1. Stony Brook University
- Soft Physics -
Flow & Bulk Properties
Roy A. Lacey
Chemistry Dept.
Stony Brook University
Soft Physics is like an old friend - highly thought of, but often taken for granted
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

2. Phase Diagram (H2O) This knowledge is elemental to the phase
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; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

3. Schematic Phase Diagram (QCD)
A fundamental understanding
Of the QCD phase diagram
is still lacking
A central goal of our field is to
map out the QCD Phase diagram
and to establish the properties
of the different phases
--LHC, RHIC, SPS, FAIR, etc
Soft physics plays an
essential role in studies of QCD phase diagram
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

4. What Constitutes Soft Physics?
Straw
What Constitutes Soft Physics?
A Straw man definition of soft physics
“Hard physics”
Particle production characterized
by large momentum transfer
Interactions occur at the partonic level
Small coupling constants
Binary scaling
etc
99.5% soft
“Soft physics”
Particle production characterized
by small momentum transfer
Large coupling constants
Participant scaling
etc
Phenomenological modeling
Particle production is dominated by soft particles
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

5. The many roles of Soft Physics?
Straw
The many roles of Soft Physics?
“Interrogative Role”
Energy/entropy density?
Thermalization ?
Space-time extent?
transport coefficients – η/s?
Equation of state - cs
“Support Role”
Event Characterization
Event Plane determination
etc
Measurements
Multiplicity
Geometry
Event Anisotropy
– Reaction plane
Measurements
Multiplicity
Femtoscopy
Flow
etc
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

6. Event Characterization?
Collision Centrality
Collisions are described as a superposition of elementary nucleon-nucleon collisions
(e.g. Glauber model)
The number of nucleon-nucleon collisions ( Ncoll ) and the number of participant nucleons ( Npart ) depend on the impact parameter
Each collision/participant contributes to particle production and consequently to multiplicity
Numerical calculations give Ncoll, Npart, ε, R, S, etc
Soft physics plays a crucial role in the determination of important geometrical quantities routinely used in our field.
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

7. Event Characterization?x y
YRP
Reaction Plane
The reaction plane is the plane defined by the impact parameter and the beam direction
The orientation of the reaction plane can be estimated from the global event anisotropy
Anisotropic transverse flow is a correlation between the azimuth [=tan-1 (py/px)] of the produced particles and the reaction plane!
Unambiguous signature of collective behavior
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

8. “Interrogative Role” of Soft Physicsu
Phases and Properties of QCD ?
Flow Correlations
Multiplicity & particle ratios
“Interrogative Role” of Soft Physics
Femtoscopic Correlations
Soft physics provide crucial information on reaction
thermodynamics, dynamics, and provide constraints for
the extraction of transport coefficients (η/s, cs, λ, etc)
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

9. Multiplicity Measurements!
Why ?
Multiplicity provides insights on:
The Entropy of the system created in the collision
How the initial energy is redistributed to produce particles in the final state
Energy density of the system
(via Bjorken formula)
Mechanisms of particle production
(hard vs. soft)
Thermalization
In central AuAu collisions at RHIC (s=200 GeV) about 5000 particles are created
Multiplicities are commonly expressed as charged particle densities in a given range of polar angle
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

10. Multiplicity Measurements!
pT = pL
q = 45 (135) degrees
h = ±0.88
pT>pL
Mid-rapidity region
Particles with pT>pL produced at q angles around 90°
Bjorken formula to estimate the energy density in case of a broad plateau at midrapidity invariant for Lorentz boosts:
pL>>pT
eBJ ~ GeV/fm3
~ 35 – 100 ε0
Fragmentation regions:
Particles with pL>>pT produced in the fragmentation of the colliding nuclei at q angles around 0° & 180°
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

11. Multiplicity Measurements!
central
central
peripheral
peripheral
energy s
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

12. Scaling properties of Multiplicity Measurements!
Scaling variables:
Rationale
Simple test of the scaling with Npart
If particle production scales with Npart, these variables should not depend on the centrality of the collisions
Facilitates rudimentary comparison with pp collisions where Npart=2
total multiplicity normalized to the
number of participant pairs
particle density at mid-rapidity
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

13. Scaling properties of Multiplicity Measurements!
Scaling variables:
Rationale
Simple test of the scaling with Npart
If particle production scales with Npart, these variables should not depend on the centrality of the collisions
Facilitates rudimentary comparison with pp collisions where Npart=2
total multiplicity normalized to the
number of participant pairs
particle density at mid-rapidity
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

14. Scaling properties of Multiplicity Measurements!
Yield per participant pair increases by ≈ 25% from peripheral to central Au-Au collisions
Is this due to a contribution of the hard component of particle production?
The ratio 200 / 19.6 is independent of centrality
A two-component fit with dN/dh  [ (1-x) Npart /2 + x Ncoll ] gives compatible values of x (≈ 0.13) at the two energies
From Ratio:
Factorization of centrality (geometry) and s (energy) dependence
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

15. Scaling properties of Multiplicity Measurements!
The dN/dh per participant pair at mid-rapidity in central heavy ion collisions increases with ln s from AGS to RHIC energies
The s dependence is different for pp and AA collisions
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

16. Scaling properties of Multiplicity Measurements!
Total multiplicity:
Nch scales with Npart
Nch per participant pair different from p-p, but compatible with e+e-, collisions at the same energy
Simple scaling rules dominate!
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009 16

17. Extrapolation of dNch/dhmax vs s
Soft physics at the LHC
Extrapolation of dNch/dhmax vs s
Fit to dN/dh  ln s
Saturation model (dN/dh  sl with l=0.288)
The first 10k events at the LHC could be decisive
Central collisions
Saturation model
Armesto Salgado Wiedemann, PRL 94 (2005)
Models prior to RHIC
Extrapolation of dN/dhln s
5500
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

18. Soft physics & Hadrochemisty
Questions of Interest
At freeze-out;
is the fireball in thermal and chemical equilibrium?
what is the temperature Tch ?
what is the baryonic content of the fireball ?
find T and mB values that minimize the difference between model predicted and measured particle ratios
Analysis with a statistical hadronization ansatz
Chemical equilibrium assumed
One can calculate the multiplicity of various hadronic species
Model comparisons could then be made to data.
Free parameters of the model - µ and T.
Riexp and Rimodel are the measured and predicted particle ratios
si is the (statistical + systematic) error on experimental points
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

19. Soft physics & Hadrochemisty
A. Andronic et al., Nucl. Phys. A772 (2006) 167.
Fit to measured particle ratios
c2 contour lines
PbPb - Ebeam=40 GeV/ nucleon - s=8.77 GeV
Minimum of c2 for: T=156±3 MeV mB=403±18 MeV
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

20. Soft physics & Hadrochemisty
A. Andronic et al., Nucl. Phys. A772 (2006) 167.
Fit to measured particle ratios
c2 contour lines
AuAu - s=130 GeV
Minimum of c2 for: T=166±5 MeV mB=38±11 MeV
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

21. Soft physics & Hadrochemisty
Extracted T & µB values
neutron stars
Baryonic Potential B [MeV]
early universe
Chemical Temperature Tch [MeV]
200
250
150
100 50
400
600
800
1000
1200
AGS
SIS
SPS
RHIC
quark-gluon plasma
hadron gas
deconfinement
chiral restauration
Lattice QCD
atomic nuclei
For s >≈ 10 GeV chemical freeze-out very close to phase boundary
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

22. Source Imaging Methodology (3D)
Expand R(q) and S(r) in
Cartesian Harmonic basis
(Danielewicz and Pratt nucl-th/ )
3D Koonin Pratt Eqn.
Substitute (2) and (3) into (1)
The 3D integral equation is reduced to a set of 1D relations for
different l coefficients  moments
Reliable measurement of the full Source Function in 3D !
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

23. Robust Experimental Source Functions obtained from moments
Correlation Moments
PHENIX Data
Robust Experimental Source Functions obtained from moments
Contributions from
l > 6 is negligible
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

24. Thermal model with Bjorken longitudinal expansion and transverse Flow
Model Comparison
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; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

25. Why Flow Measurements? From ET Distributions
Control Params.
Expect Large Pressure Gradients  Hydro Flow
Straightforward to make a variety of scaling tests
Deviations of Elliptic & hexadecapole flow from ideal hydrodynamic expectations -> Constraints for thermalization, sound speed, viscosity, etc.
Detailed integral and differential Measurements now available
What do they tell us ?
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

26. Central Arms
Recent Measurements
New RXN
detector
RXN
RXN
BBC/MPC
BBC/MPC
PHENIX Preliminary
Event planes
Five separate measurements of v2 and v4 in the same experiment is decisive
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

27. Quark-Like Degrees of Freedom Evident
KET – CQN Scaling
It is often argued that
Strong coupling is
Incompatible with quark
degrees of freedom
Phys. Rev. Lett. 98, (2007)
Mesons
Baryons
How strong is “strong”?
Quark-Like Degrees of Freedom Evident
As well as an Indication for strong coupling?
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

28. Predicted Signal for hydrodynamic behavior -> local equilibrium
Recombination
P. Kolb et al
Is there value added
for v4 Measurements?
Predicted Signal for hydrodynamic behavior
-> local equilibrium
Quark recombination models predict a specific relationship between the ratio v4/(v2)2 for hadrons and partons
Ollitrault et al
This gives the scaling relation between Baryons and Mesons
These predictions can be in/validated
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

29. KET and CQN Scaling for v4 Further Indication of strong coupling?
PHENIX
Preliminary
KET & nq2 scaling validated for v4
Further Indication of strong coupling?
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

30. Flow is universal
PHENIX
Preliminary
V4 = k(v2)2 where k is the same for different particle species.
Demonstrates the universal nature of vn
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

31. Can we estimate the strength of the coupling and the degree of
thermalization ?
From First Rate Flow Data
The extraction of a small value of η/s linked to
a short mean free path λ, would lend decisive insight
Viscous hydro
Transport
Several Hybrids of
Hydro
and Transport
We now consider one hybrid approach
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

32. Hybrid Approach
Operational Ansatz (Ollitrault)
The Boltzmann equation reduces to hydrodynamics when the mean free path is small
C. Marle, Annales Poincare Phys.Theor. 10,67 (1969).
System characterized by two
Dimensionless numbers
The liquidity or dilution number (D)
The Knudsen number (Kn)
Applicability of Boltzmann
D << 1
Hydrodynamics is the limit
Kn << 1
One can then use transport to study and parameterize the approach to hydrodynamic behavior (local equilibrium)
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

33. This provides a simple fitting ansatz for the data and
Hybrid Approach
Degree of local equilibrium
Schematic calculation
For a given value of D
Functional form does not depend
on D
Determined from
fit to calculations
This provides a simple fitting ansatz for the data and
Straightforward procedure for local equilibrium estimate
“Any untaken shot is 100% missed ”
Wayne Gretzky
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

34. Use procedure to study simulated data Operational ansatz validated
An Operational Test
Use procedure to study simulated data
Operational ansatz validated
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

35. 10-15% larger than for fluid with η/s =1/4π in central events.
Data and Fits
PHENIX Preliminary
Within model ansatz straightforward to estimate degree of local equilibrium!
10-15% larger than for fluid with η/s =1/4π in central events.
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

36. Truth or Myth – Good fits
to the data
PHENIX Preliminary
Hydro like Npart dependence for v4
Similar Conclusions
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

37. function of centrality etc.
Data Fits
Fits allow η/s estimate as
function of centrality etc.
λ = 0.3 – 0.35
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

38. Centrality dependent CQN scaled v2 η/s for quarks directly ?
PHENIX Preliminary
RAA out-of-plane is relative constant with centrality at low pT.
η/s for quarks directly ?
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009
Arkadij Taranenko, QM2009
2018/8/7 38 38

39. Transport Coefficient Estimates 2 X the conjectured lower bound
Lacey & Taranenko nucl-ex/
2 X the conjectured lower bound
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

40. t eBjorken ~ 5 - 15 GeV/fm3 “Thermalized” partonic Fluid! (s)QGP?
t = z/c
t = -z/c
Particle ratio
measurements
“Thermalized” partonic Fluid!
(s)QGP?
Flow
measurements
Multiplicity
measurements
eBjorken ~ GeV/fm3
~ 35 – 100 ε0
A “little Bang” occurs
in RHIC collisions
Gold
nucleus
v~0.99c
z:collision axis
Emerging Picture
Soft Physics plays a crucial role!
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

41. End
Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009