6 Sep 2003 XXXIII ISMD - Krakow Poland 1

STARHBT

Azimuthally-sensitive HBT (asHBT) inAu+Au collisions at sNN=200 GeV

Mike Lisa, Ohio State Universityfor 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

Zero-th – order information from

^

6 Sep 2003 XXXIII ISMD - Krakow Poland 2

STARHBT

time

dN/dt

PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM

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

6 Sep 2003 XXXIII ISMD - Krakow Poland 3

STARHBT

… so why study (more complicated) asHBT ?

• sensitive to interplay b/t anisotropic geometry & dynamics/evolution (Ulrich’s talk)

• “broken symmetry” for b0 → more detailed, important physics information

• another handle on dynamical timescales – likely impt in HBT puzzle

P. Kolb and U. Heinz, hep-ph/0204061P. Kolb, nucl-th/0306081

“radial flow”

“elliptic flow”

6 Sep 2003 XXXIII ISMD - Krakow Poland 4

STARHBT

Freeze-out anisotropy as an evolution “clock”

• anisotropic pressure gradients→ preferential in-plane flow (v2)→ evolution towards in-plane shapeFO sensitive to evolution duration 0

• dilute (hadronic) stage• little effect on p-space at RHIC• significant (bad) effect on HBT radii

• related to timescale• qualitative change in FO

FO from asHBT?

hydro evolution later hadronic stage?

P. Kolb and U. Heinz, hep-ph/0204061

Teaney, Lauret, Shuryak, nucl-th/0110037

STARPHENIX

hydro onlyhydro+hadronic rescatt

Soff, Bass, Dumitru, PRL 2001Teaney et al, nucl-th0110037

in-plane-extended

out-of-plane-extended

Teaney et al, nucl-th0110037

p=0°

p=90°RS small

RS big

R.P.

6 Sep 2003 XXXIII ISMD - Krakow Poland 5

STARHBT

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

00 r~R

r)r(

Teaney, Lauret & Shuryak, nucl-th/0110037

• Schnedermann et al (’93): 2-parameter (T, max)

“hydro-inspired” functional form to fit spectra.• Useful to extract thermal, collective energy

1-2,1

max

R

0T

1T

0TTT

tanh R

r

T

sinhmK

T

sinhpImdrr

dmm

dN

R

azimuthally isotropic source model – let’s generalize for finite impact parameter …

6 Sep 2003 XXXIII ISMD - Krakow Poland 6

STARHBT

RY

RX

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

)2cos(~),( 0 bas rr

• coordinate space• transverse extents RX, RY

00 r~R

r)r(

• freezeout in proper time • evolution duration 0

• emission duration

2

20

2exp~

d

dN 00

F. Retière & MAL, in preparation

6 Sep 2003 XXXIII ISMD - Krakow Poland 7

STARHBT

RY

RX

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

)2cos(~),( 0 bas rr

• coordinate space• transverse extents RX, RY

00 r~R

r)r(

• freezeout in proper time • evolution duration 0

• emission duration

2

20

2exp~

d

dN

7 parameters describing freezeout

F. Retière & MAL, in preparation

6 Sep 2003 XXXIII ISMD - Krakow Poland 8

STARHBT

BlastWave fits to published RHIC data

• pT spectra constrain (mostly) T, 0

central

midcentralperipheral

F. Retière & MAL, in preparation

6 Sep 2003 XXXIII ISMD - Krakow Poland 9

STARHBT

R=9 fmR=12 fmR=18 fm

BlastWave fits to published RHIC data

Rout

Rside

Rlong

Rout

Rside

Rlong

F. Retière & MAL, in preparation

• pT spectra constrain (mostly) T, 0

• (traditional) HBT radii constrain R, 0,

• depend also on T, 0

6 Sep 2003 XXXIII ISMD - Krakow Poland 10

STARHBT

• pT spectra constrain (mostly) T, 0

• (traditional) HBT radii constrain R, 0,

• depend also on T, 0

• imperfect fit (esp. PHENIX RS)

BlastWave fits to published RHIC data central

midcentralperipheral

F. Retière & MAL, in preparation

6 Sep 2003 XXXIII ISMD - Krakow Poland 11

STARHBT

BlastWave fits to published RHIC data

• 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

~ 2 fm/c with Bowler CC

(Not this talk)

• reasonable centrality evolution

• OOP extended source in non-central collisions

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

2 / ndf 80.5 / 101 153.7 / 92 74.3 / 68

F. Retière & MAL, in preparation

central midcentral peripheral

6 Sep 2003 XXXIII ISMD - Krakow Poland 12

STARHBT

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…)

• But… HBT radii depend on “everything” (T, 0, …)

• can we extract FO shape from asHBT alone?

p=0°

p=90°RS small

RS big

R.P.

6 Sep 2003 XXXIII ISMD - Krakow Poland 13

STARHBT

can we extract FO shape from asHBT alone?the BlastWave view

out side

out-side long

• non-central collisions – all HBT radii exhibit 0th & 2nd - order oscillations (n>2 negligible)

• characterize each kT bin with 7 numbers:

osnsin,pR

l,s,oncos,pRpR

T2

T2

T2

n,

R2os,0 = 0 by symmetry (Ulrich’s talk)

F. Retière & MAL, in preparation

6 Sep 2003 XXXIII ISMD - Krakow Poland 14

STARHBT

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:

osnsin,pR

l,s,oncos,pRpR

T2

T2

T2

n,

• for fixed (RY2+RX

2), 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

F. Retière & MAL, in preparation

6 Sep 2003 XXXIII ISMD - Krakow Poland 15

STARHBT

FO shape from “normalized” oscillationsthe BlastWave view

• no-flow scenario: independent of pT…

20,s

22,o

20,s

22,os

20,s

22,s

2x

2y

2x

2y

R

R2

R

R2

R

R2

RR

RR

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)

F. Retière & MAL, in preparation

/2

6 Sep 2003 XXXIII ISMD - Krakow Poland 16

STARHBT

FO shape from “normalized” oscillationsthe BlastWave view

• no-flow scenario: independent of pT…

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+RX

2

• independent of (and 0)

• ~independent of T (and 0)

→ estimate from R2,2/ R2

s,0 (=o,s,os)

20,s

22,o

20,s

22,os

20,s

22,s

2x

2y

2x

2y

R

R2

R

R2

R

R2

RR

RR

fixed

F. Retière & MAL, in preparation

6 Sep 2003 XXXIII ISMD - Krakow Poland 17

STARHBT

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

6 Sep 2003 XXXIII ISMD - Krakow Poland 18

STARHBT

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--R

* cos(nm) from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C58 1671 (1998)

m-

R

6 Sep 2003 XXXIII ISMD - Krakow Poland 19

STARHBT

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

* cos(nm) from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C58 1671 (1998)

2/n

)2/nsin(

6 Sep 2003 XXXIII ISMD - Krakow Poland 20

STARHBT

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

* cos(nm) from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C58 1671 (1998)

2/n

)2/nsin(

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) ]

6 Sep 2003 XXXIII ISMD - Krakow Poland 21

STARHBT

Correcting for finite -binning & RP-resolutionHeinz, Hummel, Lisa, Wiedemann, Phys. Rev. C66 044903 (2002)

binN

1nj

expn,sj

expn,c

exp0jexp

)nsin()q(N)ncos()q(N2

)q(N),q(N

binN

1nj

expn,sj

expn,cm,n

jexpj

)nsin()q(N)ncos()q(N)(2

),q(N),q(N

bin

bin

N

1jjjexp

bin

expexp

n,s

N

1jjjexp

bin

expexp

n,c

)nsin(),q(NN

1

)nsin(),q(N)q(N

)ncos(),q(NN

1

)ncos(),q(N)q(N

Fourier coefficients for a given q-bin.

1))(ncos()2/nsin(

2/n)(

pRmm,n

correction factor for nth-order oscillations for the damping effects of

1) finite resolution in determining the mth-order event-plane

2) non-vanishing bin width () in the emission angle with respect to the event-plane (j)

bin

bin

N

1jjjexp

bin

expexp

n,s

N

1jjjexp

bin

expexp

n,c

)nsin(),q(NN

1

)nsin(),q(N)q(N

)ncos(),q(NN

1

)ncos(),q(N)q(N

Fourier coefficients for a given q bin

“raw” corrected

,qD

,qN,qC

• ~ 30% effect on 2nd-order radius oscillations• ~0% change in mean values

6 Sep 2003 XXXIII ISMD - Krakow Poland 22

STARHBT

asHBT at 200 GeV in STAR – R() vs kT

• Clear oscillations observed at all kT

• extract 7 radius Fourier Coefficients

(shown by lines)

midcentral collisions (20-30%)

osnsin,pR

l,s,oncos,pRpR

T2

T2

T2

n,

6 Sep 2003 XXXIII ISMD - Krakow Poland 23

STARHBT

Grand Data Summary – R2,n vs kT,

centrality

osnsin,pR

l,s,oncos,pRpR

T2

T2

T2

n,

• One plot w/ relevant quantities from 2x5x3x4 3D CFs

• left: R2,0 “traditional” radii

• usual kT, centrality dependence

• right: R2,2 / R2

,0

• reasonable centrality dependence• BW: sensitive to FO source shape

6 Sep 2003 XXXIII ISMD - Krakow Poland 24

STARHBT

Estimate of initial vs F.O. source shape

2x

2y

2x

2y

RR

RR

20,S

22,S

FO R

R2

• estimate INIT from Glauber

• from asHBT:

FO

= IN

IT

FO < INIT → dynamic expansion

FO > 1 → source always OOP-extended

• constraint on evolution time

RHIC1[Kolb & Heinz]

6 Sep 2003 XXXIII ISMD - Krakow Poland 25

STARHBT

A simple estimate – 0 from init and final

0Y,XY,X

t.)O.F()t(

“radial flo

w”

P. Kolb, nucl-th/0306081

• BW → X, Y @ F.O. (X > Y)

• hydro: flow velocity grows ~ t

• From RL(mT): 0 ~ 9 fm/c

consistent picture• Longer or shorter evolution times

X inconsistent

toy estimate: 0 ~ 0(BW)~ 9 fm/c

• But need a real model comparison→ asHBT valuable “evolutionary clock”

constraint for models

6 Sep 2003 XXXIII ISMD - Krakow Poland 26

STARHBT

Summary• FO source shape a “clock” for system evolution

– OOP-extended earlier kinetic FO

– further test of long-lived hadronic stage (OOPIP-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/ R2

s,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)

6 Sep 2003 XXXIII ISMD - Krakow Poland 27

STARHBT

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, SinyukovPR C67 034904 (2003)

Heinz & Kolb, hep-ph/0204061