Azimuthally-sensitive HBT in STAR
Mike Lisa
Ohio State University
• Motivation
• Noncentral collision dynamics
• Azimuthally-sensitive interferometry & previous results
• STAR results
• Hydrodynamic predictions for RHIC and “LHC”
• Summary
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
1
Central collision dynamics @ RHIC
• Hydrodynamics reproduces p-space aspects
of particle emission up to pT~2GeV/c
(99% of particles)
 hopes of exploring the early, dense stage
STAR
HBT
oct 2002
Heinz & Kolb, hep-th/0204061
Mike Lisa - XXXII ISMD - Alushta,
2
Central collision dynamics @ RHIC
• Hydrodynamics reproduces p-space aspects
of particle emission up to pT~2GeV/c
(99% of particles)
 hopes of exploring the early, dense stage
• x-space is poorly reproduced
• model source lives too long and
disintegrates too slowly?
• Correct dynamics signatures with wrong
space-time dynamics?
• Turn to richer dynamics of non-central
collisions for more detailed information
STAR
HBT
oct 2002
Heinz & Kolb, hep-th/0204061
Mike Lisa - XXXII ISMD - Alushta,
3
Noncentral collision dynamics
hydro evolution
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
• Dynamical models:
• x-anisotropy in entrance channel
 p-space anisotropy at freezeout
• magnitude depends on system
response to pressure
STAR
HBT
oct 2002
Heinz & Kolb, hep-ph/01110754
Mike Lisa - XXXII ISMD - Alushta,
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.0 GeV/c
• system response  EoS
• early thermalization indicated
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
STAR
HBT
oct 2002
Mike Lisa -Teaney,
XXXII ISMD
- Alushta,
Lauret,
& Shuryak, nucl-th/0110037
5
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
hydro only
hydro+hadronic rescatt
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
• significant (bad) effect on HBT radii
STAR
HBT
oct 2002
STAR
PHENIX
calculation:
Mike Lisa - XXXII ISMD
- Alushta,Soff, Bass, Dumitru, PRL 2001
6
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
• significant (bad) effect on HBT radii
• related to timescale? - need more info
STAR
HBT
oct 2002
Mike Lisa - XXXII
ISMD Lauret,
- Alushta,& Shuryak, nucl-th/0110037
7
Teaney,
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
in-planeextended
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
• significant (bad) effect on HBT radii
• related to timescale? - need more info
• qualitative change of freezeout shape!!
• important piece of the puzzle!
STAR
HBT
oct 2002
out-of-plane-extended
Mike Lisa - XXXII
ISMD Lauret,
- Alushta,& Shuryak, nucl-th/0110037
8
Teaney,
Possible to “see” via HBT relative to reaction plane?
fp=90°
• for out-of-plane-extended source, expect
• large Rside at 0
2nd-order
• small Rside at 90
oscillation
Rside (small)
Rside (large)
fp=0°
2
Rs [no flow expectation]
fp
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
9
“Traditional HBT” - cylindrical sources
C(qo , qs , ql )  1    e 
Decompose q into components:
qLong : in beam direction
qOut : in direction of transverse momentum
qSide :  qLong & qOut
K
 q o2 R o2  q s2 R s2  q l2 R l2
 
 
  

~2
K  ~
x out   t 

2 
2
~
R s K  x side K

~2
2
Rl K  ~
x long  l t
R o2

 

K
 
  

K
x out , x side   x, y 
~
xx x
Rout
Rside
d 4 x  S( x, K )  f ( x )

f 
4
d
 x  S( x, K )
(beam is into board)
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
10
Anisotropic sources Six HBT radii vs f
side
•Source in b-fixed system: (x,y,z)
•Space/time entangled in
pair system (xO,xS,xL)
R s2
~2
~2
y
K
fp
x
 x sin f  y cos f  ~
x~y sin 2f
2
out
2
b
~
~
~
R o2  ~
x 2 cos2 f  ~y 2 sin 2 f  2 t 2  2 ~
x t cosf  2 ~y t sin f  ~
x~y sin 2f
~
~
R l2  ~z 2  2L ~z t  2L t 2
~
~
2
R os
 ~
x~y cos 2f  12 ( ~y 2  ~
x 2 ) sin 2f   ~
x t sin f   ~y t cosf
~
~
~
~
2
R ol
( ~
x~z  L ~
x t ) cosf  ( ~y~z  L ~y t ) sin f   ~z t  L t 2
~
~
R sl2  ( ~y~z  L ~y t ) cosf  ( ~
x~z  L ~
x t ) sin f
• explicit
and implicit (xmxn(f)) dependence on f
STAR
HBT
oct 2002
Wiedemann,
PRC57 266 (1998).
!
Mike Lisa - XXXII ISMD - Alushta,
~
xx x
d 4 x  f ( x, K )  q( x )

q 
4
d
 x  f ( x, K)11
Symmetries of the emission function
I. Mirror reflection symmetry w.r.t. reactionplane
(for spherical nuclei):
S( x, y, z, t ;Y , KT , )  S( x, y, z, t ;Y , KT ,)

~
xm ~
xn (Y , KT , )  1  ~
xm ~
xn (Y , KT ,)
1  (1)
with
m 2  n 2
II. Point reflection symmetry w.r.t. collision center
(equal nuclei):
S( x, y, z, t ;Y , KT , )  S( x, y, z , t ;Y , KT ,   )
 ~
xm ~
xn (Y , KT , )  2  ~
xm ~
xn (Y , KT ,   )
2  (1)
with
STAR
HBT
oct 2002
m 0   n 0
Heinz,
nucl-th/0207003
Mike Hummel,
Lisa - XXXIIMAL,
ISMD -Wiedemann,
Alushta,
12
Fourier expansion of HBT radii @ Y=0
Insert symmetry constraints of spatial correlation tensor into Wiedemann relations
and combine with explicit -dependence:
Rs2 (f)
 Rs2,0 
2   n  2, 4,6,... Rs2, n  cos(nf)
Ro2 (f)
 Ro2,0 
2   n  2, 4,6,... Ro2, n  cos(nf)
2
2   n  2, 4,6,... Ros
, n  sin( nf)
2
Ros
(f) 
Rl2 (f)

Rl2,0 
2   n  2, 4,6,... Rl2,n  cos(nf)
Rol2 (f) 
2   n 1,3,5,... Rol2 , n  cos(nf)
Rsl2 (f)
2   n 1,3,5,... Rsl2 , n  sin( nf)

Note: These most general forms of the Fourier expansions for the HBT radii
are preserved when averaging the correlation function over a finite,
symmetric window around Y=0.
Relations between the Fourier coefficients reveal interplay between flow and
STAR geometry, and can help disentangle space and time
HBT
oct 2002
Mike Hummel,
Lisa - XXXIIMAL,
ISMD -Wiedemann,
Alushta,
Heinz,
nucl-th/0207003
13
Anisotropic HBT results @ AGS (s~2 AGeV)
xside
xout
K
R2 (fm2)
Au+Au 2 AGeV; E895, PLB 496 1 (2000)
40
side
long
ol
os
sl
20
10
0
fp = 0°
out
-10
0
180
0
180
0
180
fp (°)
• strong oscillations observed
• lines: predictions for static (tilted) out-of-plane extended source
 consistent with initial overlap geometry
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
14
Meaning of Ro2(f) and Rs2(f) are clear
What about Ros2(f) ?
xxoutout
K
K
R2 (fm2)
Au+Au 2 AGeV; E895, PLB 496 1 (2000)
side
xxside
40
side
long
ol
os
sl
20
10
0
fp =
~45°
0°
out
-10
No access to 1st-order
oscillations in STAR Y1
0
180
0
180
0
180
fp (°)
• Ros2(f) quantifies correlation between xout and xside
• No correlation (tilt) b/t between xout and xside at fp=0° (or 90°)
STAR
HBT
• Strong (positive) correlation when fp=45°
• Phase of Ros2(f) oscillation reveals orientation of extended source
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
15
Indirect indications of x-space anisotropy @ RHIC
• v2(pT,m) globally well-fit by
hydro-inspired “blast-wave”
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
STAR
HBT
0.0
oct 2002
0.04  0.01
temperature, radial flow
consistent with fits to spectra 
anisotropy of flow boost
spatial anisotropy (out-of-plane extended)
Mike Lisa - XXXII ISMD
- Alushta,
STAR,
PRL 87 182301 (2001)
16
STAR data
Au+Au 130 GeV minbias
• significant oscillations observed
• blastwave with ~ same parameters as
used to describe spectra & v2(pT,m)
• additional parameters:
• R = 11 fm
full blastwave
preliminary
2
RO
R S2
•  = 2 fm/c !!
consistent with R(pT), K-
R 2L
STAR
HBT
2
R OS
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
17
STAR data
Au+Au 130 GeV minbias
• significant oscillations observed
• blastwave with ~ same parameters as
used to describe spectra & v2(pT,m)
• additional parameters:
• R = 11 fm
full blastwave
no spatial
anisotropy
preliminary
2
RO
no flow
anisotropy
R S2
•  = 2 fm/c !!
consistent with R(pT), K-
• both flow anisotropy and source shape
contribute to oscillations, but…
• geometry dominates dynamics
• freezeout source out-of-plane extended
 fast freeze-out timescale !
STAR
HBT
oct 2002
R 2L
2
R OS
Mike Lisa - XXXII ISMD - Alushta,
18
Azimuthal HBT: hydro predictions
RHIC (T0=340 MeV @ 0=0.6 fm)
• Out-of-plane-extended source (but flips
with hadronic afterburner)
• flow & geometry work together to
produce HBT oscillations
• oscillations stable with KT
(note: RO/RS puzzle persists)
STAR
HBT
oct 2002
Heinz & Kolb, hep-th/0204061
Mike Lisa - XXXII ISMD - Alushta,
19
Azimuthal HBT: hydro predictions
RHIC (T0=340 MeV @ 0=0.6 fm)
• Out-of-plane-extended source (but flips
with hadronic afterburner)
• flow & geometry work together to
produce HBT oscillations
• oscillations stable with KT
“LHC” (T0=2.0 GeV @ 0=0.1 fm)
• In-plane-extended source (!)
• HBT oscillations reflect competition
between geometry, flow
• low KT: geometry
• high KT: flow
STAR
HBT
oct 2002
sign flip
Heinz & Kolb, hep-th/0204061
Mike Lisa - XXXII ISMD - Alushta,
20
HBT(φ) Results – 200 GeV
• Oscillations similar to those
measured @ 130GeV
• 20x more statistics 
explore systematics in centrality, kT
• much more to come…
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
21
Summary
Quantitative understanding of bulk dynamics crucial to extracting real physics at RHIC
• p-space - measurements well-reproduced by models
• anisotropy  system response to compression (EoS)
• probe via v2(pT,m)
• x-space - generally not well-reproduced
• anisotropy  evolution, timescale information, geometry / flow interplay
• Azimuthally-sensitive HBT: correlating quantum correlation with bulk correlation
• reconstruction of full 3D source geometry
• Freezeout geometry out-of-plane extended
• early (and fast) particle emission !
• consistent with blast-wave parameterization of v2(pT,m), spectra, R(pT), K-
• With more detailed information, “RHIC HBT puzzle” deepens
• what about hadronic rescattering stage? - “must” occur, or…?
• does hydro reproduce t or not??
• ~right source shape via oscillations, but misses RL(mT)
• Models of bulk dynamics severely (over?)constrained
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
22
Backup slides follow
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
23
Summary
Freeze-out scenario f(x,t,p) crucial to understanding RHIC physics
• p-space - measurements well-reproduced by models
• anisotropy  system response to compression
• probe via v2(pT,m)
• x-space - generally not well-reproduced
• anisotropy  evolution, timescale information
• Azimuthally-sensitive HBT: a unique new tool to probe crucial information from
a new angle
elliptic flow data suggest x-space anisotropy
HBT R(f) confirm out-of-plane extended source
• for RHIC conditions, geometry dominates dynamical effects
• oscillations consistent with freeze-out directly from hydro stage (???)
• consistent description of v2(pT,m) and R(f) in blastwave parameterization
• challenge/feedback for “real” physical models of collision dynamics
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
24
RHIC  AGS
• Current experimental access only to second-order event-plane
• odd-order oscillations in fp are invisible
• cannot (unambiguously) extract tilt (which is likely tiny anyhow)
• cross-terms Rsl2 and Rol2 vanish @ y=0
 concentrate on “purely transverse” radii Ro2, Rs2, Ros2
• Strong pion flow  cannot ignore space-momentum correlations
• (unknown) implicit f-dependences in homogeneity lengths
 geometrical inferences will be more model-dependent
• the source you view depends on the viewing angle
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
25
Summary of anisotropic shape @ AGS
• RQMD reproduces data better in
“cascade” mode
• Exactly the opposite trend as
seen in flow (p-space anisotropy)
• Combined measurement much
more stringent test of flow
dynamics!!
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
26
hydro: time evolution of anisotropies at
RHIC and “LHC”
STAR
HBT
oct 2002
Heinz & Kolb, hep-th/0204061
Mike Lisa - XXXII ISMD - Alushta,
27
Blastwave Mach II - Including asymmetries
analytic description of freezeout distribution: exploding thermal source
t
•
R
•
 
 mT

f x, p   K1
cosh  
 T

pT
sinh  cosf s  f p 
T
e



•
•


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
 1  y 2  2 x 2 / R y 
STAR
HBT
e
2
 toct
/ 2002
 2
Mike Lisa - XXXII ISMD - Alushta,
28
Sensitivity to 0 within blast-wave
“Reasonable”
variations in radial
flow magnitude (0)

parallel pT dependence
for transverse HBT
radii
STAR
HBT
oct 2002
0
Mike Lisa - XXXII ISMD - Alushta,
29
Sensitivity to  within blast-wave
RS insensitive to 
RO increases with pT as
 increases
STAR
HBT
oct 2002

Mike Lisa - XXXII ISMD - Alushta,
30
Thermal motion superimposed on radial
flow
Hydro-inspired “blast-wave”
thermal freeze-out fits to , K, p, L
s
R
preliminary
s
un (t , r , z  0)  (cosh  , er sinh  , 0)
  tanh 1 r
STAR
HBT
 r   s f (r )
Tth = 107 MeV
 = 0.55
M. Kaneta
E.Schnedermann et al, PRC48 (1993) 2462
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
31
C(q)
Previous Data: - HBT(f) @ AGS
Au(4 AGeV)Au, b4-8 fm
2D projections f 
1D projections, f=45°
out
side
long
lines: projections of 3D Gaussian fit

 q i q j R ij2 f 
C(q, f)  1  f   e
• 6 components to radius tensor: i, j = o,s,l
STAR
E895,HBT
PLB 496
1 (2000)
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
32
Cross-term radii Rol, Ros, Rsl
quantify “tilts” in correlation functions
in q-space
f 
 fit results to correlation functions
Lines: Simultaneous
STAR
HBT
oct 2002
fit to HBT radii
Mike Lisa -geometry
XXXII ISMD - Alushta,
to extract underlying
33
First look at centrality dependence!
Hot off the presses PRELIMINARY
c/o Dan Magestro
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
34
But is that too naïve?
Hydro predictions for R2(f)
• correct phase (& ~amplitude) of oscillations
• (size (offset) of RO, RS , RL still wrong)
retracted Feb 02
but their freezeout source is in-plane extended?
• stronger in-plane (elliptic) flow “tricks” us
• “dynamics rules over geometry”
STAR
HBT
oct 2002
Mike Lisa - XXXII
ISMD
- Alushta,
Heinz
& Kolb
hep-ph/0111075
35
Experimental indications of x-space anisotropy @ RHIC
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
STAR
Meaning
HBT
0.0
0.04  0.01
of a is clear  how to interpret s2?
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
STAR, PRL 87 182301 (2001)
36
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
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
37
Hydro-inspired model calculations (“blast wave”)
consider results in context of blast wave model
• ~same parameters describe R(f) and v2(pT,m)
s2=0.033, T=100 MeV, 00.6
a0.033, R=10 fm, =2 fm/c
• both elliptic flow and aniostropic geometry
contribute to oscillations, but…
• geometry rules over dynamics
• R(f) measurement removes ambiguity over
nature of spatial anisotropy
case 1
STAR
HBT
case 2
oct 2002
early version of data
Mike Lisa -but
XXXII
ISMD - Alushta,
message
the same
38
To do
• Get “not-preliminary” plot of experimental spectra versus hydro
• Get Heinz/Kolb plot of epsilon and v2 versus time (from last paper)
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
39
Spatial anisotropy calculation
Shuryak/Teaney/Lauret define
s2, STL
x2  y 2
 2
x  y2
which of course is just the opposite to what, e.g. Heinz/Kolb call e:
e HK
y 2  x2
 2
x  y2
I think Raimond in some paper called the Heinz/Kolb parameter s2 also
(in analogy to v2). Great….
Better still, in the BlastWave, another s2 (in Lisa-B)
is related to Ry/Rx via:
s2, BW
1 3  1
  3
2  1

Ry
Rx
Anyway, if we say s2,BW = 0.04, this corresponds to  = 1.055 (5.5% extended)
which gives s2,STL = -0.05, or eHK = +0.05
This is in the range of the H/K hydro calculation, but seems a huge number for STL ?
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
40
Symmetries of the emission function
I. Mirror reflection symmetry w.r.t. reactionplane
(for spherical nuclei):
S( x, y, z, t ;Y , KT , )  S( x, y, z, t ;Y , KT ,)
Smn (Y , KT , )  1  Smn (Y , KT ,)

1  (1)
with
m 2  n 2
II. Point reflection symmetry w.r.t. collision center
(equal nuclei):
S( x, y, z, t ;Y , KT , )  S( x, y, z , t ;Y , KT ,   )
 Smn (Y , KT , )  2  Smn (Y , KT ,   )
2  (1)
with
STAR
HBT
oct 2002
m 0   n 0
Mike Lisa - XXXII ISMD - Alushta,
41
Fourier expansion of spatial correlation tensor Smn

S(f)  C0  2  Cn  cos(nf)  Sn  sin( nf)
n 1

Cn   
df
S(f)  cos(nf)
2
STAR
HBT
df
S(f)  sin( nf)
2
Sn = 0 for all terms containing even powers of y
Cn = 0 for all terms containing odd powers of y
I
II 

Sn   
For terms with even powers of t, Sn, Cn are odd (even)
functions of Y for odd (even) n
For terms with odd powers of t, it’s the other way around
The odd functions vanish at Y=0
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
42
Spatial correlation
tensor @ Y=0:
Smn
~
x2 ~
y2
2
~
x 2 ~
y2
Symmetry
Implications
1
2
1
1
2
1
~
x~
y
1
1
1
Fourier expansion
A0  2
B0  2
 An  cos(nf)
-
 Bn  cos(nf)

n  2, even
n  2, even
 Cn  sin( nf)
2
Zeros
0 ,90
n  2, even
~
t2
1
~
t ~
x
1
1
1
D0  2
2
 Dn  cos(nf)

n  2, even
 En  cos(nf)
90
 Fn  sin( nf)
0
 Gn  cos(nf)
90
n  2, odd
~
t ~
y
1
1
2
n  2, odd
~
t ~
z
1
1
2
n  2, odd
~
x ~
z
~
y ~
z
1
1
1
1
H0  2
2
 H n  cos(nf)

n  2, even
 I n  sin( nf)
0 ,90
n  2, even
STAR
HBT
oct 2002
~
z2
1
1
J 2
Mike Lisa - XXXII ISMD0 - Alushta,
 J n  cos(nf)
n  2, even

43
Fourier expansion of HBT radii @ Y=0
Insert symmetry constraints of spatial correlation tensor into Wiedemann relations
and combine with explicit -dependence:
Rs2 (f)
 Rs2,0 
2   n  2, 4,6,... Rs2, n  cos(nf)
Ro2 (f)
 Ro2,0 
2   n  2, 4,6,... Ro2, n  cos(nf)
2
2   n  2, 4,6,... Ros
, n  sin( nf)
2
Ros
(f) 
Rl2 (f)

Rl2,0 
2   n  2, 4,6,... Rl2,n  cos(nf)
Rol2 (f) 
2   n 1,3,5,... Rol2 , n  cos(nf)
Rsl2 (f)
2   n 1,3,5,... Rsl2 , n  sin( nf)

Note: These most general forms of the Fourier expansions for the HBT radii
are preserved when averaging the correlation function over a finite,
symmetric window around Y=0.
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
44
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
45
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
oct 2002
STAR preliminary
color: c2 levels
from HBT data
Mike Lisa - XXXII ISMD - Alushta,
error contour from
elliptic flow data
46
Joint view of  freezeout: HBT & spectra
• common model/parameterset
describes different aspects of f(x,p)
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
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
47
Typical 1-s Error contours for BP fits
•
Primary correlation is the
familiar correlation between 
and radii
•
Large acceptance
 no strong correlations
between radii
•
Cross-term uncorrelated with
any other parameter
STAR
HBT
oct 2002
E895 @ AGS
(QM99)
Mike Lisa - XXXII ISMD - Alushta,
48
Event mixing: zvertex issue
mixing those events generates artifact:
• too many large qL pairs in denominator
• bad normalization, esp for transverse radii
STAR
HBT
oct 2002
BP analysis with
1 z bin from -75,75
Mike Lisa - XXXII ISMD - Alushta,
49
2D contour plot of the pair emission angle CF….
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
50
Out-of-plane elliptical shape indicated in blast wave
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
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
51
Effect of dilute stage (RQMD) on v2
SPS and RHIC:
STAR
HBT
Teaney, Lauret, & Shuryak, nucl-th/0110037
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
52
Hydrodynamics: good description of radial
and elliptical flow at RHIC
RHIC; pt dependence quantitatively
described by Hydro
Charged
particles
• good agreement with hydrodynamic calculation
data: STAR, PHENIX, QM01
model: P. Kolb, U. Heinz
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
53
Hydrodynamics: problems describing HBT
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
oct 2002
Right dynamic effect / wrong space-time evolution?
 the “RHIC HBT Puzzle”
Mike Lisa - XXXII ISMD - Alushta,
54
“Realistic” afterburner does not help…
pure hydro
hydro + uRQMD
RO/RS
Currently, no “physical” model
reproduces explosive space-time
scenario indicated v2, HBT
1.0
STAR data
STAR
0.8
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
55
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
• “finger physics”: what (essentially) dominates observations?
• Isolate features generating discrepancy with “real” physics models
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
56
Characterizing the freezeout:
An analogous situation
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
57
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 m  f ( x , p)
0
x m p T , fp  2 
R
d
f
s 0 r  dr  f ( x , p)
0
2
R
d
f
s 0 r  dr  x m x n  f ( x , p)
~
~
0
x m x n p T , fp 
2
R
d
f
s 0 r  dr  f ( x , p)
Mike Lisa0- XXXII ISMD
- Alushta,

STAR
HBT


oct 2002









 xm xn
58
mT distribution from
Hydrodynamics-inspired model
s
R
Infinitely long
solid cylinder
 m cosh 
 pT sinh 
f ( x, p)  K1 T

exp
 cos fb  fp


T


 T

  tanh 1 (r )
  R  r 

(r )  s  g(r )
fb = direction of flow boost (= fs here)
2-parameter (T,) fit to mT distribution
STAR
HBT
E.Schnedermann et al, PRC48 (1993) 2462
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
59
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
s [c]
<r >= 0.8s
s [c]
1/mT dN/dmT (a.u.)
•
c2
K-
p
thanks to M. Kaneta
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
mT - m [GeV/c2]60
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
calculations using Schnedermann model
with parameters from spectra fits
x (fm)
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
61
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
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
62
Space-time asymmetry
from K- correlations
• Evidence of a space – time
asymmetry
– -K ~ 4fm/c ± 2 fm/c, static
sphere
– Consistent with “default” blast
wave calculation

pT = 0.12 GeV/c
STAR
HBT
oct 2002
K
pT = 0.42 GeV/c
Mike Lisa - XXXII ISMD - Alushta,
63
Non-central collisions: coordinate- and
momentum-space anisotropies
P. Kolb, J. Sollfrank, and U. Heinz
Equal energy density lines
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
64
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
STAR
Meaning
HBT
0.0
0.04  0.01
of a is clear  how to interpret s2?
oct 2002
STAR, in press PRL (2001)
Mike Lisa - XXXII ISMD - Alushta,
65
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
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
66
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
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
67
A consistent picture


T
 
 mT
 T sinh  cosfs fp 
2
2 2
t 2 / 2 2
f x, p   K1
cosh e
1 y   x / Ry  e
 T

p
parameter
Temperature
T  110 MeV
Radial flow
0  0.6
velocity
Oscillation in a  0.04
radial flow
Spatial
anisotropy
Radius in y
s2  0.04
spectra

elliptic flow

HBT

K-









Ry  10-13 fm


(depends on b)
Nature of x
anisotropy
Emission
duration
STAR
HBT
oct 2002
*

  2 fm/c

Mike Lisa - XXXII ISMD - Alushta,

68
Summary
Combined data-driven analysis of freeze-out distribution
• Single parameterization simultaneously describes
• spectra
• elliptic flow
• HBT
• K- correlations
• most likely cause of discrepancy is extremely rapid emission timescale suggested by
data - more work needed!
Spectra & HBT R(pT)
• Very strong radial flow field superimposed on thermal motion
v2(pT,m) & HBT Rf
• Very strong anisotropic radial flow field superimposed on thermal motion, and
geometric anisotropy
Dominant freezeout characteristics extracted
• STAR low-pT message
• constraints to models
• rapid freezeout timescale and (?) rapid evolution timescale
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
69
C(q)
Previous Data: - HBT(f) @ AGS
Au(4 AGeV)Au, b4-8 fm
2D projections f 
1D projections, f=45°
out
side
long
lines: projections of 3D Gaussian fit

 q i q j R ij2 f 
C(q, f)  1  f   e
• 6 components to radius tensor: i, j = o,s,l
STAR
E895,HBT
PLB 496
1 (2000)
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
70
Cross-term radii Rol, Ros, Rsl
quantify “tilts” in correlation functions
f 
 fit results to correlation functions
Lines: Simultaneous
STAR
HBT
oct 2002
fit to HBT radii
Mike Lisa -geometry
XXXII ISMD - Alushta,
to extract underlying
71
Meaning of Ro2(f) and Rs2(f) are clear
What about Ros2(f)
R2 (fm2)
E895 Collab., PLB 496 1 (2000)
xx
side
side
xout
xout
K
K
40
side
long
ol
os
sl
20
10
0
fp =
~45°
0°
out
-10
0
180
0
180
0
180
fp (°)
• Ros2(f) quantifies correlation between xout and xside
• No correlation (tilt) b/t between xout and xside at fp=0° (or 90°)
STAR
HBT
• Strong (positive) correlation when fp=45°
• Phase of Ros2(f) oscillation reveals orientation of extended source
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
72
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
73
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
74
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
75
Hydro predictions
for R2(f)
• correct phase of oscillations
• ~ correct amplitude of oscillations
• (size (offset) of RO, RS , RL still
inconsistent with data)
Heinz & Kolb hep-ph/0111075
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
76
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
77
Meaning of Ro2(f) and Rs2(f) are clear
What about Ros2(f)
R2 (fm2)
E895 Collab., PLB 496 1 (2000)
xx
side
side
xout
xout
ffp p=
~45°
0°
K
K
40
side
long
ol
os
sl
20
10
0
-10
0
STAR
HBT
out
180
0
180
0
180
fp (°)
• Ros2(f) quantifies correlation between xout and xside
• No correlation (tilt) b/t between xout and xside at fp=0
• Strong (positive) correlation when fp=45°
• Phase
of Ros2(f)Mike
oscillation
reveals
ext
oct
2002
Lisa - XXXII ISMD
- Alushta, orientation of 78
Just for fun, one for the road…
Let’s go to “high” pT…
if different, freeze-out is earlier or later?
so s2 (~ellipticity) should be lower or higher?
and a (diff. between flow out-of-plane and in-plane)
should be higher or lower?
OK, to look at higher pT, what happens with higher s2 and lower a?
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
79
v2(pT) for “early time” parameters
• “saturation” of v2 @ high pT
• mass - dependence essentially gone
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
80
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
STAR
Meaning
HBT
0.0
0.04  0.01
of a is clear  how to interpret s2?
oct 2002
STAR, in press PRL (2001)
Mike Lisa - XXXII ISMD - Alushta,
81
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
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
82
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
oct 2002
STAR preliminary
Mike Lisa - XXXII ISMD - Alushta,
83
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(f)
• 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- correlations
• most likely cause of discrepancy is extremely rapid emission
timescale suggested by data - more work needed!
STAR
HBT
oct 2002
Mike Lisa - XXXII ISMD - Alushta,
84