Dynamic timescales from STAR Year1
Mike Lisa, Ohio State University, STAR Collaboration
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
1
Overview
• ~ 1.5 year from initial data-taking in new energy regime (s=130 GeV)
• overall picture / underlying driving physics not fully clear
Outline
• Ultrarelativistic heavy ion collisions
• STAR at RHIC
• Collective (radial and elliptic) flow measurements
• Initial quantitative success of hydrodynamics
• Blast-wave parameterization
• Two-particle correlations (HBT)
• STAR HBT and the “HBT Puzzle”
• Data/fit-driven extraction of dynamical timescales - consistent description of data?
• azimuthally-sensitive HBT
• K-p correlations
• short-lived resonance yields
• balance functions
• Summary
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
2
Why heavy ion collisions?
The “little bang”
• Bulk properties of strongly-interacting matter
• Extreme conditions (high density/temperature):
expect a transition to new phase of matter…
• Quark-Gluon Plasma (QGP)
• partons are relevant degrees of freedom over large
length scales (deconfined state)
• believed to define universe ~ ms after BB
• Study of QGP crucial to understanding QCD
• low-q (nonperturbative) behaviour
• confinement (defining property of QCD)
• nature of phase transition
• Heavy ion collisions ( “little bang”): the only
way to experimentally probe the deconfined state
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
3
Stages of the collision - several timescales
low-pT hadronic observables
QGP and
hydrodynamic expansion
initial state
hadronization
hadronic phase
and freeze-out
pre-equilibrium
CYM & LGT
dN/dt
PCM & clust. hadronization
NFD
NFD & hadronic TM
1 fm/c
string & hadronic TM
10 fm/c
50 fm/c
time
PCM & hadronic TM
Chemical freeze out
“endSTAR
result” looks very similar
Kinetic freeze out
whether
HBTa QGP was formed or not!!!
3 Apr 2002
5 fm/c
malisa - colloquium at Duke
4
uRQMD simulation of Au+Au @ s=200 GeV
pure hadronic & string
description (cascade)
~OK at lower energies
applicability @ very high
density (RHIC) unclear
produces too little
collective flow at RHIC
STAR
HBT
courtesy uRQMD collaboration
3 Apr 2002
malisa - colloquium at Duke
5
Achieving the collision experimentally
STAR
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
6
Measuring the
ashes: Geometry
of STAR
a midrapidity, large-acceptance hadron detector
Magnet
Time
Projection
Chamber
Coils
Silicon
Vertex
Tracker
TPC Endcap
& MWPC
FTPCs
ZCal
ZCal
Vertex
Position
Detectors
Endcap
Calorimeter
Central Trigger
Barrel or TOF
Barrel EM
Calorimeter
RICH
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
7
Peripheral Au+Au Collision at 130
AGeV
Data Taken June 25, 2000.
Pictures from Level 3 online display.
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
8
Au on Au Event at CM Energy ~ 130 AGeV
Data Taken June 25, 2000.
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
9
First RHIC spectra - an explosive source
• various experiments agree well
T
explosive
source
T,b
STAR
HBT
1/mT dN/dmT
purely thermal
source
1/mT dN/dmT
• different spectral shapes for
particles of differing mass
 strong collective radial flow
3 Apr 2002
light
heavy
mT
light
heavy
mT
• very good agreement with hydrodynamic
prediction
malisa - colloquium at Duke
data: STAR, PHENIX, QM01
model: P. Kolb, U. Heinz 10
Hydrodynamics: modeling high-density
scenarios
• Assumes local thermal equilibrium (zero mean-free-path limit) and solves
equations of motion for fluid elements (not particles)
• Equations given by continuity, conservation laws, and Equation of State (EOS)
• EOS relates quantities like pressure, temperature, chemical potential, density
– direct access to underlying physics
• Works qualitatively at lower energy
but always overpredicts collective
effects - infinite scattering limit
not valid there
• freezeout when energy density falls
below some threshold
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
lattice QCD input
11
Hydro time evolution of
non-central collisions
• entrance-channel aniostropy in x-space
 pressure gradients (system response)
 p-space anisotropy (collective elliptic flow)
• correlating observations with respect to
event-wise reaction plane allows much
more detailed study of reaction dynamics
Equal energy density lines
STAR
self-quenching
effect HBT
3 Apr 2002
sensitive to early
malisapressure
- colloquium at Duke
P. Kolb, J. Sollfrank,
and U. Heinz
12
Data: Azimuthal-angle distribution
versus reaction plane
v2  cos2
dN
~ 1  2v2 cos2
or
d
v2:
• quantifies anisotropy
• increases from central to peripheral collisions
• sensitive to EoS @ lower s
STAR
HBT
  particle-reaction plane
3 Apr 2002
malisa - colloquium at Duke
13
Very large event anisotropies seen by
STAR, PHENIX, PHOBOS
• space-momentum connection clear in
multiplicity dependence
v2
• different experiments agree well
• finally, we reach regime of quantitative
hydro validity
 evidence for early thermalization
centrality
• AGS & lower energies: magnitude
described by hadronic cascade models
• RHIC; Hydro description for central to
mid-central collisions
– 26% more particles in-plane than
out-of-plane (even more at high pT)!!
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
14
Local thermal equilibrium versus Low
Density Limit
SPS (s=17 GeV); Low-Density-Limit
and Hydro bracket pT dependence
p
RHIC; pt dependence quantitatively
described by Hydro
p
Charged
particles
pt dependence sensitive to early thermalization
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
15
Blastwave parameterization - “hydrolike source”
analytic description of freezeout distribution: exploding thermal source
bt
R
 
 mT

f x, p   K1
cosh  
 T

pT
sinh  cos s   p 
T
e





 1  y 2  2 x 2 / R y 
STAR
HBT
e
2
 t32 Apr
/ 2002
– Flow
• Space-momentum correlations
• <> = 0.6 (average flow rapidity)
• Assymetry (periph) : a = 0.05
– Temperature
• T = 110 MeV
– System geometry
• R = 13 fm (central events)
• Assymetry (periph event) s2 =
0.05
– Time: emission duration
•  = emission duration
malisa - colloquium at Duke
16
Spectra and v2 from blast wave
• Transverse momentum spectra
– T  110 MeV
–   0.6
1/mT dN/dmT (a.u.)
STAR preliminary
• PID Elliptic flow
– T=101  24 MeV – a = 0.04  0.01
–  = 0.61  0.05 – s2 = 0.04  0.01
pK-
p
STAR
HBT
mT -
2]
m3 Apr
[GeV/c
2002
STAR, at
PRL
87 182301 (2001)
malisa - colloquium
Duke
17
The other half of the story…
• Momentum-space characteristics of freeze-out appear well understood
• “real” model (hydro)
• parameterization of real model (blastwave)
• What about space-time degrees of freedom ?
• Probe with two-particle intensity interferometry (“HBT”)
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
18
“HBT 101” - probing source geometry
p1
r1
x1
p source
(x)
1m
x2
p2
5 fm
T 
  
  i( r2  x 2 )p 2
i ( r1  x1 )p1
1 {  
U(x1, p1)e
U(x 2 , p2 )e
2
  i( r1  x 2 )p1   i( r2  x 1 )p 2
 U(x 2 , p1)e
U(x1, p2 )e
}
r2

*TT  U1*U1  U*2 U 2  1  eiq( x1  x 2 )
Measurable!
C (Qinv)
Creation probability (x,p) = U*U
P(p1, p 2 )
2
C(p1, p 2 ) 
 1 ~
 (q )
P(p1 )P(p 2 )
F.T. of pion source
Width ~ 1/R
2
1
  
q  p 2  p1
STAR
HBT

0.05
0.10
Qinv (GeV/c)
3 Apr 2002
malisa - colloquium at Duke
19
“HBT 101” - probing the timescale of emission
C(qo , qs , ql )  1    e 
 q o2 R o2  q s2 R s2  q l2 R l2
Decompose q into components:
qLong : in beam direction
qOut : in direction of transverse momentum
qSide :  qLong & qOut
 
 
  

~2
K  ~
x out  b t 

2 
2
~
R s K  x side K

~2
2
Rl K  ~
x long  bl t
R o2
K

 

K
 
  

K
~
xx x
Rout
Rside
(beam is into board)
STAR
HBT
d 4 x  S( x, K )  f ( x )

f 
4
 d x  S( x, K )
3 Apr 2002
R o2
 R s2
 b  
2
x out , x side   x, y 
beware this “helpful” mnemonic!
malisa - colloquium at Duke
20
Large lifetime - a favorite signal of “new”
physics at RHIC
• hadronization time
(burning log) will
increase emission
timescale (“lifetime”)
• measurements at lower
energies (SPS, AGS)
observe ~3 fm/c
with
transition
~
• magnitude of predicted
effect depends strongly
on nature of transition
3D 1-fluid Hydrodynamics
Rischke & Gyulassy
NPA 608, 479 (1996)
ec
“e”
…but lifetime determination is complicated by other factors…
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
21
First HBT data at RHIC
“raw” correlation function projection
Coulomb-corrected
(5 fm full Coulomb-wave)
Data well-fit by Gaussian parametrization
C(qo , qs , ql )  1    e 
 q o2 R o2  q s2 R s2  q l2 R l2

1D projections of 3D correlation function
integrated over 35 MeV/c in unplotted components
STAR Collab., PRL 87 082301 (2001)
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
22
World HBT excitation
function
midrapidity, low pT pfrom central AuAu/PbPb
• decreasing  parameter partially due
to resonances
• saturation in radii
• geometric or dynamic
(thermal/flow) saturation
• the “action” is ~ 10 GeV (!)
• no jump in effective lifetime
• NO predicted Ro/Rs increase
(theorists: “data must be wrong”)
• Lower energy running needed!?
STAR
HBT
Collab., PRL 87 082301 (2001)
3STAR
Apr 2002
malisa - colloquium at Duke
23
Hydro attempts to reproduce data
generic
hydro
long
out
side
STAR
HBT
3 Apr 2002
• KT dependence approximately reproduced
 correct amount of collective flow
• Rs too small, Ro & Rl too big
 source is geometrically too small and
lives/emits too long in models
• Right dynamic effect / wrong space-time
evolution???
 the “RHIC HBT Puzzle”
malisa - colloquium at Duke
24
“Realistic” afterburner not enough
pure hydro
hydro + uRQMD
RO/RS
explosive space-time scenario
suggested by observation not
reproduced by realistic models
1.0
STAR data
STAR
0.8
HBT
3 Apr 2002
malisa - colloquium at Duke
25
Now what?
• “Realistic” dynamical models cannot adequately describe freeze-out distribution
• Seriously threatens hope of understanding pre-freeze-out dynamics
• Raises several doubts
– is the data consistent with itself ? (can any scenario describe it?)
– analysis tools understood?
• Attempt to use data itself to parameterize freeze-out distribution
• Identify dominant characteristics
• Examine interplay between observables (e.g. flow and HBT)
• Isolate features generating discrepancy with “real” physics models
• focus especially on timescales
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
26
Blastwave parameterization:
Implications for HBT: radii vs pT
Assuming b, T obtained from spectra fits
 strong x-p correlations, affecting RO, RS differently
K
2
RO
pT=0.2
2
 RS
 b  
2
RO
K
RS
pT=0.4
STAR
HBT
3 Apr 2002
“whole source” not viewed
malisa - colloquium at Duke
27
Blastwave: radii vs pT
Magnitude of flow and temperature from
spectra can account for observed drop in
HBT radii via x-p correlations, and Ro<Rs
…but emission duration must be small
K
Four parameters affect HBT radii
STAR data
pT=0.2
model: R=13.5 fm, =1.5 fm/c
T=0.11 GeV, 0 = 0.6
K
pT=0.4
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
28
Pion source geometry in peripheral events
Typical evolution in the hydro world
Out-of-plane
Circular
In-plane
Time
• In peripheral events
– Start out-of-plane
– Evolve towards in-plane source
• Source shape: a measure of the freeze-out time scale
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
29
Measuring the anisotropic shape: HBT with
respect to reaction plane
– For example Rside
p=90°
Out-of-plane Circular
In-plane
Rside2 (fm2)
• Anisotropic geometry leads to
oscillations of the radii
Rside (small)
Rside (large)
Reaction
plane
Naïve view with no flow
 (degree)
p=0°
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
30
Out-of-plane extended source
~ short system evolution time
• Same blastwave parameters as required to
describe v2(pT,m), plus two more:
– Ry = 10 fm  = 2 fm/c
• Both p-space and x-space anisotropies
contribute to R()
– mostly x-space: definitely out-of-plane
STAR preliminary
• calibrating with hydro, freezeout ~ 7 fm/c
Ros2 - new “radius” important for
azimuthally asymmetric sources
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
31
Kaon – pion correlation:
dominated by Coulomb interaction
Smaller source  stronger
(anti)correlation
K-p correlation well-described by:
• Static sphere (no radial flow):
– R= 7 fm
• Blast wave with same
parameters as spectra, HBT
But with non-identical particles, we
can access more information…
STAR preliminary
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
32
Initial idea: probing emission-time ordering
purple K emitted first
green p is faster
• Catching up: cosY  0
•
•
purple K emitted first
green p is slower
• Moving away: cosY  0
•
•
Crucial point:
kaon begins farther in “out” direction
(in this case due to time-ordering)
STAR
HBT
3 Apr 2002
long interaction time
strong correlation
short interaction time
weak correlation
• Ratio of both scenarios
allow quantitative study of
the emission asymmetry
malisa - colloquium at Duke
33
measured K-p correlations - natural consequence
of space-momentum correlations
• clear space-time asymmetry observed
• C+/C- ratio described by:
– static (no-flow) source w/ tK- tp=4 fm/c
– “standard” blastwave w/ no time shift
• We “know” there is radial flow
 further evidence of very rapid freezeout
• Direct proof of radial flow-induced
space-momentum correlations
STAR preliminary
Pion
STAR
<pt> HBT
= 0.12 GeV/c
3 Apr 2002
Kaon
<pt> = 0.42 GeV/cmalisa - colloquium at Duke
34
A consistent picture within blastwave

pT
 mT
 T sinh  coss p 
cosh e
1
 
f x, p   K1
 T
parameter
Temperature
T  110 MeV
Radial flow
0  0.6
velocity
Oscillation in a  0.04
(minbias)
radial flow
Spatial
anisotropy
Radius in y
s2  0.04



y   x / Ry e
2
2 2
spectra

v2(m,pT)

HBT(pT,)

K-p









t 2 / 22
(minbias)
Ry  10-13 fm




(depends on b)
Emission
duration
time delay
STAR
HBT
3 Apr 2002
  2 fm/c

<tK>-<tp>=0
malisa - colloquium at Duke
35
Consistency with other probes?
• Focussing on transverse plane, consistent picture within simple parameterization
• explosive freezeout - short duration of kinetic freezeout kinetic
• out-of-plane-extended shape: “short” evolution time to kinetic freezeout tkinetic
• Other probes of timescales:
• RL(mT):
tkinetic
• short-lived resonance survival: tkinetic - tchemical
• Balance Functions:
STAR
HBT
3 Apr 2002
(kinetic ?)
tkinetic - tcharge creation (kinetic ??)
tkinetic
malisa - colloquium at Duke
36
Rlong from HBT
• R.H.I.C. - strong longitudinal expansion
• Rlong probes longitudinal homogeneity lengths
 size of region emitting a given pZ
• In Bjorken picture: probe emission time tkinetic
– How wide does the cell become after evolving during tkinetic?
bt
Rlong
STAR
HBT
bl
3 Apr 2002
Kt = pair Pt
Rside
Rout
bl
malisa - colloquium at Duke
37
From Rlong: tkinetic = 8-10 fm/c
(compare ~7 fm/c from anisotropic shape)
Simple Sinyukov formula (S. Johnson)
– RL2 = tkinetic2 T/mT
• tkinetic = 10 fm/c (T=110 MeV)
STAR
HBT
3 Apr 2002
B. Tomasik (~3D blast wave)
– tkinetic = 8 fm/c (p+p+)
– tkinetic = 9.2 fm/c (p-p-)
malisa - colloquium at Duke
38
Resonance survival rate
kinetic rescattering
d1
d2
R
R
chemical freeze out
T~170 MeV
thermal freeze out
T~110MeV
• short-lived resonances
– K*(892)  = 3.9 fm/c
– (1520)  = 12.8 fm/c
d1 • Rescattering of daughters
between chemical and kinetic
d2
freeze-out washes out the
time resonance signal
– Sensitive to tkinetic - tchemical
UrQMD: signal loss in invariant mass reconstruction
K*(892) (1520)
SPS
(17 GeV) [1]

66%
50%
26%
RHIC (200GeV) [2]
55%
STAR
HBT
3 Apr 2002
30%
23%
malisa - colloquium at Duke
39
Resonance reconstruction (via combinatorics):
K* and (1520) from STAR
K*0 K+ + p-
K*0 K- + p+
(1520)  p + K-
minv (GeV/c2)
multiplicity for |y| <0.5
STAR
0
K*
= 10.0  0.8  25%
HBT
|y|<0.5
3 Apr 2002
Upper limit estimation: dN/dy preliminary
(1520) |y|<1 < 1.2 at 95% C. L.
malisa - colloquium at Duke
40
Resonance survival rate:
Rafelski’s picture
• Combining both K* and (1520):
–   tkinetic - tchemical ~ 0-3 fm/c
Upper limit
• Caveats:
– partial  “quenching” (width
broadening) allows for higher T,
still small 
– Tchem~100 MeV ?!?
• Thermal fit: T ~ 170 MeV
– no evidence of low-pT suppression
– Possible K* regeneration?
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
41
Summary
• Strong collective flow at RHIC
• Blastwave parameterization
– clear from p-space observables
• well-described by hydro
– important implications for x-space
observables (HBT, balance functions)
– incorporates implicitly x-p correlations
– consistent picture of several observables
• central: dN/dpT, HBT(pT), K-p
– 3 views of radial flow
• peripheral: v2(m,pT), HBT()
• Problem! - HBT systematics not
reproduced by hydro
– out-of-plane extended source!
– just a “toy,” but consistency suggests the x-p
interplay and basic description is right
• useful feedback to modelers (?)
– short evolution time, ~”instant” freezout!
– right dynamic effects, but wrong
evolution?
– analysis tools “miscalibrated,” or
something wrong in model, or…
– systematics point to timescale
• Other estimators of timescales
• Try to provide feedback to modelers...
STAR
HBT
3 Apr 2002
**
– RL(mT), resonance yields**, balance fctns**
– suggest timescales ~consistent with
blastwave estimates
rathermalisa
different
analysis/models,
with several open issues
- colloquium
at Duke
42
Summary:
Collision time scale from STAR data
~1 fm/c
explosive!!
Balance function (require flow)
Resonance survival
Rout, Rside
Rlong (and HBT wrt reaction plane)
dN/dt
~7-10 fm/c
rapid!!
1 fm/c
STAR
HBT
3 Apr 2002
5 fm/c
10 fm/c
20 fm/c
Chemical freeze out
malisa - colloquium at Duke Kinetic freeze out
time
43
The End
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
44
Some speculative ideas
• Super-cooling of the QGP
phase
• Many bubble system (M.
Gyulassy)
• Brutal breaking of the chiral
symmetry (A. Dumitru)
– Bubble carry flow
– Each bubble break very rapidly
– Product of bubble don’t
reinteract with each other
– Dynamical fluctuations?
STAR
HBT
3 Apr 2002
– Pion become off-shell and can
freeze out
– If system has evolve long enough:
no re-interaction
• Short emission duration
– Caveat:
• Too long lifetime?
• Dynamical fluctuations?
• Back to back pp correlations
malisa - colloquium at Duke
45
Speculation:
A. Dumitru
• A way to get short emission
duration
• pions take a long time to become
on-shell and freeze-out
– Freeze-out a low density: no
reinteractions, short emission
duration
– Wouldn’t the system live too long?
– Imply back to back pp
correlations?
– Dynamical fluctuations?
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
46
Summary
Spectra
• Very strong radial flow field superimposed on thermal motion
• T saturates rapidly ~ 140 MeV
• b higher at RHIC
•space-momentum correlations important
•“stiffer” system response?
• consistent with hydro expectation
Momentum-space anisotropy
• sensitive to EoS and early pressure and thermalization
• significantly stronger elliptical flow at RHIC, compared to lower
energy
• indication of coordinate-space anisotropy as well as flow-field
anisotropy (v2 cannot distinguish its nature, however)
• for the first time, consistent with hydro expectation
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
47
Summary (cont’)
HBT
• radii grow with collision centrality R(mult)
• evidence of strong space-momentum correlations R(mT)
• non-central collisions spatially extended out-of-plane R()
• The spoiler - expected increase in radii not observed
• presently no dynamical model reproduces data
Combined data-driven analysis of freeze-out distribution
• Single parameterization simultaneously describes
•spectra
•elliptic flow
•HBT
•K-p correlations
• most likely cause of discrepancy is extremely rapid emission
timescale suggested by data - more work needed!
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
48
Can we learn from
blasphemy?
HBT R, 
• purely hadronic model, even at
T = 300 MeV,  ~ 6 GeV/fm3
• details of elliptic flow and HBT
~well-reproduced
• worked similarly well at SPS (impt!)
STAR
HBT
centrality
3 Apr 2002
malisa - colloquium at Duke
mT (GeV/c2)
T. Humanic
nucl-th/0203004
49
dN/dt
A “typical” emissiontime distribution
hydro+RQMD
D. Teaney
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
50
K*(892)
• Tchem ~ 170 MeV describes K* and
other ratios consistently
• No need for in-medium effects
STAR
HBT
3 Apr 2002
• Tslope ~ 300-400 MeV consistent with
mass systematics
• No extra suppression at low pT due to
in-medium effects
malisa - colloquium at Duke
51
more recent HBT wrt RP
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
52
C(Qinv)
K0-K0 interferometry in year-2
preliminary
• K0spp identified topologically
(not combinatorically)
• S/N ~ 5
• No issues with Coulomb correction
• Trackmerging essentially a non-issue
• Full 3D treatment possible with Y2 statistics
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
53
Minv distribution from topological cuts
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
54
Balance functions:
How they work
For each charge +Q, there is one extra balancing charge –Q.
STAR
Charges:
electric, strangeness, baryon number
HBT
3 Apr 2002
malisa - colloquium at Duke
55
Balance functions:
basic idea
• Early hadronization
• Large 
• Delayed
hadronization
• Small 
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
56
Balance functions:
Preliminary data on +- pairs
*No
electrons
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
57
Balance functions:
Summary plot
Charged Particles
Pions
Something fundamentally different from p-p is happening
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
58
Balance functions:
Quantitative results
• Bjorken + thermal
model
–
–
–
–
Ti ~ Tchemical
Tf ~ Tthermal
ti ~ tchemical
tf ~ tthermall
• To reproduce data
 f = 15 fm/c >  from
Rlong (8-10)
– Extremely low Tf
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
59
Balance functions:
Using “known” parameters
p pairs
Central Data
Tf=110, i=10, f=13, rate=5.42, ncoll=1
0.65
• Parameters
Tf=100, i=9, f=11, rate=7.5, ncoll=2
– Ti = 175 MeV
• From particle ratios
 i = 9-10 fm/c
• From HBT RL
– Tf = 100-110 MeV
• From spectra
 f-i =  = 2-4 fm/c
• From HBT RO/RS
Tf=110, i=9, f=13, rate=5.4, ncoll=2
< y>
0.6
0.55
0.5
0
0.2
0.4
0.6
b/bmax
0.8
1
• Too large width
STAR100k Bjorken simulations, fast TPC  filter,
HBT
2002
no flow,3TApr
=175
MeV, other parameters asmalisa
given - colloquium at Duke
i
60
Balance functions:
Add radial flow
• Adding transverse flow
– We “know” it is there
– narrows balance function
– highly sensitive (more than to T)
Data
Bjorken, fast  TPC filter,
T0=175MeV, Tf=110 MeV,
i=10 fm/c, f=13 fm/c,
cooling rate = 5.42, ncoll=1
same with flow estimate
0.65
< y>
0.6
0.55
0.5
STAR
HBT
3 Apr 2002
0
0.2
malisa - colloquium at Duke
0.4 0.6
b/bmax
0.8
1
61
Already producing QGP at lower energy?
Thermal model fits to particle yields (&
strangeness enhancement, J/ suppression)
 approach QGP at CERN (s=17 GeV)?
J. Stachel, Quark Matter ‘99
• is the system really thermal?
• dynamical signatures? (no)
• what was pressure generated?
• what is Equation of State of
strongly-interacting matter?
warning: e+e- yields fall on similar line!!
Must go beyond chemistry:
 study dynamics of system well into
deconfined phase (RHIC)
STAR
HBT
lattice QCD applies
3 Apr 2002
malisa - colloquium at Duke
62
Summary
• Spectra, elliptic flow, and HBT measures consistent with a freeze-out
distribution including strong space-momentum correlations
• In non-central collisions, v2 measurements sensitive to existence of spatial
anisotropy, while HBT measurement reveals its nature
• Systematics of HBT parameters:
• flow gradients produce pT-dependence (consistent with spectra and
v2(pT,m))
• anisotropic geometry (and anisotropic flow boost) produce -dependence
• (average) out-of-plane extension indicated
• however, distribution almost “round,” --> more hydro-like evolution as
compared to AGS
While data tell consistent story within hydro-inspired parameterization,
hydro itself tells a different story - likely point of conflict is timescale
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
63
Emergence of a Consistent Picture from
First Results of STAR at RHIC?
Mike Lisa, Ohio State University
STAR Collaboration
U.S. Labs: Argonne, Lawrence Berkeley
National Lab, Brookhaven National Lab
U.S. Universities: Arkansas, UC Berkeley,
UC Davis, UCLA, Carnegie Mellon,
Creighton,
Indiana,
Kent State,
Michigan State,
CCNY,
Ohio State,
Penn State,
Purdue, Rice,
Texas A&M,
UT Austin,
Washington,
Wayne State,
Yale
STAR
HBT
3 Apr 2002
Brazil:
Universidade de Sao Paolo
China:
IHEP - Beijing, IPP - Wuhan
England: University of Birmingham
France: Institut de
Recherches Subatomiques
Strasbourg, SUBATECH Nantes
Germany: Max Planck
Institute – Munich,
University of Frankfurt
Poland: Warsaw University,
Warsaw University of
Technology
Russia: MEPHI – Moscow,
LPP/LHE JINR–Dubna,
IHEP-Protvino
malisa - colloquium at Duke
64
Stages of the collision
The “little bang”
• pre-equilibrium (deposition of initial energy density)
• rapid (~1 fm/c) thermalization (?)
QGP formation (?)
hadronization transition (very poorly understood)
hadronic rescattering
freeze-out: cessation of hard scatterings
• low-pT hadronic observables probe this stage
STAR
“end
result” looks very similar whether a QGP was formed or not!!!
HBT
3 Apr 2002
malisa - colloquium at Duke
65
Joint view of p freezeout: HBT & spectra
spectra (p)
• common model/parameterset
describes different aspects of f(x,p)
for central collisions
• Increasing T has similar effect on a
spectrum as increasing b
• But it has opposite effect on R(pT)
 opposite parameter correlations in
the two analyses
 tighter constraint on parameters
STAR preliminary
HBT
b
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
66
pTArm
Topological Strangeness
Measurements
K s0

p p

a
  p  p
     p
 p  p
Km+
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
67
Determining the reaction plane
  w i  sin 2i  

1
A,B
1  i
Y2  Tan 

2
  w i  cos2i  
 i

STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
68
Sub events
2nd order event plane of independent sub-events A&B
A
B
A
B
-1<<-0.05
STAR
HBT
3 Apr 2002
0.05<<1
malisa - colloquium at Duke
69
Reaction plane resolution
vnobs
vn 
cos( n(Yn  Yr ))
cos(n(Yn  Yr ))  C 
cos(n(Yna  Ynb ))
A.M. Poskanzer and S.A. Voloshin, Phys. Rev. C 58 (1998) 1671
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
70
STAR HBT data for central collisions
- further info? conflicting info?
pp+
R(pT) probes interplay b/t space-time
geometry and temperature/flow
STAR
HBT
STAR Collab., PRL 87 082301 (2001)
3 Apr 2002
malisa - colloquium at Duke
71
Elliptic flow (momentum-space anisotropy):
sensitive to early pressure / thermalization
v2  cos2
in-plane enhancement
v2 @ SPS:
between hydro and LDL
P. Kolb, et al., PLB 500 232 (2001)
Hydro describes flow quantitatively @ RHIC
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
72
Particle Identification via dE/dx in
TPC - June 2000
Approaching expected
resolution in dE/dx
Preliminary
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
73
Measurements at AGS; E895 and E877
(Protons)
v2
• At low beam energies
negative v2 (“squeezeout”)
• Balancing energy around
4 AGeV, sensitive to EOS
0.04
0
-0.04
-0.08
1
Elab (AGeV)
10
E895, Phys. Rev. Lett. 83 (1999) 1295
STAR
HBT
P. Danielewicz, Phys. Rev. Lett. 81 (1998) 2438
3 Apr 2002
malisa - colloquium at Duke
74
Probing f(x,p) from different angles
Transverse spectra: number distribution in mT
2p
R
dN 2p
  ds  dp  r  dr  mT  f ( x, p)
2
dmT 0
0
0
Elliptic flow: anisotropy as function of mT
v 2 (pT , m)  cos(2p ) 
2p
2p
R
d

d

p 0
s 0 r  dr  cos(2p )  f ( x , p)
0
2p
2p
R
d

d

p 0
s 0 r  dr  f ( x , p)
0






HBT: homogeneity lengths vs mT, p
2p
R
d

s 0 r  dr  x m  f ( x , p)
0
x m p T , p  2 p
R
d

s 0 r  dr  f ( x , p)
0
2p
R
d

s 0 r  dr  x m x   f ( x , p)
~
~
0
x m x  p T , p 
2p
R
d

s 0 r  dr  f ( x , p)
malisa0- colloquium
at Duke

STAR
HBT


3 Apr 2002









 xm x
75
mT distribution from
Hydrodynamics-inspired model
bs
R
 m cosh 
 pT sinh 
f ( x, p)  K1 T

exp
 cos b  p


T


 T
Infinitely long
solid cylinder

  tanh 1 b(r )
  R  r 

b(r )  bs  g(r )
b = direction of flow boost (= s here)
2-parameter (T,b) fit to mT distribution
E.Schnedermann et al, PRC48 (1993) 2462
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
76
Fits to STAR spectra; br=bs(r/R)0.5
Tth =120+40-30MeV
<br >=0.52 ±0.06[c]
tanh-1(<br >) = 0.6
contour maps for 95.5%CL
Tth [GeV]
K-
p-
p
preliminary
bs [c]
Tth [GeV]
Tth [GeV]
STAR preliminary
bs [c]
<br >= 0.8bs
bs [c]
1/mT dN/dmT (a.u.)
•
c2
pK-
p
thanks to M. Kaneta
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
mT - m [GeV/c2]77
Excitation function of spectral parameters
• Kinetic “temperature” saturates
~ 140 MeV already at AGS
• Explosive radial flow significantly
stronger than at lower energy
• System responds more “stiffly”?
• Expect dominant space-momentum
correlations from flow field
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
78
Non-central collisions: coordinate- and
momentum-space anisotropies
P. Kolb, J. Sollfrank, and U. Heinz
Equal energy density lines
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
79
More detail: identified particle elliptic flow
2p
0

v 2 pT  
db cos2b I2

 

 

p T sinh 
m T cosh 
K
1hydro-inspired
 2s 2 cos 2b
1
T
T
2p
blast-wave model
p T sinh 
m T cosh 
d

I
K
1

2
s
b 0
1
2 cos 2etal
b (2001)
Houvinen
T
T
0


 


Flow boost:   0  a cos 2b 
b = boost direction
T (MeV)
dashed
solid
135  20
100  24
b0(c)
0.52  0.02 0.54  0.03
ba (c)
0.09  0.02 0.04  0.01
S2
STAR
Meaning
HBT
0.0
0.04  0.01
of a is clear  how to interpret s2?
3 Apr 2002
malisa - colloquium at Duke
STAR, in press PRL (2001)
80
Ambiguity in nature of the spatial anisotroy
2p
p sinh 
m cosh 






1  2s2 cos2b 
d

cos
2

I
K

b
b 2
1
T
T
0
v 2 pT  
2p
p sinh 
m cosh 



1  2s2 cos2b 
d

I
K
0
b 0
1
T
T
T
T
T
T
b = direction of the boost  s2 > 0 means more source elements emitting in plane
case 1: circular source with modulating density
pT
 mT
 T sinh  coss p 
cosh e
1  2s
 
f x, p   K1
 T




r



cos
2

2
s R  r 
R

RMSx > RMSy
case 2: elliptical source with uniform density


T
 
 mT
 T sinh  coss p 
f x, p   K1
cosh e
 1  y2  2 x 2 / R y
 T

Ry
1 3  1

s2 
RMSx < RMSy
3
Rx
2  1
p
STAR
HBT
3 Apr 2002
malisa - colloquium at Duke
81
Out-of-plane elliptical shape indicated
using (approximate) values of
s2 and a from elliptical flow
case 1
case 2
opposite R() oscillations would
lead to opposite conclusion
STAR
HBT
3 Apr 2002
STAR preliminary
malisa - colloquium at Duke
82
s2 dependence dominates HBT signal
s2=0.033, T=100 MeV, 00.6
a0.033, R=10 fm, =2 fm/c
STAR
HBT
3 Apr 2002
STAR preliminary
color: c2 levels
from HBT data
malisa - colloquium at Duke
error contour from
elliptic flow data
83