Transcript Characterizing the freezeout at RHIC

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
 q o2 R o2  q s2 R s2  q l2 R l2 
C(q o , qs , q l )  1    e
Decompose q into components:
qLong : in beam direction

~2 
2
~
qOut : in direction of transverse momentum
R o K  x out   t
K
qSide :  qLong & qOut


K
  
  
R s2 K   ~
x side2 K 

~2 
2
~
R l K   x long  l t  K 
xout, xside  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 cos 2 f  ~y 2 sin 2 f  2 t 2  2 ~
x t cos f  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 cos f
~
~
~
~
2
R ol
( ~
x~z  L ~
x t ) cos f  ( ~y~z  L ~y t ) sin f   ~z t  L t 2
~
~
R sl2  ( ~y~z  L ~y t ) cos f  ( ~
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)
2
Rol
(f) 
2
2   n 1,3,5,... Rol
, 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) ?
xxside
side
xxoutout
K
K
R2 (fm2)
Au+Au 2 AGeV; E895, PLB 496 1 (2000)
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