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
24 Oct 2001
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
Mike Lisa - UIUC Seminar
1
Overview
• ~ 1 year from initial data-taking in new energy regime
• overall picture / underlying driving physics unclear
Outline
• Ultrarelativistic heavy ion collisions
• STAR at RHIC
• Transverse momentum spectra
• Momentum-space anisotropy (elliptic flow)
• Initial quantitative success of hydrodynamics
• Two-particle correlations (HBT)
• STAR HBT and the “HBT Puzzle”
• Characterization of freeze-out from the data itself
• particle-identified elliptical flow
• azimuthally-sensitive HBT
• Summary
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
2
Why heavy ion collisions?
The “little bang”
• Study bulk properties of strongly-interacting
matter far from ground state
• 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 until ~ ms
• 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
24 Oct 2001
Mike Lisa - UIUC Seminar
3
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
24 Oct 2001
Mike Lisa - UIUC Seminar
4
Already producing QGP at lower energy?
Thermal model fits to particle yields (&
strangeness enhancement, J/ suppression)
 approach QGP at CERN?
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
24 Oct 2001
Mike Lisa - UIUC Seminar
5
uRQMD simulation of Au+Au @ s=200 GeV
pure hadronic & string
description (cascade)
generally OK at lower
energies
applicability in very high
density (RHIC) situations
unclear
produces too little
collective flow at RHIC
freeze-out given by last
hard scattering
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
6
Geometry of
STAR
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
24 Oct 2001
Mike Lisa - UIUC Seminar
7
Peripheral Au+Au Collision at 130
AGeV
Data Taken June 25, 2000.
Pictures from Level 3 online display.
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
8
Au on Au Event at CM Energy ~ 130 AGeV
Data Taken June 25, 2000.
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
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
24 Oct 2001
light
heavy
mT
light
heavy
mT
• very good agreement with hydrodynamic
prediction
Mike Lisa - UIUC Seminar
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, volume
– 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
24 Oct 2001
Mike Lisa - UIUC Seminar
lattice QCD input
11
Hydro time evolution of
non-central collisions
• correlating observations with respect to
event-wise reaction plane allows much
more detailed study of reaction dynamics
• entrance-channel aniostropy in x-space
 pressure gradients (system response)
 p-space anisotropy (collective elliptic flow)
Equal energy density lines
STAR
self-quenching
effect HBT
24 Oct 2001
sensitive to early
Mike pressure
Lisa - UIUC Seminar
P. Kolb, J. Sollfrank,
and U. Heinz
12
Azimuthal-angle distribution versus
reaction plane
• v2 increases from
central to
peripheral
collisions
v2  cos2
dN
~ 1  2v2 cos2
or
d
STAR
HBT
  particle-reaction plane
24 Oct 2001
Mike Lisa - UIUC Seminar
13
Measurements at AGS; E895 and E877
(Protons)
0.04
v2
• At low beam energies
negative v2 (“squeezeout”)
• Balancing energy around
4 AGeV, sensitive to EOS
0
-0.04
E895, Phys. Rev. Lett. 83
(1999) 1295
P. Danielewicz, Phys. Rev.
Lett. 81 (1998) 2438
STAR
HBT
24 Oct 2001
-0.08
1
Elab (AGeV)
Mike Lisa - UIUC Seminar
10
14
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: magnitude described by 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
24 Oct 2001
Mike Lisa - UIUC Seminar
15
Local thermal equilibrium versus Low
Density Limit
SPS; Low-Density-Limit and
Hydro miss pt dependence
p
RHIC; pt dependence quantitatively
described by Hydro
p
Charged
particles
pt dependence sensitive to early thermalization?
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
16
The other half of the story…
• Momentum-space characteristics of freeze-out appear well understood
• Coordinate-space ?
• Probe with two-particle intensity interferometry (“HBT”)
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
17
“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  p2  p1
STAR
HBT

0.05
0.10
Qinv (GeV/c)
24 Oct 2001
Mike Lisa - UIUC Seminar
18
“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)
24 Oct 2001
R o2
 R s2
 b  
2
x out , x side   x, y 
beware this “helpful” mnemonic!
Mike Lisa - UIUC Seminar
19
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
24 Oct 2001
Mike Lisa - UIUC Seminar
20
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/cin unplotted components
STAR Collab., PRL 87 082301 (2001)
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
21
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
STAR
Collab., PRL 87 082301 (2001)
24
Oct 2001
Mike Lisa - UIUC Seminar
22
First STAR HBT data - systematics
• p+, p- HBT parameters similar
• Grossly similar to AGS/SPS
• all radii increase with multiplicity
• Ro, Rs - geometric effect
• Rl - increase not seen at AGS/SPS
• With increasing mT
•  increases  fewer resonances
• radii decrease  x-p correlations
• stronger effect in Ro than at
AGS/SPS
systematic errors
STAR Collab., PRL 87 082301 (2001)
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
23
y (fm)
mT dependence at ycm for 2 AGeV central
collisions
x (fm)
• collective flow 
dynamical correlation between
position and momentum  R(mT)
• R’s are “lengths of homegeity”
• p- from decays  (mT)
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
24
Hydro attempts to reproduce data
generic
hydro
long
out
KT dependence approximately reproduced
 correct amount of collective flow
Rs too small, Ro & Rl too big
 source is geometrically too small and
lives too long in model
side
STAR
HBT
24 Oct 2001
Right dynamic effect / wrong space-time evolution?
 the “RHIC HBT Puzzle”
Mike Lisa - UIUC Seminar
25
“Realistic” afterburner makes things worse
pure hydro
hydro + uRQMD
RO/RS
Currently, no physical model
reproduces explosive space-time
scenario indicated by observation
1.0
STAR data
STAR
0.8
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
26
Now what?
• No dynamical model adequately describes 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
• Isolate features generating discrepancy with “real” physics models
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
27
Characterizing the freezeout:
An analogous situation
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
28
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)
24 Oct 2001
Mike 0Lisa - UIUC
Seminar

STAR
HBT











 xm x
29
mT distribution from
Hydrodynamics-inspired model
bs
R
 m cosh 
 pT sinh 
f ( x, p)  K1 T

exp
 cos b  p


T


 T

  tanh 1 b(r )
Infinitely long
solid cylinder
  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
24 Oct 2001
Mike Lisa - UIUC Seminar
30
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
<br >= 0.8bs
bs [c]
bs [c]
1/mT dN/dmT (a.u.)
•
c2
pK-
p
thanks to M. Kaneta
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
mT - m [GeV/c2]31
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
24 Oct 2001
Mike Lisa - UIUC Seminar
32
Implications for HBT: radii vs pT
Assuming b, T obtained from spectra fits
 strong x-p correlations, affecting RO, RS differently
y (fm)
pT=0.2
2
RO
2
 RS
 b  
2
x (fm)
y (fm)
pT=0.4
x (fm)
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
33
Implications for HBT: 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
pT=0.2
y (fm)
STAR data
x (fm)
y (fm)
Four parameters affect HBT radii
pT=0.4
model: R=13.5 fm, =1.5 fm/c
T=0.11 GeV, 0 = 0.6
x (fm)
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
34
Non-central collisions: coordinate- and
momentum-space anisotropies
P. Kolb, J. Sollfrank, and U. Heinz
Equal energy density lines
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
35
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?
24 Oct 2001
Mike Lisa - UIUC Seminar
STAR, in press PRL (2001)
36
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
24 Oct 2001
Mike Lisa - UIUC Seminar
37
Azimuthal HBT: (transverse) spatial anisotropy
•Source in b-fixed system: (x,y,z)
•Space/time entangled in
pair system (xO,xS,xL)
y
side
K
out

x
b
 
R s2 pT , p   ~
x 2 sin 2 p  ~y 2 cos2 p  ~
x  ~y sin 2p
2
pT , p   ~x  ~y cos2p  12  ~y 2  ~x 2 sin 2p
R os
R o2
2
2
2
2
2 ~2
~
~
~
~
pT , p  x cos p  y sin p  x  y sin 2p  b t
large flow @ RHIC induces space-momentum correlations
 p-dependent homogeneity lengths ~
xm~
x  p T , p
 sensitive to more than “just” anisotropic geometry

STAR
HBT
24 Oct 2001

U. Wiedemann, PRC 57, 266 (1998)
Mike Lisa - UIUC Seminar
38
Reminder: observations for Au(2 AGeV)Au
p=90°
R2 (fm2)
E895 Collab., PLB 496 1 (2000)
40
out
side
long
ol
os
sl
20
10
0
p=0°
out-of-plane
extended source
-10
0
Lines are global fit
Oscillation magnitude  eccentricity
Oscillation phases  orientation
STAR
HBT
24 Oct 2001
180
0
180
0
180
p (°)
interesting physics, but not
currenly accessible in STAR
with 2nd-order reaction plane
Mike Lisa - UIUC Seminar
39
RS2 (fm2)
“Out”
1.0
1.3
“Side”
1.0
data
fit
1.0
STAR
HBT
raw
corrected for
reactionplane resolution
“Long”
1.3
0
STAR preliminary
ROS2 (fm2)
C(Q)
1.3
Correlation function:
p=45º
RO2 (fm2)
STAR HBT
p- from semi-peripheral events
0.1
0.2
Q (GeV/c)
24 Oct 2001
• only mix events with “same” RP
• retain relative sign between q-components
• HBT radii oscillations similar to AGS
• curves are not a global fit
• Mike
RS almost
flatSeminar
Lisa - UIUC
40
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
24 Oct 2001
STAR preliminary
Mike Lisa - UIUC Seminar
41
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
24 Oct 2001
STAR preliminary
color: c2 levels
from HBT data
Mike Lisa - UIUC Seminar
error contour from
elliptic flow data
42
A consistent picture

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
radial flow
Spatial
anisotropy
Radius in y

y   x / Ry e
2
2 2
spectra

elliptic flow

HBT








s2  0.04
Ry  10-13 fm
t 2 / 2 2

(depends on b)
Nature of x
anisotropy
main source
of discrepancy? Emission
duration
STAR
HBT
24 Oct 2001
*

  2 fm/c

Mike Lisa - UIUC Seminar
43
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
24 Oct 2001
Mike Lisa - UIUC Seminar
44
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
24 Oct 2001
Mike Lisa - UIUC Seminar
45
The End
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
46
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
24 Oct 2001
Mike Lisa - UIUC Seminar
47
STAR TPC
• Active volume: Cylinder r=2 m, l=4 m
– 139,000 electronics channels
sampling drift in 512 time buckets
– active volume divided into 70M
3D pixels
On-board FEE Card:
Amplifies, samples,
digitizes 32 channels
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
48
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
24 Oct 2001
Mike Lisa - UIUC Seminar
49
Meaning of Ro2() and Rs2() are clear
What about Ros2()
R2 (fm2)
E895 Collab., PLB 496 1 (2000)
side
xxside
xxoutout
KK
p =
~45°
0°
40
out
side
long
ol
os
sl
20
10
0
-10
0
180
0
180
0
180
p (°)
• Ros2() quantifies correlation between xout and xside
• No correlation (tilt) b/t between xout and xside at p=0° (or 90°)
• Strong (positive) correlation when p=45°
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
50
Experimental correlation functions
  
q  p2  p1
P(p1, p2 )
A(q)
In Practice
C(p1, p2 ) 
   C(q) 
P(p1 )P(p2 )
B(q)
# pairs from
same event
B(q)
q (GeV/c)
# pairs from
different events
STAR
HBT
24 Oct q2001
(GeV/c)
• shape of A(q), B(q) dominated by phasespace
and single-particle acceptance (complicated in
principle, especially in multiple dimensions)
• only correlated effects
persist in ratio
(including residual
detector artifacts…)
C(q)
A(q)
• most pairs at high q (need statistics!)
• Correlation functions
from different
experiments (and from
theory) can be
compared
Mike Lisa - UIUC Seminar
2
1
0
0
0.1
0.2
0.3
q (GeV/c)
51
Time-averaged freezeout shape

Ry
Rx
3
1  2s 2
1  2s 2
• close to circular @ RHIC
• info on evolution duration?
STAR preliminary
(E895)
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
52
Evolution of mT dependence (y=ycm0.5)
E895 @ AGS
• magnitude of RO(mT) falls with Ebeam.
• Decline of RS with Ebeam driven
primarily by increased falloff with mT
at high energy.
• RL(mT) roughly constant as function of
Ebeam
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
53
RO2 (fm2)
Hydro predictions
60
40
• phases and ~ magnitude of HBT radii oscillations OK
• RO too large
• RS too small
RS2 (fm2)
20
15
10
ROS2 (fm2)
5
0.8
0
-0.8
0
STAR
HBT
90
24 Oct 2001
180
p (º)
Mike Lisa - UIUC Seminar
54
Operation of a Time Projection Chamber
SCA/ADC
V
STAR
HBT
DAQ
ADC
t
24 Oct 2001
Mike Lisa - UIUC Seminar
bucket #
55
If p+p (or e+e, or e+A)
is still under study...
Then why on Earth study Pb+Pb?
The same question may be asked of condensed matter physicist by an
atomic physicist or someone doing QED….
And the answer is the same: different areas of physics available
Heavy Ion physics seeks to understand the bulk properties of nuclear
matter, and to study a new phase of matter not achievable in p+p
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
56
Heavy Ion Physics
• Study the bulk properties of matter far from the ground state
• Ultrarelativistic collisions: Study bulk properties of parton matter
– low-q (nonperturbative) behavior
– confinement
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
57
pTArm
Topological Strangeness
Measurements
K s0

p p

a
  p  p
     p
 p  p
Km+
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
58
Determining the reaction plane
  w i  sin 2i  

1
A,B
1  i
2  Tan 

2
  w i  cos2i  
 i

STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
59
Sub events
2nd order event plane of independent sub-events A&B
A
B
A
B
-1<<-0.05
STAR
HBT
24 Oct 2001
0.05<<1
Mike Lisa - UIUC Seminar
60
Reaction plane resolution
vnobs
vn 
cos( n(n  r ))
cos(n(n  r ))  C 
cos(n(na  nb ))
A.M. Poskanzer and S.A. Voloshin, Phys. Rev. C 58 (1998) 1671
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
61
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)
24 Oct 2001
Mike Lisa - UIUC Seminar
62
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
24 Oct 2001
Mike Lisa - UIUC Seminar
63
Particle Identification via dE/dx in
TPC - June 2000
Approaching expected
resolution in dE/dx
Preliminary
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
64
RHIC at BNL
STAR
HBT
24 Oct 2001
Mike Lisa - UIUC Seminar
65