Two-particle correlations and Heavy Ion
Collision Dynamics at RHIC/STAR
Mike Lisa, Ohio State University
STAR Collaboration
Characterizing the soft sector:
• Central collision dynamics – spectra & HBT(pT) & K-
• Non-central collision dynamics – elliptic flow & HBT()
• Consistent picture of RHIC dynamics?
• Recent developments (in progress) – preliminary Y2 data
• Y2 HBT() – first systematics
• Bowler/Sinyukov Coulomb correction
• Conclusions
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
1
Who cares about the soft sector (the “brown muck”)?
• Well-justified excitement
about high-pT physics
99.5%
• But recall that we want to
create/study a new type of
matter (= bulk system)
• large-scale (soft) deconfinement
• jets/ect are probes of this system
• Crucial to understand bulk
properties/dynamics in their
own right
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
2
Hadrochemistry: particle yields vs statistical models
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
3
STAR
HBT
lattice QCD applies
18 oct 2002
CERN H.I.F. - ma lisa
4
Already producing QGP at lower energy?
Thermal model fits to particle yields
(including strangeness, J/)
 approach QGP at CERN?
• is the system really thermal?
• warning: e+e- falls on similar line!!
(somewhat worse residuals)
• dynamical signatures? (no)
• what was pressure generated?
• what is Equation of State of
strongly-interacting matter?
Must go beyond chemistry:
 study dynamics of system well into
deconfined phase (RHIC)
STAR
HBT
lattice QCD applies
18 oct 2002
CERN H.I.F. - ma lisa
5
Collision dynamics - 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
“temperature”
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!!!
18 oct 2002
5 fm/c ?
CERN H.I.F. - ma lisa
6
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
– RHIC is first time hydro works!
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
lattice QCD input
7
Central collision dynamics @ RHIC
• Hydrodynamics reproduces p-space aspects
(spectra and elliptical flow) of particle
emission up to pT~2GeV/c (99% of
particles)
 hopes of exploring the early, dense stage
STAR
HBT
18 oct 2002
Heinz & Kolb, hep-th/0204061
CERN H.I.F. - ma lisa
8
“Blast wave” Thermal motion superimposed
on radial flow (+ geometry)
Hydro-inspired “blast-wave”
thermal freeze-out fits to , K, p, L
s
R
preliminary
s
u (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
18 oct 2002
CERN H.I.F. - ma lisa
9
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
18 oct 2002
CERN H.I.F. - ma lisa
10
“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   t 

2 
2
~
R s K  x side K

~2
2
Rl K  ~
x long  l 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 )
18 oct 2002
R o2
 R s2
   
2
x out , x side   x, y 
beware this “helpful” mnemonic!
CERN H.I.F. - ma lisa
11
Large lifetime - a favorite signal of “new”
physics at RHIC
• hadronization time
(burning log) will
increase emission
timescale (“lifetime”)
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
18 oct 2002
CERN H.I.F. - ma lisa
12
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
18 oct 2002
CERN H.I.F. - ma lisa
13
HBT excitation function
midrapidity, low pT from 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)
18
oct 2002
CERN H.I.F. - ma lisa
14
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 is too small and lives too
long and disintegrates too slowly?
• Correct dynamics signatures with wrong
space-time dynamics?
• The RHIC HBT Puzzle
• Is there any consistent way to understand the
data?
• Try to understand in simplest way possible
STAR
HBT
18 oct 2002
Heinz & Kolb, hep-th/0204061
CERN H.I.F. - ma lisa
15
Blastwave parameterization:
Implications for HBT: radii vs pT
Assuming , T obtained from spectra fits
 strong x-p correlations, affecting RO, RS differently
K
2
RO
pT=0.2
2
 RS
   
2
RO
K
RS
pT=0.4
STAR
HBT
18 oct 2002
“whole source” not viewed
CERN H.I.F. - ma lisa
16
Blastwave: radii vs pT
Using 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
Four parameters affect HBT radii
STAR data
K
pT=0.2
R o2  R s2  2 2
blastwave: R=13.5 fm,
freezeout=1.5 fm/c
K
pT=0.4
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
17
Kaon – pion correlations:
dominated by Coulomb interaction
Smaller source  stronger
(anti)correlation
K-p correlation well-described by:
• Blast wave with same parameters
as spectra, HBT
But with non-identical particles, we
can access more information…
STAR preliminary
Adam Kiesel, Fabrice Retiere
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
18
Initial idea: probing emission-time ordering
purple K emitted first
green  is faster
• Catching up: cosY  0
•
•
purple K emitted first
green  is slower
• Moving away: cosY  0
•
•
Crucial point:
kaon begins farther in “out” direction
(in this case due to time-ordering)
STAR
HBT
18 oct 2002
long interaction time
strong correlation
short interaction time
weak correlation
• Ratio of both scenarios
allow quantitative study of
the emission asymmetry
CERN H.I.F. - ma lisa
19
measured K- correlations - natural consequence
of space-momentum correlations
• clear space-time asymmetry observed
• C+/C- ratio described by:
– “standard” blastwave w/ no time shift
• Direct proof of radial flow-induced
space-momentum correlations
STAR preliminary
Pion
Kaon
STAR
<pt> HBT
= 0.12 GeV/c
18 oct 2002 <pt> = 0.42 GeV/c CERN H.I.F. - ma lisa
20
Back to pion HBT…
From  Rlong: tkinetic = 8-10 fm/c (fast!)
Simple Sinyukov formula
– RL2 = tkinetic2 T/mT
• tkinetic = 10 fm/c (T=110 MeV)
STAR
HBT
18 oct 2002
B. Tomasik (~3D blast wave)
– tkinetic = 8-9 fm/c
CERN H.I.F. - ma lisa
21
Noncentral collision dynamics
hydro evolution
v2  cos2
dN
~ 1  2v2 cos2
or
d
• Dynamical models:
• x-anisotropy in entrance channel
 p-space anisotropy at freezeout
• magnitude depends on system
response to pressure
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
22
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
18 oct 2002
Heinz & Kolb, hep-ph/0111075
23
CERN H.I.F. - ma lisa
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
RHIC
@ RHIC for pT < ~1.0 GeV/c
• system response  EoS
• early thermalization indicated
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
STAR
HBT
SPS
18 oct 2002
CERN
H.I.F. Lauret,
- ma lisa & Shuryak, nucl-th/0110037
Teaney,
24
Effect of dilute stage
hydro evolution
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
later hadronic stage?
hydro only
hydro+hadronic rescatt
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
• significant (bad) effect on HBT radii
STAR
HBT
18 oct 2002
STAR
PHENIX
Soff, Bass, Dumitru, PRL 2001
CERN H.I.F. -calculation:
ma lisa
25
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
18 oct 2002
CERN H.I.F.
- ma lisa
26
Teaney,
Lauret, & Shuryak, nucl-th/0110037
Effect of dilute stage
hydro evolution
later hadronic stage?
in-planeextended
• 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
• qualitative change of freezeout shape!!
• important piece of the puzzle!
STAR
HBT
18 oct 2002
out-of-plane-extended
CERN H.I.F.
- ma lisa
27
Teaney,
Lauret, & Shuryak, nucl-th/0110037
Possible to “see” via HBT relative to reaction plane?
p=90°
• for out-of-plane-extended source, expect
• large Rside at 0
2nd-order
• small Rside at 90
oscillation
Rside (small)
Rside (large)
p=0°
2
Rs [no flow expectation]
p
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
28
“Traditional HBT” - cylindrical sources
(reminder)
Decompose q into components:
C(qo , qs , ql )  1    eq o R o  q s R s  q l R l 
qLong : in beam direction

~2 
2
~
R o K  x out   t
K
qOut : in direction of transverse momentum
qSide :  qLong & qOut


2
K
2
2
2
2
2
  
  
R s2 K   ~
x side2 K 

~2 
2
~
R l K   x long  l t  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
18 oct 2002
CERN H.I.F. - ma lisa
29
Anisotropic sources Six HBT radii vs 
side
•Source in b-fixed system: (x,y,z)
•Space/time entangled in
pair system (xO,xS,xL)
R s2
~2
~2
y
K
p
x
 x sin   y cos   ~
x~y sin 2
2
out
2
b
~
~
~
R o2  ~
x 2 cos2   ~y 2 sin 2   2 t 2  2 ~
x t cos  2 ~y t sin   ~
x~y sin 2
~
~
R l2  ~z 2  2L ~z t  2L t 2
~
~
2
R os
 ~
x~y cos 2  12 ( ~y 2  ~
x 2 ) sin 2   ~
x t sin    ~y t cos
~
~
~
~
2
R ol
( ~
x~z  L ~
x t ) cos  ( ~y~z  L ~y t ) sin    ~z t  L t 2
~
~
R sl2  ( ~y~z  L ~y t ) cos  ( ~
x~z  L ~
x t ) sin 
• explicit
and implicit (xmx()) dependence on 
STAR
HBT
18 oct 2002
Wiedemann,
PRC57 266 (1998).
!
CERN H.I.F. - ma lisa
~
xx x
d 4 x  f ( x, K )  q( x )

q 
4
d
 x  f ( x, K)30
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 ~
x (Y , KT , )  1  ~
xm ~
x (Y , KT ,)
with
1  (1)
m 2   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 ~
x (Y , KT , )  2  ~
xm ~
x (Y , KT ,   )
with
STAR
HBT
2  (1)
18 oct 2002
m 0    0
Heinz, Hummel,
MAL,
Wiedemann, nucl-th/0207003
CERN H.I.F.
- ma lisa
31
Fourier expansion of HBT radii @ Y=0
Insert symmetry constraints of spatial correlation tensor into Wiedemann relations
and combine with explicit -dependence:
Rs2 ()
 Rs2,0 
2   n  2, 4,6,... Rs2, n  cos(n)
Ro2 ()
 Ro2,0 
2   n  2, 4,6,... Ro2, n  cos(n)
2
2   n  2, 4,6,... Ros
, n  sin( n)
2
Ros
() 
Rl2 ()

Rl2,0 
2   n  2, 4,6,... Rl2,n  cos(n)
Rol2 () 
2   n 1,3,5,... Rol2 , n  cos(n)
Rsl2 ()
2   n 1,3,5,... Rsl2 , n  sin( n)

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
18 oct 2002
CERN H.I.F.
- ma lisa
Heinz, Hummel,
MAL,
Wiedemann, nucl-th/0207003
32
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
p = 0°
out
-10
0
180
0
180
0
180
p (°)
• strong oscillations observed
• lines: predictions for static (tilted) out-of-plane extended source
 consistent with initial overlap geometry
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
33
Meaning of Ro2() and Rs2() are clear
What about Ros2() ?
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
p =
~45°
0°
out
-10
No access to 1st-order
oscillations in STAR Y1
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°)
STAR
HBT
• Strong (positive) correlation when p=45°
• Phase of Ros2() oscillation reveals orientation of extended source
18 oct 2002
CERN H.I.F. - ma lisa
34
C(q)
Previous Data: - HBT() @ AGS
Au(4 AGeV)Au, b4-8 fm
2D projections  
1D projections, =45°
out
side
long
lines: projections of 3D Gaussian fit

 q i q j R ij2  
C(q, )  1     e
• 6 components to radius tensor: i, j = o,s,l
STAR
E895,HBT
PLB 496
1 2002
(2000)
18 oct
CERN H.I.F. - ma lisa
35
Cross-term radii Rol, Ros, Rsl
quantify “tilts” in correlation functions
in q-space
 
 fit results to correlation functions
Lines: Simultaneous
STAR
HBT
18 oct 2002
fit to HBT radii
CERN
H.I.F. - ma lisa
to extract underlying
geometry
36
Experimental indications of x-space anisotropy @ RHIC
2
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
2
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
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?
18 oct 2002
CERN H.I.F. - ma lisa
STAR, PRL 87 182301 (2001)
37
Ambiguity in nature of the spatial anisotroy
2
p sinh 
m cosh 






1  2s2 cos2b 
d

cos
2

I
K

b
b 2
1
T
T
0
v 2 pT  
2
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
18 oct 2002
CERN H.I.F. - ma lisa
38
Minbias observations at 130 GeV
“raw”
•  flat within errors
• Significant (& “allowed”) oscillations
observed in HBT radii
• RP/binning correction (*) significant
• produces RL2 oscillation from
“nowhere”? – is it real?
preliminary
2
RO
after RP/binning
correction
R S2
2
R OS
(*) can return to this
[Heinz, Hummel, MAL, Wiedemann PRC 044903 (2002)]
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
R 2L
39
Removing the ambiguity with HBT()
• blastwave with ~ same parameters as used to
describe spectra & v2(pT,m)
• additional parameters:
•R = 11 fm
consistent with
• = 2 fm/c !!
s2=0.037, T=100 MeV, 00.6
a0.037, R=11 fm, =2 fm/c
preliminary
R(pT), K-
• freezeout source out-of-plane extended
 fast freeze-out timescale ! (7-9 fm/c)
2
RO
R S2
2
R OS
case 1
STAR
HBT
case 2
18 oct 2002
R 2L
CERN H.I.F. - ma lisa
40
What causes the oscillations: flow or geometry?
full blastwave
• both flow anisotropy and source shape
contribute to oscillations, but…
• geometry dominates dynamics
no spatial
anisotropy
preliminary
2
RO
no flow
anisotropy
R S2
R 2L
STAR
HBT
2
R OS
18 oct 2002
CERN H.I.F. - ma lisa
41
Summary of “nice story”
RHIC 130 GeV Au+Au
K*
Tomasik (3D blastwave): 8-9 fm/c (fit to PHENIX even smaller)
Sinyukov formula: Rlong2=2T/mT = 10 fm/c for T=110 MeV
K-
Disclaimer: all numbers (especially time) are rough estimates
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
42
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
18 oct 2002
CERN H.I.F. - ma lisaHeinz & Kolb, hep-th/0204061
43
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
18 oct 2002
sign flip
CERN H.I.F. - ma lisaHeinz & Kolb, hep-th/0204061
44
Spatial correlation tensor @ Y=0:
Symmetry Implications
Ro2, 0  A0  B2  C2  2  T  E1  F1    T2  D0
R
 J 0  2  l G0    D0
2
l
Rs2, 2  A2  12 B0  B4  C4 
2
o,2
R
 A2 
1
2
~
x2 ~
y2
2
~
x 2 ~
y2
Rs2, 0  A0  B2  C2
2
l ,0
Sm
B0  B4  C4 
 T  E1  E3  F1  F3    T2  D2
Ros2 , 2  12  ( B0  B4  C4 )
 12 T  E1  E3  F1  F3 
Rl2, 0  J 2  2  l G2   l2  D2
1
2
1
1
Fourier expansion
A0  2
2
1
1
B0  2
~
x~
y
1
1
2
Zeros
 An  cos(n)
-


n  2, even
Bn
n  2, even
 cos(n)
 Cn  sin( n)
0 ,90
n  2, even
~
t2
~
t ~
x
1
1
1
1
D0  2
2
 Dn  cos(n)

n  2, even
 En  cos(n)
90
 Fn  sin( n)
0
 Gn  cos(n)
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(n)

n  2, even
 I n  sin( n)
0 ,90
n  2, even
~
z2
1
1
J0  2

Jn
n  2, even
 cos(n)

• 7 experimental values for 15 tensor elements 
• “only” 11 elements with n<3
• careful
study of l & T sytematics may allow disentanglement of important physics
STAR
HBT
18 oct 2002
[Heinz,
Hummel,
MAL,
CERN
H.I.F. - ma
lisa Wiedemann PRC 044903 (2002)]45
First systematics at 200 GeV
Centrality dependence of HBT()
R2
R2
R2
R2
curves: fits to allowed oscillations
STAR preliminary
•
Oscillation phases suggest out-of-plane extended source
•
Source size increases, oscillations decrease with increasing centrality
•
Oscillation amplitudes: As < Ao (may encode impt information)
•
RL oscillation solid?
STAR
HBT
18 oct 2002
200 GeV data – Dan Magestro
46
CERN H.I.F. - ma lisa
Summary
Hadrochemistry suggests creation of QGP @ RHIC (and SPS)
Quantitative understanding of bulk dynamics crucial to extracting real physics at RHIC
• p-space - measurements well-reproduced by models
• anisotropy [v2(pT,m)]  system response to compression (EoS)
• x-space - generally not well-reproduced
• anisotropy [HBT()] evolution, timescale information, geometry/flow interplay
• Azimuthally-sensitive HBT: correlating quantum correlation with bulk correlation
• reconstruction of full 3D source geometry
• relevant here: OOP freeze-out
Data do suggest consistent (though surprising) scenario
• strong collective effects
• rapid evolution, then emission in a “flash” (key input to models)
• where is the hadronic phase?
• K-, HBT(pT), HBT(), K*…
By combining several (novel) measurements, STAR severely challenges our
understanding of dynamics in the soft sector of RHIC
Systematics of HBT() encode a wealth of important dynamical information
STAR
The
program of this new aspect of correlations is just beginning!
HBT
18 oct 2002
CERN H.I.F. - ma lisa
47
The End
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
48
Various Coulomb Corrections
A(q)
 N  (1    G (q))
B(q)  K coul (q)
account for Coulomb suppression
in all background pairs
A(q)
 N  (1    G (q))  K coul (q)
B(q)
“Standard Correction”
*
K coul (q)  K coul
(q)  1    1    K coul (q)
A(q)
 N  (1    G (q))
*
B(q)  K coul (q)
only Coulomb-suppress the
fraction of pairs () which are
direct pions
A(q)
 N  (1    G (q))  1   ( K coul (q)  1) 
B(q)
A(q)
 N  (1   ) 1    K coul (q)  1  G (q)
B(q)
A(q)

 N  1    K coul (q)  1  G (q) 1
B(q)
STAR
HBT
18 oct 2002
G (q)  exp( qi q j Rij2 )
“Diluted Correction”
a pair either participates
in both BE and Coulomb,
or neither
Bowler-Sinyukov
method
CERN H.I.F. - ma lisa
K coul (q)   coul x, q 
2
x
49
Results from the different methods
“Standard” correction
• Ro is most affected radius
• ~10% effect
(e.g. Ro goes from 6.06 to 6.71 at
lowest pT)
“Diluted” correction
Bowler-Sinyukov
• Dilution similar to Bowler-Sinyukov
• (not obvious from math)
• Dilution & Bowler-Sinyukov suggest
lower  than Standard
• checking details with simulations
• Though in the right direction, not
enough to solve “HBT puzzle”
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
50
Backup slides follow
• 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
18 oct 2002
CERN H.I.F. - ma lisa
51
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() 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() in blastwave parameterization
• challenge/feedback for “real” physical models of collision dynamics
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
52
RHIC  AGS
• Current experimental access only to second-order event-plane
• odd-order oscillations in p 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 -dependences in homogeneity lengths
 geometrical inferences will be more model-dependent
• the source you view depends on the viewing angle
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
53
Peripheral +
200 GeV
“raw”
preliminary
• Oscillations similar to 130 GeV
minbias
• RS oscillation < RO oscillation
• Oscillation in RL clear in raw
2
RO
after RP/binning
correction
R S2
2
R OS
R 2L
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
54
Projections of 3-d correlation function
centrality:
STAR preliminary
•
pair-RP ~ 0° , -
•
Lines are projections of 3-d fit:
•
Width increases with increasing b  smaller radii
STAR
HBT
18 oct 2002

 q i q j R ij2  
C(q, )  1     e
200 GeV data – Dan Magestro
55
CERN H.I.F. - ma lisa
R2
R2
Combine pions to reduce fluctuations for comparing to calculations
R2
•
Blast wave: a first look @ 200 GeV
STAR preliminary
• Blast wave reproduces all oscillations,
but Rs2 amplitudes are too low

• Blast wave in trouble for year 2?
Ry
• Need spectra, HBT(pT), v2(pT,m)
0-10%
1.02
12 fm
•  increases with b, indicates source
is more out-of-plane extended
10-30%
1.05
11 fm
30-70%
1.10
9.25 fm
STAR
HBT
18 oct 2002
caveat: other BW parameters kept fixed
T=100 MeV, a=0.04, 0=0.9, askin=0.01
CERN H.I.F. - ma lisa
Ry
Rx

Ry
Rx
56
Note: correcting for RP resolution
•
New model-independent method1 corrects for:
1.
2.
•
Reaction plane resolution
Effect of finite binning in 
Correction applied bin-by-bin
separately for numerator and
denominator of C (q, )
overall effect: amplitudes of
oscillations increase
STAR preliminary
STAR
HBT
18 oct 2002
1 Heinz,
Hummel, Lisa, Wiedemann, nucl-th/0207003
CERN H.I.F. - ma lisa
57
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
18 oct 2002
CERN H.I.F. - ma lisa
58
hydro: time evolution of anisotropies at
RHIC and “LHC”
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
Heinz & Kolb, hep-th/0204061
59
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
18 oct 2002
CERN H.I.F. - ma lisa
60
Spatial correlation
tensor @ Y=0:
Sm
~
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(n)
-
 Bn  cos(n)

n  2, even
n  2, even
 Cn  sin( n)
2
Zeros
0 ,90
n  2, even
~
t2
~
t ~
x
1
1
1
1
D0  2
2
 Dn  cos(n)

n  2, even
 En  cos(n)
90
 Fn  sin( n)
0
 Gn  cos(n)
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(n)

n  2, even
 I n  sin( n)
0 ,90
n  2, even
STAR
HBT
18 oct 2002
~
z2
1
1
J 2
CERN H.I.F. - ma0lisa
 J n  cos(n)
n  2, even

61
Experimental indications of x-space anisotropy @ RHIC
2
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
2
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
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?
18 oct 2002
CERN H.I.F. - ma lisa
STAR, PRL 87 182301 (2001)
62
Ambiguity in nature of the spatial anisotroy
2
p sinh 
m cosh 






1  2s2 cos2b 
d

cos
2

I
K

b
b 2
1
T
T
0
v 2 pT  
2
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
18 oct 2002
CERN H.I.F. - ma lisa
63
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
18 oct 2002
CERN H.I.F. - ma lisa
64
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
18 oct 2002
CERN H.I.F. - ma lisa
65
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 s   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
2
 t18
/oct
2002
CERN H.I.F. - ma lisa
66
Sensitivity to 0 within blast-wave
“Reasonable”
variations in radial
flow magnitude (0)

parallel pT dependence
for transverse HBT
radii
STAR
HBT
18 oct 2002
0
CERN H.I.F. - ma lisa
67
“HBT 101” - probing source geometry
p1
 source
(x)
1m
x2
p2
5 fm
r2
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
}

*TT  U1*U1  U*2 U 2  1  eiq( x1  x 2 )
1-particle probability
(x,p) = U*U
2-particle probability
P(p1, p 2 )
2
C(p1, p 2 ) 
 1 ~
 (q )
P(p1 )P(p 2 )
C (Qinv)
r1
x1

  
q  p 2  p1
Width ~ 1/R
2
1
Measurable!
STAR
HBT
F.T. of pion source
0.05
18 oct 2002
CERN H.I.F. - ma lisa
0.10
68
Qinv (GeV/c)
Sensitivity to  within blast-wave
RS insensitive to 
RO increases with pT as
 increases
STAR
HBT
18 oct 2002

CERN H.I.F. - ma lisa
69
Thermal motion superimposed on radial
flow
Hydro-inspired “blast-wave”
thermal freeze-out fits to , K, p, L
s
R
preliminary
s
u (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
18 oct 2002
CERN H.I.F. - ma lisa
70
First look at centrality dependence!
Hot off the presses PRELIMINARY
c/o Dan Magestro
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
71
But is that too naïve?
Hydro predictions for R2()
• 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
18 oct 2002
CERN Heinz
H.I.F. - ma
& lisa
Kolb
hep-ph/0111075
72
Experimental indications of x-space anisotropy @ RHIC
2
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
2
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
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?
18 oct 2002
CERN H.I.F. - ma lisa
STAR, PRL 87 182301 (2001)
73
Ambiguity in nature of the spatial anisotroy
2
p sinh 
m cosh 






1  2s2 cos2b 
d

cos
2

I
K

b
b 2
1
T
T
0
v 2 pT  
2
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
18 oct 2002
CERN H.I.F. - ma lisa
74
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
18 oct 2002
CERN H.I.F. - ma lisa
75
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
18 oct 2002
CERN H.I.F. - ma lisa
76
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 ,)
Sm (Y , KT , )  1  Sm (Y , KT ,)

with
1  (1)
m 2   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 ,   )
 Sm (Y , KT , )  2  Sm (Y , KT ,   )
with
STAR
HBT
2  (1)
18 oct 2002
m 0    0
CERN H.I.F. - ma lisa
77
Fourier expansion of spatial correlation tensor Sm

S()  C0  2  Cn  cos(n)  Sn  sin( n)
n 1

Cn   
I
II 
STAR
HBT
d
S()  cos(n)
2

Sn   
d
S()  sin( n)
2
Sn = 0 for all terms containing even powers of y
Cn = 0 for all terms containing odd powers of y
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
18 oct 2002
CERN H.I.F. - ma lisa
78
Fourier expansion of HBT radii @ Y=0
Insert symmetry constraints of spatial correlation tensor into Wiedemann relations
and combine with explicit -dependence:
Rs2 ()
 Rs2,0 
2   n  2, 4,6,... Rs2, n  cos(n)
Ro2 ()
 Ro2,0 
2   n  2, 4,6,... Ro2, n  cos(n)
2
2   n  2, 4,6,... Ros
, n  sin( n)
2
Ros
() 
Rl2 ()

Rl2,0 
2   n  2, 4,6,... Rl2,n  cos(n)
Rol2 () 
2   n 1,3,5,... Rol2 , n  cos(n)
Rsl2 ()
2   n 1,3,5,... Rsl2 , n  sin( n)

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
18 oct 2002
CERN H.I.F. - ma lisa
79
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
80
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
18 oct 2002
STAR preliminary
color: c2 levels
from HBT data
CERN H.I.F. - ma lisa
error contour from
elliptic flow data
81
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
18 oct 2002
CERN H.I.F. - ma lisa
82
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
18 oct 2002
E895 @ AGS
(QM99)
CERN H.I.F. - ma lisa
83
Indirect indications of x-space anisotropy @ RHIC
• v2(pT,m) globally well-fit by
hydro-inspired “blast-wave”
(Houvinen et al)
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
18 oct 2002
0.04  0.01
temperature, radial flow
consistent with fits to spectra 
anisotropy of flow boost
spatial anisotropy (out-of-plane extended)
CERN H.I.F. - maSTAR,
lisa
PRL 87 182301 (2001)
84
Event mixing: zvertex issue
mixing those events generates artifact:
• too many large qL pairs in denominator
• bad normalization, esp for transverse radii
STAR
HBT
BP analysis with 1CERN
z bin
from -75,75
H.I.F. - ma lisa
18 oct 2002
85
2D contour plot of the pair emission angle CF….
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
86
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() oscillations would
lead to opposite conclusion
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
87
Effect of dilute stage (RQMD) on v2
SPS and RHIC:
STAR
HBT
Teaney, Lauret, & Shuryak, nucl-th/0110037
18 oct 2002
CERN H.I.F. - ma lisa
88
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
18 oct 2002
CERN H.I.F. - ma lisa
89
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
18 oct 2002
Right dynamic effect / wrong space-time evolution?
 the “RHIC HBT Puzzle”
CERN H.I.F. - ma lisa
90
“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
18 oct 2002
CERN H.I.F. - ma lisa
91
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
18 oct 2002
CERN H.I.F. - ma lisa
92
Characterizing the freezeout:
An analogous situation
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
93
Probing f(x,p) from different angles
Transverse spectra: number distribution in mT
2
R
dN 2
  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 ) 
2
2
R
d

d

p 0
s 0 r  dr  cos(2p )  f ( x , p)
0
2
2
R
d

d

p 0
s 0 r  dr  f ( x , p)
0






HBT: homogeneity lengths vs mT, p
2
R
d

s 0 r  dr  x m  f ( x , p)
0
x m p T , p  2 
R
d

s 0 r  dr  f ( x , p)
0
2
R
d

s 0 r  dr  x m x   f ( x , p)
~
~
0
x m x  p T , p 
2
R
d

s 0 r  dr  f ( x , p)
0 H.I.F.
18 oct 2002
CERN
- ma lisa

STAR
HBT











 xm x
94
mT distribution from
Hydrodynamics-inspired model
s
R
 m cosh 
 pT sinh 
f ( x, p)  K1 T

exp
 cos b  p


T


 T

  tanh 1 (r )
Infinitely long
solid cylinder
  R  r 

(r )  s  g(r )
b = direction of flow boost (= s here)
2-parameter (T,) fit to mT distribution
STAR
HBT
E.Schnedermann et al, PRC48 (1993) 2462
18 oct 2002
CERN H.I.F. - ma lisa
95
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
18 oct 2002
CERN H.I.F. - ma lisa
mT - m [GeV/c2]96
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
18 oct 2002
CERN H.I.F. - ma lisa
97
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
Four parameters affect HBT radii
pT=0.2
y (fm)
STAR data
y (fm)
x (fm)
pT=0.4
model: R=13.5 fm, =1.5 fm/c
T=0.11 GeV, 0 = 0.6
x (fm)
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
98
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
18 oct 2002
K
pT = 0.42 GeV/c
CERN H.I.F. - ma lisa
99
Non-central collisions: coordinate- and
momentum-space anisotropies
P. Kolb, J. Sollfrank, and U. Heinz
Equal energy density lines
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
100
More detail: identified particle elliptic flow
2
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
2
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
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?
18 oct 2002
CERN H.I.F. - ma lisa
STAR, in press PRL (2001)
101
Ambiguity in nature of the spatial anisotroy
2
p sinh 
m cosh 






1  2s2 cos2b 
d

cos
2

I
K

b
b 2
1
T
T
0
v 2 pT  
2
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
18 oct 2002
CERN H.I.F. - ma lisa
102
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
18 oct 2002
CERN H.I.F. - ma lisa
103
A consistent picture


T
 
 mT
 T sinh  coss p 
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
18 oct 2002
*

  2 fm/c

CERN H.I.F. - ma lisa

104
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
• 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
18 oct 2002
CERN H.I.F. - ma lisa
105
C(q)
Previous Data: - HBT() @ AGS
Au(4 AGeV)Au, b4-8 fm
2D projections  
1D projections, =45°
out
side
long
lines: projections of 3D Gaussian fit

 q i q j R ij2  
C(q, )  1     e
• 6 components to radius tensor: i, j = o,s,l
STAR
E895,HBT
PLB 496
1 2002
(2000)
18 oct
CERN H.I.F. - ma lisa
106
Cross-term radii Rol, Ros, Rsl
quantify “tilts” in correlation functions
 
 fit results to correlation functions
Lines: Simultaneous
STAR
HBT
18 oct 2002
fit to HBT radii
CERN
H.I.F. - ma lisa
to extract underlying
geometry
107
Meaning of Ro2() and Rs2() are clear
What about Ros2()
R2 (fm2)
E895 Collab., PLB 496 1 (2000)
xx
side
side
xout
xout
K
K
40
side
long
ol
os
sl
20
10
0
p =
~45°
0°
out
-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°)
STAR
HBT
• Strong (positive) correlation when p=45°
• Phase of Ros2() oscillation reveals orientation of extended source
18 oct 2002
CERN H.I.F. - ma lisa
108
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
109
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
110
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
111
Hydro predictions
for R2()
• 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
18 oct 2002
CERN H.I.F. - ma lisa
112
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
113
Meaning of Ro2() and Rs2() are clear
What about Ros2()
R2 (fm2)
E895 Collab., PLB 496 1 (2000)
xx
side
side
xout
xout
p p=
~45°
0°
K
K
40
side
long
ol
os
sl
20
10
0
-10
0
STAR
HBT
out
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
• Strong (positive) correlation when p=45°
• Phase
of Ros2() oscillation
orientation of114ext
18
oct 2002
CERN H.I.F. - mareveals
lisa
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
18 oct 2002
CERN H.I.F. - ma lisa
115
v2(pT) for “early time” parameters
• “saturation” of v2 @ high pT
• mass - dependence essentially gone
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
116
More detail: identified particle elliptic flow
2
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
2
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
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?
18 oct 2002
CERN H.I.F. - ma lisa
STAR, in press PRL (2001)
117
Ambiguity in nature of the spatial anisotroy
2
p sinh 
m cosh 






1  2s2 cos2b 
d

cos
2

I
K

b
b 2
1
T
T
0
v 2 pT  
2
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
18 oct 2002
CERN H.I.F. - ma lisa
118
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
18 oct 2002
STAR preliminary
CERN H.I.F. - ma lisa
119
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- correlations
• most likely cause of discrepancy is extremely rapid emission
timescale suggested by data - more work needed!
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
120
Resonance survival measurements
• Resonances which decay in-medium (between chemical
and kinetic freeze-out):
– Daughters rescatter, preventing reconstruction
– Leads to suppression of measured yields which may be related to
time scale for rescattering
– Caveat: regeneration of resonances possible?
• Short-lived resonances measured in STAR:
– 0(770), w0, 0, K*0(892), f0(980) , 0 , ,
S/(1385), L(1520)
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
121
+ - Invariant Mass Distribution
Au+Au
40% to 80%
0.2  pT  0.9 GeV/c
|y|  0.5
Statistical error only
STAR
HBT
18 oct 2002
pp
STAR Preliminary
sNN = 200 GeV
STAR Preliminary
0.2  pT  0.8 GeV/c
|y|  0.5
0
f0
K0S
w
K*0
0
f0
K0S
w
K*0
Statistical error only
CERN H.I.F. - ma lisa
122
Survival rate interpretation according
to Rafelski
Upper limit
• Combining both K* and
L(1520) results
  ~ 0-3 fm/c
• But Tchem too low compared
to other measurements
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
123
The K*0 story
• K*0/ not enhanced
• K*0/K suppressed in AA versus pp
STAR
HBT
18 oct 2002
CERN H.I.F. - ma lisa
124
Particle ID in STAR
RICH
STAR
dE/dx
dE/dx PID range:
s (dE/dx) = .08]
RICH PID range:
p  ~ 0.7 GeV/c for K/
1 - 3 GeV/c for K/
 ~ 1.0 GeV/c for p/p
Topology
1.5 - 5 GeV/c for p/p
Decay vertices
Ks   + +  -
L  p +-
L  p +  +
X +
L +  +
Combinatorics
Ks   + +  -
  K++K-
X- L + -
L  p + -
L  p +  +
W  L + K-
    + +  -
  p +  -
dn/dm
 from K+ K- pairs
background
subtracted
Vo
m inv
dn/dm
same event dist.
mixed event dist.
“kinks”:
K m + 
STAR
HBT
18 oct 2002
K+ K- pairs
CERN H.I.F. - ma lisa
125
m
inv
Kaon Spectra at Mid-rapidity vs
Centrality
K-
K+
Centrality
cuts
Centrality
cuts
STAR preliminary
Exponential fits to mT spectra:
STAR
HBT
18 oct 2002
(K++K-)/2
Ks
STAR preliminary
1 dN
 m 
 A exp   T 
mT dmT
 T 
Centrality
cuts
STAR preliminary
Good agreement between
different PID methods
CERN H.I.F. - ma lisa
126