical Points : Linear model with quarks

QM09 : C. Sasaki

Conventional picture

QM09 : J. Kapusta

Aim : Study phase diagram of Linear  model

coupled to two light flavour quarks of same mass

Includes thermal fluctuations of meson and

fermion fields

Vacuum pion mass varied : 0 to 300 MeV

(Can compare to Lattice studies)

Studies at non-zero chemical potential

No phase transition

For m,vac > 321 MeV

Constants in the model

Pion decay constant f = 92.4 MeV

 mass (m)= 700 MeV

Mass of quark = 313 MeV

m varied : 0 - m/2

Exotic picture

Two critical points


qcd models critical point
QCD Models : Critical Point

Compilation by Mikhail Stephanov

QM09 : C. Sasaki

Need first principle calculations - Lattice

lattice qcd critical point
Lattice : QCD Critical Point

Expectation value of an observable

M : Dirac Matrix

SG : Gluonic action

For > 0 the quark determinant becomes complex

Issue for non Zero , Det M is not positive definite

-- Sign problem

  • Four approaches
  • Reweighting : Z = < e -S() det D() / e-S(0) det D(0) >=0
  • Taylor expansion of thermodynamic observables in /T about  = 0
  • Imaginary chemical potential :  imaginary, fermion determinant positive
  • Canonical ensemble - predicts existence of QCD critical point

(TE ~ 160 MeV and E ~ 600 MeV, m ~ 700 MeV)

QM09 : A. Li

lattice qcd critical point1


Taylor Expansion

R. Gavai and S. Gupta Phys. Rev. D 78, 14503 (2008)

Z. Fodor and S.D. Katz JHEP 0404, 50 (2004)

TE = 162 +/- 2 MeV

E = 360 +/- 40 MeV

TE/TC = 0.94 +/- 0.01

E /TE = 1.8 +/- 0.1

QM09 : Owe Philipsen

Imaginary Chemical Potential

P. De Forcrand and O. Philipsen PoS LATTICE2008, 208 (2008)

c1 > 0

c1 < 0

nf = 2+1 continuum limit ?

Spatial volume, stable results for

different Nt ?

Lattice : QCD critical point
signature of qcd critical point higher moments

Higher Moments

At Critical point

< (N)2> ~ 2

< (N)3> ~ 4.5

 = Correlation length

Value limited in heavy-ion collisions

Finite size effects < 6 fm

Critical slowing down, finite time

effects  ~ 2 - 3 fm (model assumptions)

< (N)4> - 3 < (N)2>2 ~ 7

Higher sensitivity as

stronger dependence on 

M. A. Stephanov, Phys. Rev. Lett. 102, 032301 (2009)

Non Gaussian features increase if the system freezes-out closer to QCD Critical point

Signature of QCD Critical Point : Higher Moments

Challenging to measure

B. Berdnikov & K. Rajagopal, Phys. Rev. D 61, 105017 (2000)

Stephanov, Rajagopal, Shuryak, Phys. Rev. D 60, 114028 (1999)

Experimentally : Look for non-monotonic variation of higher moments of multiplicity distributions and mean pT distributions as a function of beam energy

signature of qcd critical point net protons

Q = B/2 + I3

Q ~ (1/VT) < (Q)2> = (1/4) B + I

~ (1/VT) < (Np-pbar)2>

Net Proton number fluctuations ~ singularity of the charge and baryon number susceptibility

-iso-spin blindness of  field

S. Gupta

Y. Hatta and M. A. Stephanov, Phys. Rev. Lett. 91, 102003 (2003)

Signature of QCD Critical Point : Net protons

Equilibrium thermodynamic system

Divergence of susceptibilities at Tc

Susceptibilities are related to higher

moments of multiplicity observables.

Also seen in QCD model based calc.

B = 0

QM09 : C. Sasaki

QM09 :Chuan Miao

Net Proton number is sufficient

Connection between Lattice and

Experimental data possible

M. Cheng et al., arXiv: 0811.1006

experimental results on higher moments
Experimental Results on Higher Moments

QM09 : T.K. Nayak

B. Mohanty

Net Protons

First look at net-protons

First look at higher moments

Monotonic behavior observed

We are probing a small B region

STAR Preliminary

F2 = (2 - <N>)/<N>2

STAR Preliminary

Setting the baseline for the future

QCD critical point search program


signature of qcd critical point pbar p
Signature of QCD Critical Point : pbar/p

QM09 : C. Nonaka

The presence of a critical point deforms the isoentropic trajectories (S/nB = constant)

The critical point serves as an attractor of the hydrodynamical trajectories.

pbar/p ~ exp (-2B/T)

Below TC :

Both T and B decrease

for critical point

B remains fairly constant

for others trajectories

Experimentally observable : Drop in pbar/p vs. pT (Coalescence region)

Provided nucleons of high pT are

chemically frozen out earlier - supported

by UrQMD simulations

M. Asakawa et al, PRL 101, 122302 (2008)

experimental results on pbar p vs p t
Experimental Results on pbar/p vs. pT

Slope vs. Beam Energy/B

Phys. Rev. C73, 044910 (2006)

Phys.Rev. C78, 034918 (2008)

QM09 : K. Grebieszkow

Fitting Procedure :

y = a (mT - m) + b

No large drop in ratio observed

for intermediate pT range


STAR : PLB 655, 104 (2007)

PRL 97, 152301 (2006)

signature of qcd critical point disappearance of mach cone
Signature of QCD Critical Point : Disappearance of Mach Cone

QM09 : Teiji Kunihiro

Study focused on critical dynamics around QCD critical point with relativistic dissipative hydrodynamics

Uses the idea of coupling the density fluctuations to thermal energy

Rayleigh peak

At the soft mode around QCD critical point is the thermally induced density fluctuations (Rayleigh peak) and the sound modes get suppressed (Brillouin peak)

Brillouin peak

Brillouin peak

Experimentally : Disappearance of mach cone like


STAR : Phys. Rev. Lett. 102, 052302 (2009)

sps fluctuation results on qcd critical point

Critical Point ?

B ~ 250 MeV

T ~ 178 MeV

SPS Fluctuation Results on QCD Critical Point

QM09 : K. Grebieszkow

Assuming correlation length 3-6 fm and experimental acceptances

No signature for energy


System size dependence shows a jump

Stephanov, Rajagopal, Shuryak, Phys. Rev. D 60, 114028 (1999)

Hatta, Ikeda Phts. Rev. D 67, 014028 (2003)

part 3
Part - 3

New Phase of QCD

New Experimental Programs

new phase of matter in large colour limit
New Phase of Matter in Large Colour Limit

In the limit of large number of colors (Nc)

There could exist three phase of matter

Confined phase

De-confined phase

Quarkyonic phase

Matter has and p that of a gas of quarks yet confined. (O(Nc))

QM09 : C. Sasaki

QM09 : L. McLerran


Debye Screened

Baryons Number

N ~ Nc



Quark Gluon Plasma



Critical Point

Baryon energy density ~ Meson energy density



No Baryons

N ~0(1)

Not Chiral



N ~ NcNf




Color Superconductivity

Order parameter

Baryon number

Quarkyonic Matter

Confined Matter

Liquid Gas Transition

Conjectured Phase Diagram for Nc = 3

Experimental signature :

Baryon-Baryon correlations to look for nucleation of baryon rich bubbles surrounded by baryon free regions

QM09 : P. Sorensen & A. Mocsy

new program explore qcd phase diagram

Looking for onset of various observations

New Program : Explore QCD phase diagram

Pb+Pb 17.3 GeV

Au+Au 200 GeV

PHENIX : PRL 101, 232301 (2008)

Jet quenching

WA98 : PRL 100, 242301 (2008)

Partonic collectivity

Baryon-meson difference

meson will play a crucial role

QM09 : S. Shi


QM09 : S. Voloshin

Chiral Magnetic effect

new program look for qcd critical point

Cross over


critical point


1st order


R.V. Gavai and S. Gupta, Phys.Rev.D71:114014,2005

New Program : Look for QCD critical point


Most lattice calculation predicts critical point B > 160 MeV

Current studies at RHIC probes B ~ 14 -60 MeV

Need a beam energy scan program - but fixed target experiments were there ..

The real voyage of discovery consists not in seeking new lands but seeing with new eyes.

-- Marcel Proust, French novelist, 1871-1922.

rhic critical point search program advantage
RHIC Critical Point Search Program - Advantage

Hadron Mass

200 GeV

Beam Energy

62.4 GeV

9.2 GeV

Uniform acceptance for different particle species and for different beam

energies in the same experimental setup(advantage over fixed traget expt.)

rhic critical point search program advantage1
RHIC Critical Point Search Program - Advantage

G. Roland

Collider experiment : Variation of particle density with

beam energy slower. Occupancy in detectors reasonable

compared to fixed target experiments at similar collision energy

rhic collider demonstrated capabilities
RHIC - Collider Demonstrated Capabilities

All setup worked very well with RF harmonic number 366

Defocusing sextupole reversal and octupole improved blue

lifetime by factor 4

~ 50-60% injection efficiency

STAR collisions about 13h after 1st beam and

PHENIX about 24h after 1st beam

Experiment useful event rates 0.7-1Hz with 56 bunches.

Maximum luminosity 3.5 1023 cm-2s-1

Average luminosity 1.2 1023 cm-2 s-1

Factor of 3 increase in luminosity easily achievable

rhic experiments demonstrated capabilities

STAR Preliminary

RHIC - Experiments Demonstrated Capabilities

Results with only 3000 events !

QM09 : L. Kumar

These results from the lowest beam energy collisions at

RHIC demonstrate experiment’s readiness to take

up the proposed Beam Energy Scan Program.

Large and uniform acceptance for all beam energies in a

collider set up, excellent particle identification (TPC+TOF) and higher statistics will provide ideal data to experimentally measure fluctuations/Kurtosis to locate QCD critical point

rhic critical point search future plans
RHIC Critical Point Search - Future Plans

Experiments have proposed the following plan

May a good idea to start with energies common to both experiments

Run Number 9071097

First paper from RHIC was based on ~ few thousand events; PHOBOS : PRL 85 (2000) 3100

“The measurements shown here represent the first step toward the development of a full picture of the dynamical evolution of nucleus-nucleus collisions at RHIC energies.”

The results shown at QM2009 from

RHIC low energy test running :

“These measurements shown here could become the first step towards

a detailed study of the QCD phase diagram at RHIC”

new program sps shine

What is the difference vs. NA49 ?

Experimental set up :

New spectator calorimeter for

centrality selection

Forward Time-Of-Flight

Beam pipe

TPC readout

Physics Program :

Studying QCD Critical Point and Onset of various observations with varying colliding ion size, collision centrality and having a proper p+p baseline

QM09 : A. Laszlo

New Program : SPS - SHINE

A significant difference between freeze-out and transition temperature can lead to dilution of the signatures of the QCD critical point. One way address this is to vary system size/colliding ion size.

F. Becattini et al., PRC 73, 044905

new program fair cbm
New Program : FAIR - CBM

Claudia Hoehne

  • CBM at SIS 300 will start in 2017
  • 10-45A GeV beam energy, high availability of beam (order of 10 weeks per year), interaction rates up to 10 MHz
  • “CBM light” at SIS 100 in 2015 Au beam up to 11A GeV, p beam up to 30 GeV (multistrange hyperons, charm production in pA)
  • Assume 10 weeks beam time, 25A Gev Au+Au (minbias), no trigger, 25 kHz interaction (and storage) rate:
    • “unlimited statistics” of bulk observables, e.g. ~1010-11 kaons, 1010Λ
    • low-mass di-electrons with high statistics, 106 -mesons (each)
    • multistrange hyperons with high statistics, 108, 106

QM09 : C. Höhne, J. Heuser

High luminosity, rare probes, higher B reach

current status
Current Status

Lattice and other QCD based models :

B = 0 - Cross-over

TC ~ 170-195 MeV

B > 160 MeV - QCD critical point

Experiments :

See distinct signatures that relevant d.o.f

are quark and gluons

[Tinitial(direct photons) > TC(Lattice)]

No signatures of QCD critical point established, possible hints at SPS.

New distinct signatures proposed by Lattice and QCD based model calculations.

Future program :

Exploring the QCD phase diagram

needs to be vigorously pursued to know

properties of basic constituents of matter

under extreme conditions.


With the starting of LHC (B~ 0) - we have unique opportunity to understand the properties of matter governed by quark-gluon degrees of freedom at unprecedented initial temperatures achieved in the collisions.

To make the QCD phase diagram a reality equal attention needs to be given to high baryon density region.

These two complementary programs will make our understanding clearer on

  • characterization of quark-gluon matter

at varying baryon density

  • finding the QCD critical point and
  • locating the QCD phase boundary

Thanks to the Organizers.

Thanks to ……..

J. Alam, R. Bhalerao, A. Bhasin , X. Dong, K. Grebieszkow, S. Gupta, J. M. Heuser, C. Hoehne, J. Kapusta, T. Kunihiro, L. Kumar, A. Laszlo, M. Lisa, L. Mclerran, T. K. Nayak, C. Nonaka, P. Petercky, C. Pruneau, S. Raniwala, K. Rajagopal, L. Ruan, C. Sasaki, P. Sorensen,M. Stephanov, G. Westfall, N. Xu, Z. Xu, and

All other STAR & WA98 Collaborators … for inputs/discussions/suggestions

See you at next Quark Matter …

multiplicity fluctuation results
Multiplicity Fluctuation Results




QM09 : K. Grebieszkow

p t fluctuation correlation results
pT Fluctuation/Correlation Results

QM09 : K. Grebieszkow





old program fixed target
Old Program : Fixed Target

Hadron Mass

NA49 : arXiv : 0808.1237

6.3 GeV

7.6 GeV

Beam Energy

8.7 GeV

12.3 GeV

17.3 GeV

Non-Uniform acceptance for different particle species

and for different beam energies in the same experimental setup