^ Azimuthally-sensitive HBT (asHBT) in
Au+Au collisions at sNN=200 GeV
Mike Lisa, Ohio State University
for the STAR Collaboration
• motivation – why study asHBT @ RHIC?
• BlastWave parameterization of freeze-out
• fits/predictions @ 130 GeV
• sensitivity of asHBT to F.O. shape
• asHBT in Au+Au collisions at s NN=200 GeV
• RP/binning resolution correction
• radii vs centrality, kT, 
• physics implications
• Summary
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
1
Already a problem with “traditional” HBT @ RHIC…
• p-space observables well-understood
within hydrodynamic framework
→ hope of understanding early stage
• x-space observables not well-reproduced
• correct dynamical signatures with
incorrect dynamic evolution?
• Too-large timescales modeled?
• emission/freezeout duration (RO/RS)
• evolution duration (RL)
Soff, Bass, Dumitru
Heinz & Kolb, hep-ph/0204061
dN/dt
CYM & LGT
PCM & clust. hadronization
NFD
NFD & hadronic TM
string & hadronic TM
STAR
HBT
PCM & hadronic TM
16 Oct 2003
time
2nd Warsaw Meeting on Correlations and Resonances
2
Already a problem with “traditional” HBT @ RHIC…
• p-space observables well-understood
within hydrodynamic framework
→ hope of understanding early stage
hydro only
hydro+hadronic rescatt
• x-space observables not well-reproduced
• correct dynamical signatures with
incorrect dynamic evolution?
• Too-large timescales modeled?
• emission/freezeout duration (RO/RS)
• evolution duration (RL)
dN/dt
STAR
PHENIX
“Realistically” treating FO with
hadronic afterburner makes it worse
CYM & LGT
PCM & clust. hadronization
NFD
NFD & hadronic TM
string & hadronic TM
STAR
HBT
PCM & hadronic TM
16 Oct 2003
time
2nd Warsaw Meeting on Correlations and Resonances
3
… so why study (more complicated) asHBT ?
• sensitive to interplay b/t anisotropic geometry & dynamics/evolution
Kolb & Heinz, Phys. Lett. B542 216 (2002)
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
4
… so why study (more complicated) asHBT ?
• sensitive to interplay b/t anisotropic geometry & dynamics/evolution
• “broken symmetry” for b0 → more detailed, important physics information
• another handle on dynamical timescales – likely impt in HBT puzzle
P. Kolb, nucl-th/0306081
P. Kolb and U. Heinz, hep-ph/0204061
“elliptic flow”
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
5
Freeze-out anisotropy as an evolution “clock”
hydro evolution
later hadronic stage?
Teaney et al, nucl-th0110037
• dilute (hadronic) stage
• little effect on p-space at RHIC
• significant (bad) effect on HBT radii
• related to timescale
• qualitative change in FO
in-planeextended
P. Kolb and U. Heinz,
hep-ph/0204061
RS small
• anisotropic pressure gradients
→ preferential in-plane flow (v2)
→ evolution towards in-plane shape
• FO sensitive to evolution duration 0
hydro only
hydro+hadronic rescatt
p=90°
RS big
R.P.
p=0°
STAR
PHENIX
Soff,
Bass,nucl-th/0110037
Dumitru, PRL 2001
Teaney, Lauret,
Shuryak,
out-of-plane-extended
Teaney et al, nucl-th0110037
• FO from asHBT?
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
6
Need a model of the freezeout- BlastWave
BW: hydro-inspired parameterization of freezeout
• longitudinal direction
• infinite extent geometrically
• boost-invariant longitudinal flow
• Momentum space
• temperature T
• transverse rapidity boost ~ r
 (r ) 
R
r
0  ~r 0
R
• Schnedermann et al (’93): 2-parameter (T, max)
“hydro-inspired” functional form to fit spectra.
• Useful to extract thermal, collective energy
R
dN
 p sinh  
 m sinh  
 0 r  dr  mT  I0  T
  K1 T

mT dmT
T
T




Teaney, Lauret & Shuryak, nucl-th/0110037
1, 2
r
   max  
R
  tanh -1
azimuthally isotropic source model – let’s generalize for finite impact parameter …
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
7
Need a model of the freezeout- BlastWave
BW: hydro-inspired parameterization of freezeout
• longitudinal direction
• infinite extent geometrically
• boost-invariant longitudinal flow
• Momentum space
• temperature T
• transverse rapidity boost ~ r
r
 (r )    ~r 
 (r ,  )  ~
r    cos( 2 ) 
R
0
0
s
0
a
RY
b
RX
• coordinate space
• transverse extents RX, RY
• freezeout in proper time 
• evolution duration 0
• emission duration 

00
    0 2 
dN

~ exp  
2 
d
 2 
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
2nd Warsaw Meeting on Correlations and Resonances
8
Need a model of the freezeout- BlastWave
BW: hydro-inspired parameterization of freezeout
• longitudinal direction
• infinite extent geometrically
• boost-invariant longitudinal flow
• Momentum space
• temperature T
• transverse rapidity boost ~ r
r
 (r )    ~r 
 (r ,  )  ~
r    cos( 2 ) 
R
0
0
s
0
a
RY
b
RX
• coordinate space
• transverse extents RX, RY
• freezeout in proper time 
• evolution duration 0
• emission duration 
7 parameters describing freezeout
    0 2 
dN

~ exp  
2 
d
 2 
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
2nd Warsaw Meeting on Correlations and Resonances
9
BlastWave fits to published RHIC data
• pT spectra constrain (mostly) T, 0
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
2nd Warsaw Meeting on Correlations and Resonances
central
midcentral
peripheral
10
BlastWave fits to published RHIC data
• pT spectra constrain (mostly) T, 0
• (traditional) HBT radii constrain R, 0, 
• depend also on T, 0
RoutRout
RsideRside
R=9 fm
R=12 fm
R=18 fm
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
RlongRlong
2nd Warsaw Meeting on Correlations and Resonances
11
BlastWave fits to published RHIC data
• pT spectra constrain (mostly) T, 0
central
midcentral
peripheral
• (traditional) HBT radii constrain R, 0, 
• depend also on T, 0
• imperfect fit (esp. PHENIX RS)
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
2nd Warsaw Meeting on Correlations and Resonances
12
BlastWave fits to published RHIC data
central
midcentral
peripheral
• pT spectra constrain (mostly) T, 0
• (traditional) HBT radii constrain R, 0, 
• depend also on T, 0
• imperfect fit (esp. PHENIX RS)
• v2(pT,m) constrain RY/RX, a
Central
Midcentral
Peripheral
T (MeV)
108  3
106  3
95  4
0
0.88  0.01
0.87  0.02
0.81  0.02
a
0.06  0.01
0.05  0.01
0.04  0.01
RX (fm)
12.9  0.3
10.2  0.5
8.0  0.4
RY (fm)
12.8  0.3
11.8  0.6
10.1  0.4
0 (fm/c)
8.9  0.3
7.4  1.2
6.5  0.8
 (fm/c)
0.0  1.4
0.8  3.2
0.8  1.9
153.7 / 92
74.3 / 68
2 / ndf
STAR
80.5 / 101
HBT
16 Oct 2003
F. Retière & MAL, in preparation
• reasonable centrality
evolution
• OOP extended source in
non-central collisions
2nd Warsaw Meeting on Correlations and Resonances
~ 2 fm/c with
Bowler CC
(Not this talk)
13
Minbias v2, asHBT @ 130 GeV
STAR, PRL 87 182301 (2001)
• v2(pT,m) globally well-fit by
hydro-inspired “blast-wave”
• a ~ 0.04, RY/RX ~ 1.05
• Minbias asHBT well-reproduced with
same BlastWave from minbias v2(pT,m)
• Ry = 11.4 fm
• Rx = 10.8 fm
• 0 = 8.3 fm/c
•  = 0 ( → ~1.5 fm/c w/ Bowler CC))
• asHBT: geometry dominates dynamics
STAR
• Source out-of-plane extended
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
14
So far
• v2(pT,m) indicates OOP-extended FO source for non-central collisions
• (confirmation from minbias asHBT)
• Would rather “view” the geometry more directly
→ analyze asHBT in higher-statistics 200 GeV dataset (next…)
p=90°
RS small
RS big
R.P.
p=0°
• But… HBT radii depend on “everything” (T, 0, …)
• can we extract FO shape from asHBT alone?
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
15
can we extract FO shape
from asHBT alone?
the BlastWave view
out
side
• non-central collisions – all HBT radii exhibit
0th & 2nd - order oscillations (n>2 negligible)
• characterize each kT bin with 7 numbers:
 R 2 pT ,   cosn 
R 2 ,n pT    2
 R  pT ,   sin n 
  o, s, l
; n  0,2
  os
R2os,0 = 0 by symmetry (*)
out-side
long
(*) Heinz, Hummel, MAL, Wiedemann, Phys. Rev. C66 044903 (2002)
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
2nd Warsaw Meeting on Correlations and Resonances
16
can we extract FO shape
from asHBT alone?
the BlastWave view
• non-central collisions – all HBT radii exhibit
0th & 2nd - order oscillations (n>2 negligible)
• characterize each kT bin with 7 numbers:
 R 2 pT ,   cosn 
R 2 ,n pT    2
 R  pT ,   sin n 
  o, s, l
; n  0,2
  os
• for fixed (RY2+RX2), increasing RY/RX
• R2,0 unchanged
• |R2,2| increases (sensitivity to FO shape)
• both R2,0 and |R2,2| fall with pT
• same dependence/mechanism?
(flow-induced x-p correlations)
• examine “normalized” oscillations R2,2/R2,0
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
2nd Warsaw Meeting on Correlations and Resonances
17
FO shape from
“normalized” oscillations
the BlastWave view
• no-flow scenario: independent of pT…

R 2y  R 2x
R 2y

R 2x
2
R s2, 2
R s2,0
2
2
R os
,2
R s2,0
 2
R o2, 2
R s2,0
U. Wiedemann PR C57 266 (1998)
MAL, U. Heinz, U. Wiedemann PL B489 287 (2000)
• in BW: this remains ~true even with flow
(esp @ low pT)
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
/2
2nd Warsaw Meeting on Correlations and Resonances
18
FO shape from
“normalized” oscillations
the BlastWave view
fixed 
• no-flow scenario: independent of pT…

R 2y  R 2x
R 2y

R 2x
2
R s2, 2
R s2,0
2
2
R os
,2
R s2,0
 2
R o2, 2
R s2,0
U. Wiedemann PR C57 266 (1998)
MAL, U. Heinz, U. Wiedemann PL B489 287 (2000)
• in BW: this remains ~true even with flow
(esp @ low pT)
• independent of RY2+RX2
• independent of  (and 0)
• ~independent of T (and 0)
→ estimate  from R2,2/ R2s,0 (=o,s,os)
STAR
HBT
16 Oct 2003
F. Retière & MAL,
in preparation
2nd Warsaw Meeting on Correlations and Resonances
19
asHBT at 200 GeV in STAR – R() vs centrality
12 (!) -bins b/t 0-180 (kT-integrated)
• 72 independent CF’s
• clear oscillations observed in transverse radii
of symmetry-allowed* type
• Ro2, Rs2, Rl2 ~ cos(2)
• Ros2 ~ sin(2)
• centrality dependence reasonable
• oscillation amps higher than 2nd-order ~ 0
→ extract 0th, 2nd Fourier coefficients vs kT
with 4 -bin analysis
(*) Heinz, Hummel, MAL, Wiedemann, Phys. Rev. C66 044903 (2002)
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
20
Correcting for finite -binning & RP-resolution
• Reaction-plane estimation (from event-wise
p-space anisotropy) is imperfect
→ nth-order oscillations reduced by
cos(n(m--R)) *
mm--R
R
* cos(nm) from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C58 1671 (1998)
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
21
Correcting for finite -binning & RP-resolution
• Reaction-plane estimation (from event-wise
p-space anisotropy) is imperfect
→ nth-order oscillations reduced by
cos(n(m--R)) *
•  bins have finite width 
→ nth-order oscillations reduced by
sin( n / 2)
n / 2
* cos(nm) from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C58 1671 (1998)
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
22
Correcting for finite -binning & RP-resolution
• Reaction-plane estimation (from event-wise
p-space anisotropy) is imperfect
→ nth-order oscillations reduced by
cos(n(m--R)) *
•  bins have finite width 
→ nth-order oscillations reduced by
sin( n / 2)
n / 2
oscillations of what?
• not the HBT radii
• what is measured (and averaged/smeared)
are pair number distributions N(q), D(q)
[ C(q) = N(q) / D(q) ]
* cos(nm) from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C58 1671 (1998)
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
23
Correcting for finite -binning & RP-resolution


Nq,  
Cq,    
Dq,  
Heinz, Hummel, MAL, Wiedemann, Phys. Rev. C66 044903 (2002)


N exp (q,  j )  N exp
(
q
)
0
N bin


exp 
2  N exp
(
q
)
cos(
n

)

N
c ,n
j
s ,n (q ) sin( n j )
n 1

N(q,  j )  N exp (q,  j ) 
N bin

exp
2   n ,m () N exp
c ,n (q ) cos(n j )  N s ,n (q ) sin( n j )
n 1
Fourier coefficients for a given q-bin.
n / 2

N c,n (q) coefficients
 sin(
N exp
cos(

Fourier
a ngiven
n(q/,2) )for
cos(
()m qbin
R ))
 n ,mexp() 

“raw”
corrected
1
p

 N1exp N
(qbin, ) cos(n)
 factor
N exp
q,  j ) cos(
n j ) for
correction
for
nth(-order
oscillations
N
bin

1
j1N
the damping
effects
ofj ) cos(n j )
 N bin 
exp (q, 
N


bin j1
1)exp finite
resolution
in determining the mthN
s ,nexp(q)  N exp (q,  ) sin( n )
event-plane
Ns,order
n (q )  N exp (q,  ) sin( n )

1 NNbinbin bin width
2) non-vanishing
() in the
• ~ 30% effect on 2nd-order radius oscillations
1  N exp(q,  j ) sin( n j )

emission
 N angle
(q, respect
 N with
j ) sin( nto
j ) the event• ~0% change in mean values
bin jj11 exp
N
STAR
plane (binj)
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
24

N exp
(
q
)
c ,n
asHBT at 200 GeV in STAR – R() vs kT
• Clear oscillations observed at all kT
• extract 7 radius Fourier Coefficients
(shown by lines)
2

 R  pT ,   cosn 
R  ,n pT    2
R p ,   sin n 

  T
2
STAR
HBT
16 Oct 2003
midcentral collisions (20-30%)
  o, s, l
  os
2nd Warsaw Meeting on Correlations and Resonances
25
Grand Data Summary – R2,n vs kT, centrality
• One plot w/ relevant quantities from
2x5x3x4=120 3D CFs (*)
2

 R  pT ,   cosn 
R  ,n pT    2
R p ,   sin n 

  T
2
  o, s, l
  os
• left: R2,0  “traditional” radii
• usual kT, centrality dependence
• right: R2,2 / R2,0
• reasonable centrality dependence
• BW: sensitive to FO source shape
(*) first STAR HBT paper: 10 CFs
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
26
Estimate of initial vs F.O. source shape

R 2y  R 2x
R 2y  R 2x
• estimate INIT from Glauber
• from asHBT:
 FO  2
RHIC1
[Kolb & Heinz]
R S2, 2
R S2,0
• FO < INIT → dynamic expansion
• FO > 1 → source always OOP-extended
• constraint on evolution time
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
27
A simple estimate – 0 from init and final
• BW → X, Y @ F.O. (X > Y)
• hydro: flow velocity grows ~ t
  X ,Y ( t )   X ,Y (F.O.) 
t
0
• From RL(mT): 0 ~ 9 fm/c
consistent picture
• Longer or shorter evolution times
X inconsistent
P. Kolb, nucl-th/0306081
toy estimate: 0 ~ 0(BW)~ 9 fm/c
• But need a real model comparison
→ asHBT valuable “evolutionary clock”
constraint for models
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
28
Summary
• FO source shape a “clock” for system evolution
– OOP-extended  earlier kinetic FO
– further test of long-lived hadronic stage: OOPIP-extended source  inconsistent w/ data
• BlastWave parameterization of FO at RHIC -- sNN=130 GeV
– not perfect fit @ 130 GeV, but can provide some guidance/insight
– “traditional HBT” in fit suggest short emission, evolution timescales
• qualitatively supported by OOP from v2, minbias asHBT
– Fourier decomposition of HBT radius oscillations
• even with flow-induced x-p correlations, asHBT alone useful to estimate FO (R2u,2/ R2s,0)
• asHBT @ sNN=200 GeV
– 0th, 2nd-order oscillation amplitudes characterize -dependence of HBT radii
• of type allowed by symmetry
– centrality dependence reasonable
– oscillations at all kT
• OOP FO shape  “consistent” story of fast evolution (~9 fm/c)
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
29
To do…
• Us
– finalize analysis/systematic errors
– BW fits to final 200 GeV data (spectra, v2, asHBT) – does it hang consistently together?
• Theorists
– can satisfactory FO be reached faster (e.g. more explosive EoS)?
• and can it be done consistently???
P.T.  soft spot
in EOS & “stall”
2 fm/c
4 fm/c
6 fm/c
8 fm/c
no P.T. in EOS
 explosive
STAR
HBT
P. Kolb, Ph.D. thesis (2002)
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
30
To do…
• Us
– finalize analysis/systematic errors
– BW fits to final 200 GeV data (spectra, v2, asHBT) – does it hang consistently together?
• Theorists
– can satisfactory FO be reached faster (e.g. more explosive EoS)?
• and can it be done consistently?
– modification of hadronic stage needed??
Csörgő, Akkelin, Hama, Lukács, Sinyukov
PRC67 034904 (2003)
Heinz & Kolb, hep-ph/0206278
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
31
To do…
• Us
– finalize analysis/systematic errors
– BW fits to final 200 GeV data (spectra, v2, asHBT) – does it hang consistently together?
• Theorists
– can satisfactory FO be reached faster (e.g. more explosive EoS)?
• more constraints in that direction!
– modification of hadronic stage needed??
Csörgő, Akkelin, Hama, Lukács, Sinyukov
PRC67 034904 (2003)
Heinz & Kolb, hep-ph/0206278
STAR
HBT
16 Oct 2003
2nd Warsaw Meeting on Correlations and Resonances
32