Exploring the QCD Phase Diagram
through Relativistic Heavy Ion Collisions
Bedanga Mohanty
National Institute of Science Education and Research
(NISER)
Outline:
 Phase diagram of QCD
 Theoretical and Experimental status
 Summary
1
QCD Phase Diagram
Physical systems undergo phase
transitions
when
external
parameters such as the
temperature (T) or a chemical
potential (μ) are varied.
K. Rajagopal and F. Wilczek, Handbook of QCD
Conserved Quantities:
Baryon Number ~ 
Electric Charge ~ Q ~ small
Strangeness
~ S ~ small
Rich phase structure:
-- Phases QGP & Hadronic
-- Cross over
-- 1st order
-- Critical Point
2
QCD Phase Diagram - Experimental
Conservation in strong interactions
-- Charge
-- Baryon number
-- Strangeness
Vary: T, B, S, Q
Nature 448 (2007) 302
Vary beam energy to change Temperature & Baryon Chemical Potential
3
Transition Temperature
Prog. Theor. Phys. Suppl. 153, 106 (2004)
gparton ~ 47
 ~ g (2/30)
g ~ 3
Nucl. Phys. A 830 (2009) 805c
195
190
Physical ml/ms
Tc [MeV]
185
180
HISQ/tree
175
Asqtad
170
165
160
155
Combined continuum extrapolation
150
High Temperature
 De-confined state of quarks
and gluons
-2
HISQ/tree: quadratic in N t
145
Asqtad: quadratic in
-2
Nt
N-2
t
140
135
0
0.005
0.01
0.015
0.02
0.025
Phys.Rev. D85 (2012) 054503
0.03
0.035
4
Cross-over
Nature443:675-678,2006
JHEP 1208 (2012) 053
0.2
No significant volume dependence
v2
v3
v4
v5
(1/2p) dN/dy pT dpT
5
10
4
10
3
ALICE
0-5%
ávn á
10
2 1/2
0.15
IP-Glasma+MUSIC
p+ + p+
K +K
—
p+p
1
10
0
10-1
narrow: h/s(T)
wide: h/s=0.2
0.1
0.05
102
10
ATLAS 20-30%, EP
0
0
0.5
1
pT [GeV]
1.5
2
Phys. Rev. Lett. 110, 012302 (2013)
0
0.5
1
1.5
pT [GeV]
2
2.5
At high T and  = 0 is a cross over.
5
Establishing Quark Gluon Phase
Eur.Phys.J. C72 (2012) 1945
(a)
(b)
RAA
1.5
CMS PbPb sNN = 2.76 TeV
(c)
±
h CMS PbPb (0-5%) sNN = 2.76 TeV
h± ALICE PbPb (0-5%) sNN = 2.76 TeV
h± STAR AuAu (0-5%) sNN = 0.2 TeV
p0 PHENIX AuAu (0-10%) sNN = 0.2 TeV
W
+
W
W
Z0
ALICE pPb sNN = 5.02 TeV
STAR dAu sNN = 0.2 TeV
1.0
0.5
Isolated photon
CMS PbPb (0-10%) sNN = 2.76 TeV
PHENIX AuAu (0-5%) sNN = 0.2 TeV
0.0
1
2 3 4 56
10
20 30
p (GeV/c)
T
100 2
4
6
8 10 12 14 16 18 20 22
p (GeV/c)
T
20
40
60
80
100
120
p (GeV/c)
T
initial > c (Lattice)
2
AA
1 d N / dpT dh
RAA ( pT ) =
TAA d 2s NN / dpT dh
STAR: QM2012
At and below 11.5 GeV – Hadronic
interactions dominate. Need pA data
for a quantitative statement.
6
QGP turned off ?
Establishing Quark Gluon Phase
v2 = cos 2j =
3
0.12
0.1
px2 - py2
px2 + p2y
p + +p - (PHENIX)
He+3 He (STAR)
-
K S (STAR)
0
K + +K (PHENIX)
f (STAR)
p+p (PHENIX)
L (STAR)
d+d (PHENIX)
v2/nq
0.08
b)
0.2
7.7 GeV
Au+Au, 0-80%
h-sub EP
p
L+
X+
W
0.1
pK
0
Ks
f
11.5 GeV
19.6 GeV
0.04
0.02
0
39 GeV
27 GeV
62.4 GeV
0
0.5
1
1.5
KET/nq (GeV/c2)
0.1
0
0
STAR Preliminary
0
v2
0.2
0.06
1
2
3
arXiv:1301.2347
40
1
2
3
40
2
mT-m0 (GeV/c )
1
2
3
4
 Partonic Collectivity
 De-confinement
Turned off at low energy ? 7
2
Establishing Quark Gluon Phase
QM2012: STAR
At and below 11.5 GeV – Hadronic interactions dominate.
8
QCD Phase structure at B ~ 0
 Close to zero baryonic chemical potential the
QCD transition corresponding to a state of deconfined quarks and gluons takes place at high
temperature.
 First principle QCD calculations suggest it is a
cross over.
 Transition
temperature
using
chiral
condensates ~ 154 MeV, using Susceptibilities
and Polyakov loop ~ 175 MeV – width around
15 MeV
9
JHEP 1104 (2011) 001
Transition Line - Theory
 Width of transition line wide
 Freeze-out line close to transition line at Lower B
 Larger B deviations of freeze-out curve from transition line
 Interesting T vs. B dependence at lower beam energies
10
Transition line - Experiment
First step: Locate beam energy (T, B) point where the system did not
undertake the QCD transition
b)
0.2
7.7 GeV
Au+Au, 0-80%
h-sub EP
p
L+
X+
W
0.1
pK
0
Ks
f
11.5 GeV
19.6 GeV
39 GeV
62.4 GeV
v2
0
0.2
27 GeV
0.1
0
0
1
2
3
40
1
2
3
40
2
mT-m0 (GeV/c )
1
2
3
4
arXiv:1301.2347
At and below 11.5 GeV – Hadronic
interactions dominate. Need higher
statistics data for a quantitative
statement.
QM2012: STAR
11
QCD Phase structure at B > T
 Transition line from lattice QCD has large
uncertainties.
 Transition line close to chemical freeze-out line
at small B but deviates at large B. Interesting
trends of T vs. B at lower energies.
 Experimental hints towards no QCD transition
to de-confined state ~ 11.5 GeV center of mass
energy.
12
Search for Critical Point - Theory
Numerical QCD calculations difficult at large B – sign problem
Techniques: Reweighting, Taylor expansion & imaginary potential
Real world
Heavy quarks
m
QCD critical point DISAPPEARED
X
0
mu,d
S. Gupta, QM2009
Phys. Rev. D 78, 14503 (2008);
Phys.Rev.D71:114014,2005
crossover
1rst ¥
ms
Acta Phys.Polon.Supp. 5 (2012) 825-835
JHEP 0404, 50 (2004)
Issues (not common to all) : lattice spacing, physical quark mass,
continuum limit, Volume
Theory still some more work to be done …… need more CPU 13
Search for Critical Point - Experiment
Nuclear liquid-gas
transition with a critical
end point
Observables : Related to correlation length or susceptibility
< (N)4> - 3 < (N)2>2 ~ 7
< (N)2> ~ 2
< (N)3> ~ 4.5
S  ~ 
Phys.Rev.Lett. 107 (2011) 052301
Phys. Rev. Lett. 102, 032301 (2009)
Phys. Rev. Lett. 91, 102003 (2003)
Phys. Rev. D 61, 105017 (2000)
Challenging to measure :
Finite size effects < 6 fm
Critical slowing down, finite
time effects  ~ 2 - 3 fm

Phys.Lett. B696 (2011) 459
Phys.Rev.Lett. 105 (2010) 022302
No dynamical theoretical
estimates exists. Experimentally
look for non-monotonic variations
with beam energy (T, B).
14
Search for Critical Point - Experiment
 Deviations from Poissonian
for 0-5% central collisions
STAR: QM2012
Phys.Rev.Lett. 105 (2010) 022302
 Higher statistics needed at 7.7
& 11.5 GeV + a new data point
around ~15 GeV
15
QCD Phase structure: Critical Point
 Theory: Lattice QCD calculations have uncertainties.
 Experiment: If signal survives hadronization then
ruled out for beam energies > 39 GeV
Promising prospects below 39 GeV.
High statistics data set needed below 39 GeV.
 Theory+Experiment: Need quantitative dynamical
theory calculations with realistic correlation lengths
to compare to data.
Science 332 (2011) 1525-1528
16
Phase structure: Interesting Possibilities
Rept.Prog.Phys. 74 (2011) 014001
Quarkyonic phase (Theoretical)  Experimental signature
Nucl.Phys. A830 (2009) 709C-712C
(Baryon correlations, Photons) ?
Nucl. Phys. A 796, 83 (2007
arXiv:1302.1119
17
Summary
What is known about the QCD phase diagram and to what degree ?
De-confined transition: Exists, – Theory & experiment
Cross over: Exists, B ~ 0 Theory & experiment (indirectly)
Critical point: Search on, Theory (Uncertain) & experiment (inconclusive)
Transition line: Theory (some uncertainties) & Experiment (indications)
QGP properties: Progress - Theory (EOS at B = 0, need better handle for
EOS at large B & Experiment tremendous progress
Hadronic properties: Progress - Theory (Freeze-out properties using QCD)
Experiment tremendous progress
Phys. Lett. B 696 (2011) 459 Phys.Rev.Lett. 109 (2012) 192302
New Phases: Theory (Quarkyonic) and experiment (signatures ?)
Theory predicted signals needed.
18