Outline
III. Why an energy scan ?
 Is there an overarching reasons for it ?
IV. Status of studies of the low
mhigh
T region of the phase diagram
B
VI. What new insights will an energy scan afford?
 Lingering Questions
 Onset of opacity for light and heavy quarks
 Onset of quark number scaling
 Requirements
VII. Opportunities for Discovery & New Constraints
 Search for the critical point
 Studies of the first order phase transition
 New constraints for the hadronic EOS
 Requirements
VIII.Summary
Roy A. Lacey, Stony Brook;
INT Workshop on the QCD Critical
Point, July 28 - Aug. 22, 2008
2
Phase Diagram for H2O
The location of the critical
End point and the phase
coexistence lines are
fundamental to the phase
diagram of any substance !
Roy A. Lacey, Stony Brook;
INT Workshop on the QCD Critical
Point, July 28 - Aug. 22, 2008
3
Conjectured Phase Diagram for QCD?
Consensus (I)
Continuous/rapid
Crossover Transition
p
Consensus (II)
Our understanding of the QCD
Phase diagram, as well as the
properties of the different
phases is still limited
Energy scans at RHIC provide
access to a broad range of the µ -T plane!
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
4
Learn the past, charge the present and create
the future!
A quick summary of the present !
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
5
A “little Bang” occurs
in RHIC collisions
t
c
t=
/c
-z
z/
t=
Thermalized partonic Fluid!
1 1 dET
e Bj =
p R 2 t 0 dy
Experimental results
favor a (s)QGP
ε Bjorken ~ 5 - 15 GeV/fm3
~ 35 – 100 ε0
0
Gold
v~0.99c
nucleus
z:collision axis
Gold
nucleus
Challenge:  Develop Constraints for the Properties of the
sQGP ?
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
6
Which observable/s provide important
constraints?
Jet Quenching
 Scattering power
• Flow
 sound speed
 shear viscosity
• Medium Response
 sound speed,
 shear viscosity

•
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
7
Jet Quenching
High Energy partons lose energy by
re-scattering in the hot and dense medium
Radiative:
dE
~ sr L kT2
dx
Range of Color
Force
)
q ~ rs kT2
Scattering Power
Of Medium
Color charge
scattering centers
Nuclear Modification Factor
N AA
RAA =
N coll N pp
Can access
)
r and q
Density of
Scattering centers
RAA measurements can provide estimates
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
8
Light Quark Opacity
Phys. Rev. C 77, 064907 (2008) ,
arXiv:0801.4555
2
qˆ =13.2+-2.3
GeV
/fm
2.3
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
9
The Flow Probe
(
æ
¶e
çP = r²×
¶r
è
y
From ET Distributions
e=
1 1 dET
e Bj =
p R 2 t 0 dy
)
ö
÷
s/r ø
y2 - x2
y 2 + x2
x
GeV
~ 5 - 15
fm3
Large Pressure Gradients  Hydro Flow of
partons
“Control Params.”
d 3N 1 2 N
1 + 2v1 cos( φ - R ) + 2v2 (2[φ - R ]) + ...
E 3 = d
d p p
dpT2 dy
e , cs , h
v2 n = cos(2n[φ -  R ])
Hydro Flow exhibit specific scaling properties which can be (in)validated
Roy A. Lacey, Stony Brook;
INT Workshop on the QCD Critical
Point, July 28 - Aug. 22, 2008
10
Flow shows KET and quark number scaling
Flow is dominantly pre-hadronic
PRL 98, 162301 (2007)
PRL. 99, 052301 (2007)
Indications of the QGP from flow
Courtesy S. Bass
Charm Flow
initial state
QGP and
hydrodynamic
expansion
hadronization
hadronic phase
and freeze-out
pre-equilibrium
h
æ 1 ö
~ 2 - 4ç
÷
s
è 4p ø
cs ~ 0.35
We hold these
truths to be self
evident !
Universal Scaling
PRL 98, 172301 (2007)
nucl-ex/0610029
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
11
Scaling for Higher Harmonics
1 1 v 4,q (p T )
»
+ ´ 2
2
v 2,M (2p T ) 4 2 v 2,q (p T )
v 4,M (2pT )
v 4,B (3pT )
v 22,B (3p T )
»
1 1 v 4,q (p T )
+ ´ 2
3 3 v 2,q (p T )
Courtesy S. Bass
initial state
QGP and
hydrodynamic expansion
pre-equilibrium
hadronic phase
and freeze-out
hadronization
æ 1 1 v 4,q (pT ) ö
» aç + ´ 2
ç 4 2 v (p ) ÷÷
v 22,M (2p T )
2,q
T
è
ø
v 4,M (2pT )
æ 1 1 v 4,q (p T ) ö
»
a
çç + ´ 2
÷÷
2
v 2,B (3pT )
3
3
v
(p
)
2,q
T
è
ø
v 4,B (3pT )
v 4,q (p T )
v 22,q (p T )
»
1
2
a » 1.8
The ratio of the flow harmonics for quarks is compatible
with hydrodynamic prediction
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
12
Medium Response & Transport
Coefficients
High pT
trigger
QCD Sonic Boom
Same-Side Jet
Df *
q*
x10
x20
Gs =
4 h
æ1ö
~ 0.1, 0.2, 0.5 ç ÷
3 sT
èT ø
cos ( q M ) = cs
Gives sound speed directly; Sets upper limit on viscosity.
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
13
QCD Sonic Boom?
Simulated
Deflected jet
Data
Total 3PC jet correlations
Simulated
Mach Cone
True 3PC jet correlations
cs ~ 0.35,
h
æ 1 ö
~ 2´ç ÷
s
è 4p ø
Data compatible with the presence of a Mach Cone away-side jet
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
14
Transport Coefficient
Estimates
Lacey & Taranenko nucl-ex/0610029
cs
V
Gs =
D~
4 h
3 sT
3
2p T
t Relax =
M
D
T
1-2 X the conjectured lower bound
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
15
What new insights will an Energy Scan afford?
Lingering questions about the (s)QGP?
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
16
Light Quark Opacity
Phys. Rev. C 77, 064907 (2008) ,
arXiv:0801.4555
2
qˆ =13.2+-2.3
GeV
/fm
2.3
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
17
Heavy Quark Opacity
PRL 98, 172301 (2007)
0.25
p ++ + p- -
Au+Au
K +K
sNN = 200 GeV
p+ p
D
0.20
Moore
v2
0.15
h
æ 1 ö
~ 2 - 4ç
÷
s
è 4p ø
0.10
PHENIX
Preliminary
PHENIX PRELIMINARY
nucl-ex/0610029
DATA
0.05
Au+Au 64 GeV
0.00
0
1
RAA~1
2
3
4
KET (GeV)
sNN
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
18
Onset of Quark Number Scaling?
DATA
(KAOS – Z. Phys. A355 (1996);
(E895) - PRL 83 (1999) 1295
sNN
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
19
Requirements for Heavy/Light Quark Opacity measurements
π0
Probes:
• Standard RAA measurements
for non-photonic electrons and π0
•Di-hadron correlations
• Comparison samples from
p+p and d+Au collisions
Non-photonic electrons
Di-hadron Correlations
Energy
300M
Events
100M
50M
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
5M
1M
20
p+p & d+Au Samples for Quark Opacity measurements
Probes:
• Standard RAA measurements
for non-photonic electrons and π0
•Di-hadron correlations
π0
No show stoppers !
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
21
Opportunities for CEP Discovery
&
New constraints for the EOS
Roy A. Lacey, Stony Brook;
INT Workshop on the QCD Critical
Point, July 28 - Aug. 22, 2008
22
QCD Critical End Point
``The discovery of the critical point
would in a stroke transform the
map of the QCD phase diagram
from one based only on reasonable
inference from universality, lattice
gauge theory and models into one
with a solid experimental basis’’
Krishna Rajagopal –
Phys.Rev.D61:105017,2000
Knowledge of the position
of the CEP is a powerful
constraint on possible models
of QCD thermodynamics
Search for the CEP must be a central objective
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
23
What Motivates the CEP Search at RHIC?
M. A. Stephanov, K. Rajagopal and E. V. Shuryak,
Phys. Rev. Lett. 81 (1998) 4816; Phys. Rev. D 60 (1999) 114028
Discovery of the
crossover transition
to the
Quark Gluon Plasma
•
•
•
Flow Measurements
Space-time
measurements
Jet Quenching
The Crossover is a necessary
requirement for existence
the CEP
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
24
How do we search for the CEP?
Theoretical Guidance?
Which variables?
Search Strategy?
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
25
Theoretical Guidance ?
Chemical
Freeze-out Curve
Theoretical
Predictions
from Lattice QCD
J. Cleymans, et al
Phys. Rev. C73, 034905 (2006)
Intriguing predictions but search for the CEP may require
investigations over a broad range of μ & T.
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
26
Which search variable/s?
Operational Ansatz
The physics of the critical point is
universal.
Members of a given universality
class show “identical” critical
properties
Stationary state variables
Dynamic variables
The CEP belongs to the same dynamic
universality class (Model H) as the liquid
gas phase transition
Son & Stephanov
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
27
Singular behavior of stationary state
variables near the CEP
s µx
Fluctuations
Stephanov, Rajagopal,Shuryak,
Phys. Rev. D 60, 114028 (1999)
2
Correlation length
Divergence of ξ restricted:
• Finite system size
ξ < size
• Finite evolution time
ξ < (time)1/z
t ~xz
z=3
• Non-monotonic dependence of event-by-event fluctuations as
a function of sNN
Net proton number fluctuation
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
28
Singular behavior of Dynamic
variables near the CEP
D~x
Diffusion Constant
-1
Son & Stephanov,
Correlation length
h ~x
.05 -.06
viscosity
Divergence of ξ restricted:
• Finite system size
ξ < size
• Finite evolution time
ξ < (time)1/z
t ~xz
z=3
• D “vanishes’’ at the CEP
• “mild’’ dependence for viscosity
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
29
The CEP belongs to the Model H dynamic
universality class - Son & Stephanov
Lacey et al.
arXiv:0708.3512 [nucl-ex]
mB
h
is a potent signal for the CEP
s
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
30
CEP Search
Kharzeev­Tuchin
Meyer
First estimate T ~ 165-170 μ ~ 150-180 MeV
Search in the region 20 £ sNN £ 62 GeV
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
31
New Constraints for the Hadronic EOS?
(
c 2 = ¶P
¶e )
Danielewicz, Lacey, Lynch
1034 Pa
EOS not very well
constrained experimentally
cs = K
Further constraints for the hadronic EOS
9 mN
» 0.15c, 0.21c
Soft and hard EOS
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
32
Requirements for Fluctuations & viscosity measurements
Probes:
• Standard fluctuations measurements for charged hadrons (+ PID)
• Flow measurements
• Femtoscopic measurements
Energy
300M
Events
100M
50M
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
5M
1M
33
For 20 £ sNN £ 100 GeV RHIC can make an
immediate and unique contribution to:
• The low-μB end of the critical point search
• Quantification of the onset of light-quark and
heavy-quark opacities.
• Quantification of the onset of QNO scaling
• Constraining the Hadronic EOS
This is achievable within realistic running periods
of ~ 20-25 weeks:
The reason people find it so hard to be happy is that they
always see the past better than it was, the present worse than
it is, and the future less resolved than it will be.
Marcel Pagnol
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
34
Indications of a crossover from
space-time Measurements
Hydrodynamic prediction
Are source images consistent
with the crossover transition ?
Courtesy S. Bass
QGP and
hydrodynamic expansion
initial state
pre-equilibrium
Puzzle ?
hadronic phase
and freeze-out
hadronization
hadronization
Koonin Pratt Eqn.
R (q) = C (q ) - 1 = 4p ò drr 2 K 0 (q, r )S (r ) (1)
Correlation
function
Encodes FSI
Source function
(Distribution of pair
separations)
A Cross Over strongly affects
the Space-time Dynamics
Inversion of this integral equation
 Source Function
Roy A. Lacey, Stony Brook;
INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
35
The transition is Not a Strong
First order Phase Transition?
t ~ 9 fm
Dt ~ 2 fm
DtLCM
arXiv:0712.4372
~ 12 fm
Outside-in burning
Therminator:
A.Kisiel et al. Comput.Phys.Commun.174, 669 (2006)
Thermal model with Bjorken longitudinal
expansion and transverse Flow
• Spectra & yields constrain thermal properties
• Transverse radius ρmax : controls
transverse extent
• Breakup time in fluid element rest frame,
t : controls longitudinal extent
• Emission duration Dt : controls tails in
long and out directions
• a controls x-t correlations
Source Function Comparison to Models Give robust life time
estimates  Consistent with Crossover transition
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
36
CEP Search
with CEP
æ 2m ö
p / p ~ expç- B ÷
è T ø
Focusing of Isentropic Trajectories

steeper p spectra at high PT
Roy A. Lacey, Stony Brook; INT
Workshop on the QCD Critical Point,
July 28 - Aug. 22, 2008
37