Transcript ^ Azimuthally-sensitive HBT (asHBT) in Au+Au collisions at sNN=200 GeV Mike Lisa, Ohio State University for the STAR Collaboration • motivation – why study.

^ 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
6 Sep 2003
XXXIII ISMD - Krakow Poland
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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)
Heinz & Kolb, hep-ph/0204061
dN/dt
CYM & LGT
PCM & clust. hadronization
NFD
NFD & hadronic TM
string & hadronic TM
STAR
HBT
PCM & hadronic TM
6 Sep 2003
time
XXXIII ISMD - Krakow Poland
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… so why study (more complicated) asHBT ?
• sensitive to interplay b/t anisotropic geometry & dynamics/evolution (Ulrich’s talk)
• “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
6 Sep 2003
XXXIII ISMD - Krakow Poland
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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
6 Sep 2003
XXXIII ISMD - Krakow Poland
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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 dm T
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
6 Sep 2003
XXXIII ISMD - Krakow Poland
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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
6 Sep
F. Retière & MAL,
in 2003
preparation
XXXIII ISMD - Krakow Poland
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 
 (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
6 Sep
F. Retière & MAL,
in 2003
preparation
XXXIII ISMD - Krakow Poland
7
BlastWave fits to published RHIC data
• pT spectra constrain (mostly) T, 0
STAR
HBT
6 Sep
F. Retière & MAL,
in 2003
preparation
XXXIII ISMD - Krakow Poland
central
midcentral
peripheral
8
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
6 Sep
F. Retière & MAL,
in 2003
preparation
RlongRlong
XXXIII ISMD - Krakow Poland
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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
6 Sep
F. Retière & MAL,
in 2003
preparation
XXXIII ISMD - Krakow Poland
10
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
6 Sep 2003
F. Retière & MAL,
in preparation
XXXIII ISMD - Krakow Poland
• reasonable centrality
evolution
• OOP extended source in
non-central collisions
~ 2 fm/c with
Bowler CC
(Not this talk)
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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
6 Sep 2003
XXXIII ISMD - Krakow Poland
12
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:
2

R
 pT ,   cos n 

2
R  ,n pT    2
R p ,   sin n 

  T
  o, s, l
  os 
R2os,0 = 0 by symmetry (Ulrich’s talk)
STAR
HBT
6 Sep
F. Retière & MAL,
in 2003
preparation
out-side
XXXIII ISMD - Krakow Poland
long
13
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:
2

R
 pT ,   cos n 

2
R  ,n pT    2
R p ,   sin n 

  T
  o, s, l
  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
6 Sep
F. Retière & MAL,
in 2003
preparation
XXXIII ISMD - Krakow Poland
14
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
6 Sep
F. Retière & MAL,
in 2003
preparation
/2
XXXIII ISMD - Krakow Poland
15
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
6 Sep
F. Retière & MAL,
in 2003
preparation
XXXIII ISMD - Krakow Poland
16
asHBT at 200 GeV in STAR – R() vs centrality
12 (!) -bins b/t 0-180 (kT-integrated)
• clear oscillations observed in transverse radii
of symmetry-allowed (Heinz’s talk) type
• centrality dependence reasonable
• oscillation amps higher than 2nd-order ~ 0
→ extract 0th, 2nd Fourier coefficients vs kT
with 4 -bin analysis
STAR
HBT
6 Sep 2003
XXXIII ISMD - Krakow Poland
17
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
6 Sep 2003
XXXIII ISMD - Krakow Poland
18
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
6 Sep 2003
XXXIII ISMD - Krakow Poland
19
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
6 Sep 2003
XXXIII ISMD - Krakow Poland
20
Correcting for finite -binning & RP-resolution


Nq,  
Cq,    
Dq,  
Heinz, Hummel, Lisa, 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 )  Nexp (q,  j ) 
N bin

exp
2  n ,m () Nexp
(
q
)
cos(
n

)

N
c ,n
j
s ,n (q) sin( n j )
n 1
Fourier coefficients for a given q-bin.
n ,mexp() 
n / 2

N
(
q
)

N
(
q
cos(

Fourier
coefficients
a ngiven
sin(exp
n /,2) )for
cos(
()m qbin
c ,n
R ))

“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


j1
1)expfinite
determining
the mthN
(q)  resolution
Nbinexp (q, in
) sin(
n)
s ,nexp
Ns,norder
(q)  event-plane
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
6 Sep 2003
XXXIII ISMD - Krakow Poland
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
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
6 Sep 2003
midcentral collisions (20-30%)
  o, s, l
  os 
XXXIII ISMD - Krakow Poland
22
Grand Data Summary – R2,n vs kT, centrality
• One plot w/ relevant quantities from
2x5x3x4 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
STAR
HBT
6 Sep 2003
XXXIII ISMD - Krakow Poland
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Estimate of initial vs F.O. source shape

R 2y  R 2x
R 2y  R 2x
• estimate INIT from Glauber
• from asHBT:
 FO 
RHIC1
[Kolb & Heinz]
R S2, 2
2 2
R S,0
• FO < INIT → dynamic expansion
• FO > 1 → source always OOP-extended
• constraint on evolution time
STAR
HBT
6 Sep 2003
XXXIII ISMD - Krakow Poland
24
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
6 Sep 2003
XXXIII ISMD - Krakow Poland
25
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)
• 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  fast evolution (~9 fm/c)
STAR
HBT
6 Sep 2003
XXXIII ISMD - Krakow Poland
26
To do…
• Me
– 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
PR C67 034904 (2003)
Heinz & Kolb, hep-ph/0204061
STAR
HBT
6 Sep 2003
XXXIII ISMD - Krakow Poland
27