oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine 1 STAR HBT 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
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. Central collision dynamics @ RHIC. - PowerPoint PPT Presentation
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oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
2
STARHBT
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
Heinz & Kolb, hep-th/0204061
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
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?
Heinz & Kolb, hep-th/0204061
• Turn to richer dynamics of non-central collisions for more detailed information
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
hydro evolution
• Dynamical models:• x-anisotropy in entrance channel p-space anisotropy at freezeout
• magnitude depends on system response to pressure
Noncentral collision dynamics
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response EoS• early thermalization indicated
Heinz & Kolb, hep-ph/0111075
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
hydro evolution later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.0 GeV/c
• system response EoS• early thermalization indicated
Effect of dilute stage
• dilute hadronic stage (RQMD):• little effect on v2 @ RHIC
Teaney, Lauret, & Shuryak, nucl-th/0110037
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
hydro evolution later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response EoS• early thermalization indicated
Effect of dilute stage
• dilute hadronic stage (RQMD):• little effect on v2 @ RHIC• significant (bad) effect on HBT radii
calculation: Soff, Bass, Dumitru, PRL 2001
STARPHENIX
hydro onlyhydro+hadronic rescatt
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
hydro evolution later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response EoS• early thermalization indicated
Effect of dilute stage
• dilute hadronic stage (RQMD):• little effect on v2 @ RHIC• significant (bad) effect on HBT radii
• related to timescale? - need more info
Teaney, Lauret, & Shuryak, nucl-th/0110037
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
hydro evolution later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response EoS• early thermalization indicated
Effect of dilute stage
• 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!
in-plane-extended
out-of-plane-extended
Teaney, Lauret, & Shuryak, nucl-th/0110037
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Possible to “see” via HBT relative to reaction plane?
p=0°
p=90°
Rside (large)
Rside (small)• for out-of-plane-extended source, expect• large Rside at 0• small Rside at 90
2nd-orderoscillation
Rs2 [no flow expectation]
p
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
“Traditional HBT” - cylindrical sources
K
( ) ( ) ( )( ) ( )( ) ( ) ( )Kt~x~KR
Kx~KR
Kt~x~KR
2llong
2l
2side
2s
2out
2o
rr
rr
rr
β−=
=
β−= ⊥
xxx~ −≡
∫∫
⋅⋅⋅
≡)K,x(Sxd
)x(f)K,x(Sxdf
4
4RoutRside
( ) ( )y,xx,x sideout ≠
Decompose q into components:qLong : in beam directionqOut : in direction of transverse momentumqSide : qLong & qOut
(beam is into board)
( )2l2l
2s
2s
2o
2o RqRqRq
lso e1)q,q,q(C ++−⋅λ+=
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Anisotropic sources Six HBT radii vs
•Source in b-fixed system: (x,y,z)•Space/time entangled in
pair system (xO,xS,xL)
out
p
b
K
side
x
y
φβ−−φβ−=
ββ+β−φβ−+φβ−=
φβ−φβ+φ−+φ=
β+β−=
φ−φβ−φβ−β+φ+φ=
φ−φ+φ=
⊥⊥
⊥⊥
⊥⊥⊥
sin)t~x~z~x~(cos)t~y~z~y~(R
t~t~z~sin)t~y~z~y~(cos)t~x~z~x~(R
cost~y~sint~x~2sin)x~y~(2cosy~x~R
t~t~z~2z~R
2siny~x~sint~y~2cost~x~2t~siny~cosx~R
2siny~x~cosy~sinx~R
LL2sl
2LLL
2ol
22212
os
22LL
22l
2222222o
22222s
!• explicit and implicit (xx()) dependence on
xxx~ −≡
∫∫
⋅⋅⋅
≡)K,x(fxd
)x(q)K,x(fxdq
4
4
Wiedemann, PRC57 266 (1998).
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Symmetries of the emission functionI. Mirror reflection symmetry w.r.t. reactionplane (for spherical nuclei):
),,;,,,(S),,;,,,(S Φ−−=Φ TT KYtzyxKYtzyx
),,(~~),,(~~1 Φ−⋅θ=Φ TT KYxxKYxx
with 22)1(1 δ+δ−=θ
II. Point reflection symmetry w.r.t. collision center (equal nuclei):
),,;,,,(S),,;,,,(S π+Φ−−−−=Φ TT KYtzyxKYtzyx
),,(~~),,(~~2 π+Φ−⋅θ=Φ TT KYxxKYxx
with 00)1(2 δ+δ−=θ
Heinz, Hummel, MAL, Wiedemann, nucl-th/0207003
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Fourier expansion of HBT radii @ Y=0Insert symmetry constraints of spatial correlation tensor into Wiedemann relations and combine with explicit Φ-dependence:
∑∑∑∑∑∑
=
=
=
=
=
=
φ⋅⋅=φ
φ⋅⋅=φ
φ⋅⋅+=φ
φ⋅⋅=φ
φ⋅⋅+=φ
φ⋅⋅+=φ
,...5,3,12
,2
,...5,3,12
,2
,...6,4,22,
20,
2,...6,4,2
2,
2,...6,4,2
2,
20,
2,...6,4,2
2,
20,
2
)sin(2)(
)cos(2)(
)cos(2)(
)sin(2)(
)cos(2)(
)cos(2)(
n nslsl
n nolol
n nlll
n nosos
n nooo
n nsss
nRR
nRR
nRRR
nRR
nRRR
nRRR
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 geometry, and can help disentangle space and time
Heinz, Hummel, MAL, Wiedemann, nucl-th/0207003
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
•Out-of-plane-extended source (but flips with hadronic afterburner)
• flow & geometry work together to produce HBT oscillations
•oscillations stable with KT
Heinz & Kolb, hep-th/0204061
(note: RO/RS puzzle persists)
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Azimuthal HBT: hydro predictions
“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: flowsign flip
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
Heinz & Kolb, hep-th/0204061
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
HBT(φ) Results – 200 GeV
• Oscillations similar to those measured @ 130GeV
• 20x more statistics explore systematics in centrality, kT
• much more to come…
STAR PRELIMINARY
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
SummaryQuantitative 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-π
• 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
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Backup slides follow
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
SummaryFreeze-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
• 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
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
RHIC AGS
• Current experimental access only to second-order event-plane• odd-order oscillations in p are invisible
• 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
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
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!!
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
hydro: time evolution of anisotropies at RHIC and “LHC”
Heinz & Kolb, hep-th/0204061
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Blastwave Mach II - Including asymmetries
R
βt
( )
( )
( )22
psT
/t
y222
cossinhT
p
T1
e
R/xy1
e
coshT
mKp,xf
τΔ−
φ−φρ
×η+−θ
×
×⎟⎠⎞
⎜⎝⎛ ρ=
rr
• 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
}}}
analytic description of freezeout distribution: exploding thermal source
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Sensitivity to 0 within blast-wave
“Reasonable” variations in radial flow magnitude (0)parallel pT dependence
for transverse HBT radii
0
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Sensitivity to within blast-wave
RS insensitive to
RO increases with pT as increases
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Thermal motion superimposed on radial flow
Hydro-inspired “blast-wave” thermal freeze-out fits to π, K, p,
)0 ,sinh ,(cosh )0,,( rezrtu ==
β= −tanh 1r )( rfsr ββ =
R
βs
E.Schnedermann et al, PRC48 (1993) 2462
Tth = 107 MeVβ = 0.55
preliminary
M. Kaneta
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Previous Data: π- HBT() @ AGS
Au(4 AGeV)Au, b4-8 fm
• 6 components to radius tensor: i, j = o,s,l
1D projections, =45°
2D projections
( ) ( )φ−⋅φλ+=φ2ijji Rqq
e1),q(Cr
lines: projections of 3D Gaussian fit
out side long
C(q
)
E895, PLB 496 1 (2000)
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Cross-term radii Rol, Ros, Rsl quantify “tilts” in correlation
functionsin q-space
fit results to correlation functions
Lines: Simultaneous fit to HBT radiito extract underlying geometry
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
First look at centrality dependence!
Hot off the presses PRELIMINARYc/o Dan Magestro
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
but their freezeout source is in-plane extended?• stronger in-plane (elliptic) flow “tricks” us• “dynamics rules over geometry”
But is that too naïve?Hydro predictions for
R2()• correct phase (& ~amplitude) of oscillations
• (size (offset) of RO, RS , RL still wrong)
Heinz & Kolb hep-ph/0111075
retracted Feb 02
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Experimental indications of x-space anisotropy @ RHIC
soliddashed
0.04 0.010.09 0.02βa (c)
0.04 0.01 0.0S2
0.54 0.030.52 0.02β0(c)
100 24135 20T (MeV)
( ) ( ) ( ) ( )( ) ( )∫
∫π
π
φ
φφ=
20 T
coshm1T
sinhp0b
20 T
coshm1T
sinhp2bb
T2TT
TT
KId
KI2cosdpv
( )ba0 2cos φρ+ρ=ρFlow boost:
b = boost direction
Meaning of a is clear how to interpret s2?
hydro-inspiredblast-wave modelHouvinen et al (2001)
soliddashed
0.04 0.010.09 0.02βa (c)
0.04 0.01 0.0S2
0.54 0.030.52 0.02β0(c)
100 24135 20T (MeV)
STAR, PRL 87 182301 (2001)
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Ambiguity in nature of the spatial anisotroy
b = direction of the boost s2 > 0 means more source elements emitting in plane
( )( )
( ) ( )rR2cosR
rs21ecosh
T
mKp,xf s2
cossinhT
pT
1ps
T
−θ⎟⎠⎞
⎜⎝⎛ φ+⎟
⎠⎞
⎜⎝⎛ ρ=
φ−φρrr
case 1: circular source with modulating density
RMSx > RMSy
RMSx < RMSy
( )( ) ( )y222cossinh
T
pT
1 R/xy1ecoshT
mKp,xf
psT
η+−θ⎟⎠⎞
⎜⎝⎛ ρ=
φ−φρrr
case 2: elliptical source with uniform density
x
y
R
R≡η
1
1
2
1s
3
3
2 +η−η
≅
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Hydro-inspired model calculations (“blast wave”)
s2=0.033, T=100 MeV, 0aR=10 fm, =2 fm/cconsider results in context of blast wave model
• ~same parameters describe R() and v2(pT,m)
• both elliptic flow and aniostropic geometry contribute to oscillations, but…
• geometry rules over dynamics
• R() measurement removes ambiguity over nature of spatial anisotropy
early version of databut message the same
case 1 case 2
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
To do
• Get “not-preliminary” plot of experimental spectra versus hydro• Get Heinz/Kolb plot of epsilon and v2 versus time (from last paper)
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Spatial anisotropy calculation
Shuryak/Teaney/Lauret define 22
22
,2yx
yxs STL +
−=
which of course is just the opposite to what, e.g. Heinz/Kolb call : 22
22
yx
xyHK +
−=
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: x
yBW R
Rs ≡η
+η−η
⋅= 11
21
,2
Anyway, if we say s2,BW = 0.04, this corresponds to η= 1.055 (5.5% extended) which gives s2,STL = -0.05, or HK = +0.05
This is in the range of the H/K hydro calculation, but seems a huge number for STL ?
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
41
STARHBT
Symmetries of the emission functionI. Mirror reflection symmetry w.r.t. reactionplane (for spherical nuclei):
),,;,,,(S),,;,,,(S Φ−−=Φ TT KYtzyxKYtzyx
),,(),,( 1 Φ−⋅θ=Φ TT KYSKYS
with 22)1(1 δ+δ−=θ
II. Point reflection symmetry w.r.t. collision center (equal nuclei):
),,;,,,(S),,;,,,(S π+Φ−−−−=Φ TT KYtzyxKYtzyx
),,(),,( 2 π+Φ−⋅θ=Φ TT KYSKYS
with 00)1(2 δ+δ−=θ
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Fourier expansion of spatial correlation tensor S
[ ]∑∞
=φ⋅+φ⋅+=φ
10 )sin()cos(2)(S
nnn nSnCC
∫ππ− φ⋅φπφ
= )cos()(S2
nd
Cn ∫ππ− φ⋅φπφ
= )sin()(S2
nd
Sn
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) nFor terms with odd powers of t, it’s the other way aroundThe odd functions vanish at Y=0
I
II
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Spatial correlation tensor
@ Y=0:
Symmetry Implications
−φ⋅+
φ⋅−⋅
−φ⋅+⋅
φ⋅−⋅
φ⋅−−⋅
φ⋅−⋅
−φ⋅+
φ⋅−⋅
−φ⋅+
φ⋅+
θθ
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
≥
≥
≥
≥
≥
≥
≥
≥
≥
−≥
+
even ,20
2
even ,2
even ,20
odd ,2
odd ,2
odd ,2
even ,20
2
even ,2
even ,202
~~even,2
02
~~
21
)cos(211~
90,0)sin(211~~
)cos(211~~
90)cos(211~~
0)sin(211~~
90)cos(211~~
)cos(211~
90,0)sin(211~~
)cos(211
-)cos(211
ZerosexpansionFourier
22
22
nn
nn
nn
nn
nn
nn
nn
nn
nn
yxn
nyx
nJJz
nIzy
nHHzx
nGzt
nFyt
nExt
nDDt
nCyx
nBB
nAA
S
oo
o
o
o
oo
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Fourier expansion of HBT radii @ Y=0
Insert symmetry constraints of spatial correlation tensor into Wiedemann relations and combine with explicit Φ-dependence:
∑∑∑∑∑∑
=
=
=
=
=
=
φ⋅⋅=φ
φ⋅⋅=φ
φ⋅⋅+=φ
φ⋅⋅=φ
φ⋅⋅+=φ
φ⋅⋅+=φ
,...5,3,12
,2
,...5,3,12
,2
,...6,4,22,
20,
2,...6,4,2
2,
2,...6,4,2
2,
20,
2,...6,4,2
2,
20,
2
)sin(2)(
)cos(2)(
)cos(2)(
)sin(2)(
)cos(2)(
)cos(2)(
n nslsl
n nolol
n nlll
n nosos
n nooo
n nsss
nRR
nRR
nRRR
nRR
nRRR
nRRR
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.
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
46
STARHBT
s2 dependence dominates HBT signal
error contour fromelliptic flow data
color: 2 levelsfrom HBT data
STAR preliminary
s2=0.033, T=100 MeV, 0aR=10 fm, =2 fm/c
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Joint view of π freezeout: HBT & spectra
spectra (π)
HBT
• common model/parameterset describes different aspects of f(x,p)
• Increasing T has similar effect on a spectrum as increasing β
• But it has opposite effect on R(pT) opposite parameter correlations in
the two analyses tighter constraint on parameters
• caviat: not exactly same model used here (different flow profiles)
STAR preliminary
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Typical 1- Error contours for BP fits
• Primary correlation is the familiar correlation between λ and radii
• Large acceptance no strong correlations between radii
• Cross-term uncorrelated with any other parameter
E895 @ AGS(QM99)
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT BP analysis with 1 z bin from -75,75
mixing those events generates artifact:• too many large qL pairs in denominator• bad normalization, esp for transverse radii
Event mixing: zvertex issue
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
2D contour plot of the pair emission angle CF….
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Out-of-plane elliptical shape indicated in blast wave
using (approximate) values ofs2 and a from elliptical flow
case 1
case 2
opposite R() oscillations would lead to opposite conclusion
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Effect of dilute stage (RQMD) on v2SPS and RHIC:
Teaney, Lauret, & Shuryak, nucl-th/0110037
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Hydrodynamics: good description of radial and elliptical flow at RHIC
data: STAR, PHENIX, QM01model: P. Kolb, U. Heinz
RHIC; pt dependence quantitatively described by Hydro
Charged particles
• good agreement with hydrodynamic calculation
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Hydrodynamics: problems describing HBT
out
side
long
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
Right dynamic effect / wrong space-time evolution? the “RHIC HBT Puzzle”
generichydro
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
“Realistic” afterburner does not help…
pure hydro
hydro + uRQMD
STAR data
1.0
0.8
Currently, no “physical” modelreproduces explosive space-timescenario indicated v2, HBT
RO/R
S
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
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
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Characterizing the freezeout: An analogous
situation
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
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STARHBT
Probing f(x,p) from different angles
∫ ∫ ∫π π
⋅⋅⋅φφ=2
0
2
0
R
0Tps2
T
)p,x(fmdrrdddm
dN
Transverse spectra: number distribution in mT
∫ ∫ ∫∫ ∫ ∫
π π
π π
⋅⋅φφ
⋅φ⋅⋅φφ=φ≡
20
20
R0sp
20
20
R0 psp
pT2)p,x(fdrrdd
)p,x(f)2cos(drrdd)2cos()m,p(v
Elliptic flow: anisotropy as function of mT
HBT: homogeneity lengths vs mT, p
( )
( ) π
π
π
π
−⋅⋅φ
⋅⋅⋅φ=φ
⋅⋅φ
⋅⋅⋅φ=φ
∫ ∫∫ ∫
∫ ∫∫ ∫
xx)p,x(fdrrd
)p,x(fxxdrrd,px~x~
)p,x(fdrrd
)p,x(fxdrrd,px
20
R0s
20
R0s
pT
20
R0s
20
R0s
pT
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
59
STARHBT
mT distribution from Hydrodynamics-inspired model
)r(tanh 1β= −
E.Schnedermann et al, PRC48 (1993) 2462
R
βs
( ) ( )rRcosT
sinhpexp
T
coshmK)p,x(f pb
TT1 −Θ⋅⎥⎦
⎤⎢⎣⎡ φ−φ⋅
ρ⋅⎟⎠⎞
⎜⎝⎛ ρ
=
Infinitely longsolid cylinder
b = direction of flow boost (= s here)
2-parameter (T,β) fit to mT distribution
)r(g)r( s ⋅β=β
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
60
STARHBT
• 2 contour maps for 95.5%CL
T th [
GeV
]
βs [c]
- K-p
T th [
GeV
]
βs [c]
T th [
GeV
]
βs [c]
Tth =120+40-30MeV
<βr >=0.52 ±0.06[c]
tanh-1(<βr >) = 0.6
<βr >= 0.8βs
Fits to STAR spectra; βr=βs(r/R)0.5
-
K-
p
1/m
T d
N/d
mT
(a
.u.)
mT - m [GeV/c2]thanks to M. Kaneta
preliminary
STAR preliminary
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
61
STARHBT
Implications for HBT: radii vs pT
Assuming β, T obtained from spectra fits strong x-p correlations, affecting RO, RS differently
pT=0.2
pT=0.4
y (f
m)
y (f
m)
x (fm)
x (fm)
( )22S
2O RR τ⋅β+=
calculations using Schnedermann modelwith parameters from spectra fits
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
62
STARHBT
Implications for π HBT: radii vs pT
STAR data
model: R=13.5 fm, =1.5 fm/c T=0.11 GeV, 0 = 0.6
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
pT=0.4
y (f
m)
y (f
m)
x (fm)
x (fm)
Four parameters affect HBT radii
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
63
STARHBT
Space-time asymmetry from K-π correlations
• Evidence of a space – time asymmetry– π-K ~ 4fm/c ± 2 fm/c, static
sphere
– Consistent with “default” blast wave calculation
πpT = 0.12 GeV/c
KpT = 0.42 GeV/c
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
64
STARHBT
Non-central collisions: coordinate- and momentum-space anisotropies
Equal energy density lines
P. Kolb, J. Sollfrank, and U. Heinz
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
65
STARHBT
More detail: identified particle elliptic flow
soliddashed
0.04 0.010.09 0.02βa (c)
0.04 0.01 0.0S2
0.54 0.030.52 0.02β0(c)
100 24135 20T (MeV)
STAR, in press PRL (2001)
( ) ( ) ( ) ( )( ) ( )∫
∫π
π
φ
φφ=
20 T
coshm1T
sinhp0b
20 T
coshm1T
sinhp2bb
T2TT
TT
KId
KI2cosdpv
( )ba0 2cos φρ+ρ=ρFlow boost:
b = boost direction
Meaning of a is clear how to interpret s2?
hydro-inspiredblast-wave modelHouvinen et al (2001)
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
66
STARHBT
Ambiguity in nature of the spatial anisotroy
b = direction of the boost s2 > 0 means more source elements emitting in plane
( )( )
( ) ( )rR2cosR
rs21ecosh
T
mKp,xf s2
cossinhT
pT
1ps
T
−θ⎟⎠⎞
⎜⎝⎛ φ+⎟
⎠⎞
⎜⎝⎛ ρ=
φ−φρrr
case 1: circular source with modulating density
RMSx > RMSy
RMSx < RMSy
( )( ) ( )y222cossinh
T
pT
1 R/xy1ecoshT
mKp,xf
psT
η+−θ⎟⎠⎞
⎜⎝⎛ ρ=
φ−φρrr
case 2: elliptical source with uniform density
x
y
R
R≡η
1
1
2
1s
3
3
2 +η−η
≅
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
67
STARHBT
case 1
using (approximate) values ofs2 and a from elliptical flow
case 2
opposite R() oscillations would lead to opposite conclusion
Out-of-plane elliptical shape indicated
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
68
STARHBT
A consistent picture
parameter spectra elliptic flow HBT K-π
Temperature T≈11MeV √ √ √ √
Radialflowvelocity
≈. √ √ √ √
Oscillationinradialflow
a≈.4 √ √
Spatialanisotropy
s2≈.4 √ √
Radiusiny Ry≈1-1fm(dependsonb)
√ √
Natureofxanisotropy
* √
Emissionduration
≈2fm/c √ √
( )( ) ( ) 22ps
T
2/ty
222cossinhT
pT
1 eR/xy1ecoshT
mKp,xf τφ−φρ
⋅η+−θ⎟⎠⎞
⎜⎝⎛ ρ=
rr
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
69
STARHBT
SummaryCombined data-driven analysis of freeze-out distribution• Single parameterization simultaneously describes
• spectra• elliptic flow• HBT• K-π 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
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
70
STARHBT
Previous Data: π- HBT() @ AGS
Au(4 AGeV)Au, b4-8 fm
• 6 components to radius tensor: i, j = o,s,l
1D projections, =45°
2D projections
( ) ( )φ−⋅φλ+=φ2ijji Rqq
e1),q(Cr
lines: projections of 3D Gaussian fit
out side long
C(q
)
E895, PLB 496 1 (2000)
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
71
STARHBT
Cross-term radii Rol, Ros, Rsl quantify “tilts” in correlation
functions
fit results to correlation functions
Lines: Simultaneous fit to HBT radiito extract underlying geometry
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
72
STARHBT
xout
xside
K
Meaning of Ro2() and Rs
2() are clearWhat about Ros
2()
p (°) 0 180
0
0 180 0 180
10
-10
20
40
R2 (
fm2 ) out side long
ol os sl
E895 Collab., PLB 496 1 (2000)
• Ros2() quantifies correlation between xout and xside
• No correlation (tilt) b/t between xout and xside at p=0° (or 90°)
K
x out x sid
e K x out x sid
e
K x out x side
K xout
x side
K xout
xside
K xout
xside
p = 0°p ~45°
• Strong (positive) correlation when p=45°
• Phase of Ros2() oscillation reveals orientation of extended source
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
73
STARHBT
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
74
STARHBT
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
75
STARHBT
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
76
STARHBT
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
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
77
STARHBT
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
78
STARHBT
xout
xside
K
Meaning of Ro2() and Rs
2() are clearWhat about Ros
2()
p (°) 0 180
0
0 180 0 180
10
-10
20
40
R2 (
fm2 ) out side long
ol os sl
E895 Collab., PLB 496 1 (2000)
• Ros2() quantifies correlation between xout and xside
• No correlation (tilt) b/t between xout and xside at p=0° (or 90°)
K
x out x sid
e K x out x sid
e
K x out x side
K xout
x side
K xout
xside
K xout
xside
p = 0°p
~45°
• Strong (positive) correlation when p=45°
• Phase of Ros2() oscillation reveals orientation of extended source
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
79
STARHBT
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?
so s2 (~ellipticity) should be lower or higher?
and a (diff. between flow out-of-plane and in-plane) should be higher or lower?
if different, freeze-out is earlier or later?
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
80
STARHBT
v2(pT) for “early time” parameters
• “saturation” of v2 @ high pT
• mass - dependence essentially gone
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
81
STARHBT
More detail: identified particle elliptic flow
soliddashed
0.04 0.010.09 0.02βa (c)
0.04 0.01 0.0S2
0.54 0.030.52 0.02β0(c)
100 24135 20T (MeV)
STAR, in press PRL (2001)
( ) ( ) ( ) ( )( ) ( )∫
∫π
π
φ
φφ=
20 T
coshm1T
sinhp0b
20 T
coshm1T
sinhp2bb
T2TT
TT
KId
KI2cosdpv
( )ba0 2cos φρ+ρ=ρFlow boost:
b = boost direction
Meaning of a is clear how to interpret s2?
hydro-inspiredblast-wave modelHouvinen et al (2001)
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
82
STARHBT
Ambiguity in nature of the spatial anisotroy
b = direction of the boost s2 > 0 means more source elements emitting in plane
( )( )
( ) ( )rR2cosR
rs21ecosh
T
mKp,xf s2
cossinhT
pT
1ps
T
−θ⎟⎠⎞
⎜⎝⎛ φ+⎟
⎠⎞
⎜⎝⎛ ρ=
φ−φρrr
case 1: circular source with modulating density
RMSx > RMSy
RMSx < RMSy
( )( ) ( )y222cossinh
T
pT
1 R/xy1ecoshT
mKp,xf
psT
η+−θ⎟⎠⎞
⎜⎝⎛ ρ=
φ−φρrr
case 2: elliptical source with uniform density
x
y
R
R≡η
1
1
2
1s
3
3
2 +η−η
≅
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
83
STARHBT
Out-of-plane elliptical shape indicated
case 1
using (approximate) values ofs2 and a from elliptical flow
case 2
opposite R() oscillations would lead to opposite conclusion STAR preliminary
oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine
84
STARHBT
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-π correlations
• most likely cause of discrepancy is extremely rapid emission timescale suggested by data - more work needed!