1. Current status of Thermalization from available STAR results
Outline
Why we need to address this issue
What are the characteristic signatures
What have we learned so far
Bedanga Mohanty
VECC,Kolkata

2. Thermalization : Why address this topic
(A) To establish Quark-Gluon Plasma
“For our purposes here, we take the QGP to be a (locally)
thermally equilibrated state of matter in which quarks and
gluons are deconfined from hadrons, so that color degrees
of freedom become manifest over nuclear, rather than merely
nucleonic, volumes.”
STAR Collaboration : Nucl. Phys. A 757 (2005) 102

3. Thermalization : Why address this topic
(B) To explore the QCD Phase Diagram
Temperature for in the phase diagram has a meaningful definition for a system in thermal equilibrium
Our Run 10 physics

4. Thermalization : Why address this topic
(C) To understand several physics conclusions at RHIC
Most theories in our field based on assumption of thermal
equilibrium or close to thermal equilibrium
(1)
(2) Lattice QCD assumes it and provides EOS for many phenomenology/theoretical work
Phys. Rev. Lett. 99 (2007)
(3)
Boltzman equation for isotropic system,
no external force and with relaxation
time approximation
-df/dt = f - f0/relax
f = f0 + A exp (-t/relax)
f --> f0 (equilibrium dist) if t >> relax
Most models now days work with such
approximations
Recombination/coalescence

5. Basic features for a Thermalized System
What happens when we have a thermalized system :
(A) Maximum Entropy - dS/dt = 0
Processes are reversible (Initial <===> Final) (Ideal case)
-- To show experimentally is challenging (impossible?)
(B) Space-momentum distributions reach equilibrium values
-- Can we access this experimentally
(C ) Interactions among constituents saturate. (State in thermal
equilibrium has no knowledge of past)
-- Can we demonstrate this experimentally

6. STAR Experiment

7. Kinetic Freeze-out Distributions
Exponential distribution does not uniquely mean we have a thermal system.
Multi-particle production process
(no assumption of thermalization)
dN/dyd2pT ~ Exp ( - pT/E/2N )*
Thermal system
dN/dyd2pT ~ Exp ( - pT/E/3N )
Factor of 3/2 : invariant momentum
space (d3p/E) not equal to
Thermodynamic Momentum space
(d3p).
Experimentally difficult to distinguish
the two.
Assumption : average matrix element square is not strongly pT dependent.

8. Kinetic Freeze-out Distributions
Slope of pT distribution : Two component - Random part +
Collective part
Random Part ~ E/N
Intensive quantity independent
of system size
Collective part can also occur for systems away from equilibrium
Indicates final state interactions,
which will eventually drive system
towards equilibrium.
scattering > expansion
STAR : Phys. Rev. C 79 (2009) 64903
Comparison with pp leads to
Interpretations being inconclusive ?
STAR : Phys. Rev. C 78 (2008) 44906

9. Kinetic Freeze-out Distributions
STAR : Phys. Rev. C 74 (2006) 54902
Ideal hydrodynamics
Rx ~ 1/√mT
Viscous terms break scaling
R2L ~ 0 T/mT - 19/16 s/0
STAR Preliminary
Both Au+Au and p+p
show scaling with 1/√mT
Conclusions inconclusive ?

10. Chemical Freeze-out Distributions
Tch = 163 ± 4 MeV
B = 24 ± 4 MeV
STAR : Phys. Rev. C 79 (2009) 34909
In central collisions, thermal model fit well with S = 1. The system is thermalized at RHIC ? .

11. Chemical Freeze-out Distributions
(A) Assumptions :
,T are constant along freeze-out hyper surface
Simultaneous freeze-out
(but mean free path different for different particles)
Flow 4-velocity common to all particle species
Hadron masses and decay widths do not change with T
(B) Nice fits also to e+e-, pA
( C )Multi-particle production
Ed/d3p1 ~ F(P-p1) < | M (P, p1…pN)|2>
Matrix element
For 2->N process
Phase space
+ Conservation
~ Exp(-pT1/Tslope)
Fugacity
~ exp (/T)
Decides yields
J. Cleymans, K. Relich
Phys.Rev.C60:054908,1999
Equilibrium picture not unique

12. Freeze-Out Distributions
By definition a state in thermodynamic equilibrium has
no knowledge of past
May be we should look at early time distributions

13. Early time Collectivity
Substantial portion of Elliptic flow developed early
Low pT : Heavier hadrons lower flow ( ~ hydrodynamic pattern)
High pT : Flow grouped along baryon-meson lines ( ~ Hadronization by partonic recombination)
All pT : Flow similar for hadrons with strange and light quark (~ developed at partonic stage)
Does this collectivity reflect enough partonic interactions to claim Thermalization ?

14. Early Time collectivity
STAR : Phys. Rev. Lett. 95 (2005)
Away side associated hadron mean pT
The away side jet traverses a large amount of matter. The interactions seem to drive particles from the two sources, jet fragmentation and the bulk medium, toward equilibration. This may in turn imply a high degree of thermalization within the medium itself.

15. Loss of correlation due to interactions
For a thermal system
Correlations (in momentum) reach equilibrium values
Physical observables which are sensitive to interactions -
Such as average elliptic flow saturate with density and time
Momentum correlations saturate with density and time
Hints available : But we have not ruled out other physical
Processes (minijets ?)

16. Saturation of interactions : v2 saturate
Proposed by Borghini & Ollitrault,
PLB (2006)
v4/v22
Part of it in
STAR : Phys. Rev. C 66 (2002) 34904
The scaling is expected to be poor for pions. It is expected to break down when pt/m exceeds
umax, the maximum value of the transverse 4-velocity of the fluid.
Hints available, but U+U collisions
in Run 11 Or LHC Heavy Ions will
hopefully settle the issue
High statistics PID
results needed

17. Other STAR Measurements
Heavy quark Meson (D-Dbar) Correlations
Loss of correlations in AA relative to pp

18. Conclusions Measurements Conclusive and Remark
Supports Thermalization
Conclusive and Remark
PID spectra and mean pT
yes
Not unique
Particle Ratios
Not unique & pp, e+e-, pA same description
HBT
Not unique, pp same behaviour
PID v2(pT), away side mean pT
Could be
Need models
v2 vs. dN/dy
Hints
More measurements, also for v4/v22
pT Correlations
More measurements
Next talks what we can do in coming years in STAR to address
this important topic

19. Back ups
Phys. Rev. Lett. 98 (2007) 62301