Characterizing the freezeout at RHIC:
HBT, spectra, and elliptic flow
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,
MSU, CCNY,
Ohio State,
Penn State,
Purdue, Rice,
Texas A&M,
UT Austin,
Washington,
Wayne State, Yale
STAR
HBT
30 Aug 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,
Mike Lisa - ACS Nuclear Division - IHEP-Protvino
1
Schematic goal and method - soft physics
Goal: EoS of dense matter - relationship b/t bulk properties (P,T,…)
• evidence for phase transition?
Method:
• Full characterization of freezeout distribution f(x,p)
• Consistent characterization for several observables
• Use measurements to constrain EoS via a model (hydro?),
which connects early time to freezeout
This talk:
• Focus on transverse observables: dN/dpT, v2(pT,m), HBT(pT,f)
• Consistent picture within “hydro-inspired” parameterization?
(is the data telling a consistent story, and what does it mean?)
• identify features of “real” model needing attention
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
2
An analogous situation…
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
3
Probing f(x,p) from different angles
Transverse spectra: number distribution in mT
2
R
dN 2
  dfs  dfp  r  dr  mT  f ( x, p)
2
dmT 0
0
0
Elliptic flow: anisotropy as function of mT
v 2 (pT , m)  cos(2fp ) 
2
2
R
d
f
d
f
p 0
s 0 r  dr  cos(2fp )  f ( x , p)
0
2
2
R
d
f
d
f
p 0
s 0 r  dr  f ( x , p)
0






HBT: homogeneity lengths vs mT, fp
2
R
d
f
s 0 r  dr  x   f ( x , p)
0
x  p T , fp  2 
R
d
f
s 0 r  dr  f ( x , p)
0
2
R
d
f
s 0 r  dr  x  x   f ( x , p)
~
~
0
x  x  p T , fp 
2
R
d
f
s 0 r  dr  f ( x , p)
30 Aug 2001
Mike Lisa0- ACS Nuclear
Division -

STAR
HBT











 x x
4
mT distribution from
Hydrodynamics type model
s
R
 m cosh 
 pT sinh 
f ( x, p)  K1 T

exp
 cos fb  fp


T


 T

  tanh 1 (r )
Infinitely long
solid cylinder
  R  r 

(r )  s  g(r )
fb = direction of flow boost (= fs here)
2-parameter (T,) fit to mT distribution
E.Schnedermann et al, PRC48 (1993) 2462
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
5
Fits to STAR spectra; r=s(r/R)0.5
Tth =120+40-30MeV
<r >=0.52 ±0.06[c]
tanh-1(<r >) = 0.6
contour maps for 95.5%CL
Tth [GeV]
K-
-
p
preliminary
s [c]
Tth [GeV]
Tth [GeV]
STAR preliminary
<r >= 0.8s
s [c]
s [c]
1/mT dN/dmT (a.u.)
•
c2
K-
p
thanks to M. Kaneta
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
mT - m [GeV/c2] 6
STAR HBT data for central collisions
- further info? conflicting info?
+
R(pT) probes interplay b/t space-time
geometry and temperature/flow
STAR
HBT
STAR Collab., PRL 87 082301 (2001)
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
7
Implications for HBT: radii vs pT
Assuming , T obtained from spectra fits
 strong x-p correlations, affecting RO, RS differently
y (fm)
pT=0.2
2
RO
2
 RS
   
2
x (fm)
y (fm)
pT=0.4
x (fm)
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
8
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
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
9
Joint view of  freezeout: HBT & spectra
• common model/parameterset
describes different aspects of f(x,p)
for central collisions
spectra ()
STAR preliminary
• Increasing T has similar effect on a
spectrum as increasing 
• But it has opposite effect on R(pT)
 opposite parameter correlations in
the two analyses
 tighter constraint on parameters
HBT
• caviat: not exactly same model used
here (different flow profiles)
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
10
Non-central collisions:coordinate and
momentum-space anisotropies
P. Kolb, J. Sollfrank, and U. Heinz
Equal energy density lines
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
11
Elliptic flow (momentum-space anisotropy):
sensitive to early pressure / thermalization
v2  cos2f
in-plane enhancement
v2 @ SPS:
between hydro and LDL
P. Kolb, et al., PLB 500 232 (2001)
Hydro describes flow quantitatively @ RHIC
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
12
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
f
x
b
 
R s2 pT , fp   ~
x 2 sin 2 fp  ~y 2 cos2 fp  ~
x  ~y sin 2fp
2
pT , fp   ~x  ~y cos2fp  12  ~y 2  ~x 2 sin 2fp
R os
R o2
2
2
2
2
2 ~2
~
~
~
~
pT , fp  x cos fp  y sin fp  x  y sin 2fp   t
large flow @ RHIC induces space-momentum correlations
 p-dependent homogeneity lengths ~
x~
x  p T , fp
 sensitive to more than “just” anisotropic geometry

STAR
HBT
30 Aug 2001

U. Wiedemann, PRC 57, 266 (1998)
Mike Lisa - ACS Nuclear Division 13
Reminder: observations for Au(2 AGeV)Au
fp=90°
R2 (fm2)
E895 Collab., PLB 496 1 (2000)
40
out
side
long
ol
os
sl
20
10
0
fp=0°
out-of-plane
extended source
-10
0
Lines are global fit
Oscillation magnitude  eccentricity
Oscillation phases  orientation
STAR
HBT
30 Aug 2001
180
0
180
0
180
fp (°)
interesting physics, but not
currenly accessible in STAR
with 2nd-order reaction plane
Mike Lisa - ACS Nuclear Division -
14
More detail: identified particle elliptic flow
2
0

v 2 pT  
dfb cos2fb I2

 

 

p T sinh 
m T cosh 
K
1hydro-inspired
 2s 2 cos 2fb
1
T
T
2
blast-wave model
p T sinh 
m T cosh 
d
f
I
K
1

2
s
b 0
1
2 cos 2etfal
b (2001)
Houvinen
T
T
0


 


Flow boost:   0  a cos 2fb 
fb = boost direction
T (MeV)
dashed
solid
135  20
100  24
0(c)
0.52  0.02 0.54  0.03
a (c)
0.09  0.02 0.04  0.01
S2
0.0
0.04  0.01
STAR of  is clear  how to interpret s ?
Meaning
a
2
HBT
30 Aug 2001
STAR Collab, submitted to PRL
Mike Lisa - ACS Nuclear Division -
15
Ambiguity in nature of the spatial anisotroy
2
p sinh 
m cosh 






1  2s2 cos2fb 
d
f
cos
2
f
I
K

b
b 2
1
T
T
0
v 2 pT  
2
p sinh 
m cosh 



1  2s2 cos2fb 
d
f
I
K
0
b 0
1
T
T
T
T
T
T
fb = 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fs fp 
cosh e
1  2s
 
f x, p   K1
 T




r



cos
2
f
2
s R  r 
R

RMSx > RMSy
case 2: elliptical source with uniform density


T
 
 mT
 T sinh  cosfs fp 
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
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
16
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:
fp=45º
RO2 (fm2)
STAR HBT
- from semi-peripheral events
0.1
0.2
Q (GeV/c)
30 Aug 2001
• only mix events with “same” fRP
• retain relative sign between q-components
• HBT radii oscillations similar to AGS
• curves are not a global fit
• RLisa
flat Division Mike
- ACS Nuclear
S almost
17
Out-of-plane elliptical shape indicated
using (approximate) values of
s2 and a from elliptical flow
case 1
case 2
opposite R(f) oscillations would
lead to opposite conclusion
STAR
HBT
30 Aug 2001
STAR preliminary
Mike Lisa - ACS Nuclear Division -
18
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
30 Aug 2001
STAR preliminary
color: c2 levels
from HBT data
Mike Lisa - ACS Nuclear Division -
error contour from
elliptic flow data
19
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
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
20
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
180
fp (º)
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
21
Summary - a consistent picture

pT
 mT
 T sinh  cosfs fp 
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
30 Aug 2001
*

  2 fm/c

Mike Lisa - ACS Nuclear Division -
22
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 f-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
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
23
Hydro reproduced spectra well
STAR
HBT
30 Aug 2001
Mike Lisa - ACS Nuclear Division -
24