1. The Energy scan at RHIC Roy A. Lacey
``Search for the critical point ’’
Roy A. Lacey
Chemistry Dept.
Stony Brook University
International Workshop on Hot and Cold Baryonic Matter 2010

2. A Central Question of the Field
Roy A. Lacey, Stony Brook University;
Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

3. Phase Diagram (H2O) This knowledge is elemental to the phase
Water subjected to high pressure and temperature
A fundamental understanding requires knowledge of:
The location of the Critical End Point (CEP)
The location of phase coexistence lines
The properties of each phase
This knowledge is elemental to the phase
diagram of any substance !
Roy A. Lacey, Stony Brook University;
Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

4. Schematic QCD phase diagram
Both experiment and theory
indicate a continuous/rapid
crossover transition from the
QGP to hadronic matter
Our understanding of the QCD
Phase diagram, as well as the
properties of the different
phases is still fairly limited
Strongly or weakly coupled?
Critical point?
Coexistence curves?
Properties of each phase?
Significant experimentation is
required at several facilities to gain further insight!
Roy A. Lacey, Stony Brook University;
Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

5. The Crossover is a necessary requirement for existence
What Motivates the Search for the Critical end point (CEP)?
M. A. Stephanov, K. Rajagopal and E. V. Shuryak,
Phys. Rev. Lett. 81 (1998) 4816; Phys. Rev. D 60 (1999)
Discovery of the crossover transition, as well as new techniques for studying the properties of QCD matter!
Lattice results
Space-time measurements
Flow Measurements
Jet Quenching
The Crossover is a necessary
requirement for existence
the CEP
Roy A. Lacey, Stony Brook University;
Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

6. Results from Lattice Calculations
Hot QCD Collab
Aoki et al
Lattice calculations indicate a crossover transition
The EOS is an important outcome
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

7. Indications of a crossover from space-time Measurements
Hydrodynamic prediction
Anatomy of a RHIC collision
Courtesy S. Bass
initial state
pre-equilibrium
QGP and
hydrodynamic expansion
hadronization
hadronic phase
and freeze-out
Puzzle ?
hadronization
Koonin Pratt Eqn.
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 University;
Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

8. The transition is Not a Strong First order Phase Transition?
  Phys. Rev. Lett. 100, (2008)
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,
: controls longitudinal extent
Emission duration : 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 University;
Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

9. The scaling properties of vn and RAA constitutes an important probe!
They lend profound insights, as well as constraints for
estimates of transport coefficients!
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

10. Quenching Measurements Nuclear Modification Factor
Jet Quenching
Nuclear Modification Factor
Radiative energy loss
Dead cone
effect
Phys. Lett. B519, 199 (2001)
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

11. Scaling of Jet Quenching
Phys.Rev.C80:051901,2009
Phys.Rev.Lett.103:142302,2009
Minimum L
Requirement
i.e. no corona
quenching
Scaling also validated for different system size etc!
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

12. Scaling of Jet Quenching - Reaction plane dependence
Estimates From slope
Simultaneous scaling of RAA and v2
Further validation of path length scaling!
Very important but no new information!
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

13. Is Jet Quenching Anomalous?
Phys.Rev.Lett.103:142302,2009
~3 GeV
Different
Minimum L
Requirement?
i.e. no corona
quenching
Quenching compatible with anisotropy
 Anomalous quenching?
Future B & D measurements (RAA & v2)
at high pT will help!
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

14. Universal scaling of harmonic flow at RHIC
Phys. Rev. Lett. 98, (2007)
Mesons
Baryons
v2 scaling
v4 scaling
Universal scaling
KET & nq (nq2) scaling
validated for v2 (v4)
 Partonic flow
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

15. Flow scales across centrality
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
KET & nq (nq2) scaling validated for v2 as a function of centrality
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010 15

16. η/s from hadronic phase is very large 10-12x(1/4π)
Scaling of the Φ
Demir et al
η/s from hadronic phase is very large 10-12x(1/4π)
No room for such values!
Partonic flow dominates!
Hadronic contribution cannot be large
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

17. PHENIX Preliminary Run7
Charm flows and scales
PHENIX Final Run4
PHENIX Preliminary Run7
Minimum bias
van Hees et al.
Au+Au at √sNN = 200 GeV
J/ v2 still challenged by statistics
Strong coupling
η/s - estimate
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

18. Extraction of transport coefficient
Ideal hydro
Estimate  4π(η/s) ~ 1- 2
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

19. Extraction of transport coefficient
h/s
~ 0
h/s =
1/4p
h/s =
2 x 1/4p
h/s =
3 x 1/4p
Extracted η/s is small
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

20. apparent viscous corrections decrease with pT
Knudsen Fits
For pT > 3 GeV/c
apparent viscous corrections
decrease with pT
Excellent simultaneous fits achieved
Viscous corrections grow with pT
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

21. Viscous Corrections Onset of suppression! CGC Glauber
Quadratic dependence of δf
Breakdown of hydrodynamic ansatz for K* ~ 1
Onset of jet suppression
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

22. Opportunities with an energy scan
Onset of deconfinement
onset of quark number scaling
onset of charge asymmetry
absence of “flux tubes”
Growth of viscosity
Constraints for the EOS
Evidence for first order phase transition
Critical point search
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

23. Light Quark Opacity
Phys.Rev.C80:051901,2009
At what collision energy does the onset of light quark opacity occur?; what drives it?; additional constraint ĝ?
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

24. Heavy Quark Opacity
PRL 98, (2007)
RAA~1
Au+Au 64 GeV
nucl-ex/
Where ( ) is the onset of heavy quark opacity?; what drives it?; Why a different energy range?; constraints?
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

25. Onset of Quark Number Scaling?
DATA
(KAOS – Z. Phys. A355 (1996);
(E895) - PRL 83 (1999) 1295
Passing time scaling at very low energy
particle-mass scaling at very low energy
Where ( ) is the onset of quark number
scaling? Relationship to Quark dof ?
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

26. New Constraints for the Hadronic EOS?
Danielewicz, Lacey, Lynch
EOS not very well
constrained experimentally
Soft and hard EOS
Further constraints for the hadronic EOS
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

27. QCD Critical End Point Search for the CEP is now a central objective
``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 is now a central objective
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

28. Theoretical Guidance for CEP ?
Chemical
Freeze-out Curve
Theoretical Guidance for CEP ?
Theoretical
Predictions
from Lattice QCD
Intriguing predictions but search for the CEP requires experimental investigations over a broad range of μ & T.
Roy A. Lacey, Stony Brook University;
Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

29. 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 University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

30. Singular behavior of stationary state Stephanov, Rajagopal,Shuryak,
variables near the CEP
Stephanov, Rajagopal,Shuryak,
Phys. Rev. D 60, (1999)
Fluctuations
Correlation length
Divergence of ξ restricted:
Finite system size ξ < size
Finite evolution time ξ < (time)1/z
z=3
Non-monotonic dependence of event-by-event fluctuations as
a function of
Net proton number fluctuation
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

31. Focusing of Isentropic Trajectories
CEP Search
with CEP
Focusing of Isentropic Trajectories
steeper spectra at high PT
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

32. Singular behavior of Dynamic
variables near the CEP
Son & Stephanov,
Diffusion Constant
Correlation length
viscosity
Divergence of ξ restricted:
Finite system size ξ < size
Finite evolution time ξ < (time)1/z
z=3
D “vanishes’’ at the CEP
“mild’’ dependence for viscosity
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

33. Viscosity estimates at AGS - SPS Significant deviations
Ivanov et al
Significant deviations
From hydrodynamic
calculations
From fits
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

34. is a potent signal for the CEP
The CEP belongs to the Model H dynamic
universality class -Son & Stephanov
Lacey et al.
arXiv:  [nucl-ex]
is a potent signal for the CEP
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

35. Lacey et al. arXiv:0708.3512 [nucl-ex]
Meyer
Kharzeev-Tuchin
CEP Search
Lacey et al. arXiv:  [nucl-ex]
Search in the region
Roy A. Lacey, Stony Brook University; Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010

36. Summary The RHIC energy scan has been initiated
Analysis of data from the initial scan underway
Broad range of variables under investigation
Additional beam collision energies expected in 2011
Stay tuned for a robust set of analysis results
Roy A. Lacey, Stony Brook University;
Hot and Cold Baryonic Matter, Budapest, Aug. 15 – 20, 2010