star hbt 13 february 2003winter workshop - breckenridge co1 hbt in star mike lisa*, ohio state...

13 February 2003 Winter Workshop - Breckenridge CO 1STARHBT

HBT in STARMike Lisa*, Ohio State University

• “Traditional” HBT results: 200 GeV vs 130 GeV Au+Au collisions• New experimental developments

• Bowler/Sinyukov Coulomb correction• Pushing the systematics – azimuthally-sensitive HBT

• Results from 130, 200 GeV• Interpreting asHBT results

• Hydro, Hydro+RQMD, BlastWave• Conclusions

* Work of: Mercedes López-Noriega, Dan Magestro, Randy Wells


Reminder: p-space observables reproduced by dynamical models, x-space

not

Heinz & Kolb, hep-ph/0204061


“Standard” HBT:130 vs 200 GeV

• Essentially identical analysis carried out for 200 GeV data as published 130 GeV

• (exact centrality definition, etc, being finalized)

• New: centrality dependence of pT dependence

• mostly an overall scaling of R

• Little change with increased energy• Transverse size slightly bigger @ low pT?• Similar pT-dependence• Ro/Rs problem persists

• Longitudinal radius: no change•

• Lower-energy RHIC run needed

130GeV

200GeV

( )c/fm 5.7 ,c/fm 10

:Rfit Sinyukovperiph0

cent0

mT

0L T

≈≈→

=

ττ

τ

STAR, QM02


Recent analysis developments I

))qqRexp(1(N)q(K)q(B

)q(A ji2ij

coul−⋅+⋅=

⋅λ

• RHIC analyses used “standard” Coulomb correction, used by previous experiments

• “apples-to-apples” extension of systematics

[ ]1f0 )1)q(K(f1)q(K coulcoul <<−+→

• Effects of “diluting” CC (resonances, etc) explored & reported @ QM01

• Ro affected most

“Standard”Coulomb CCNo Coulomb CC

STAR, QM01; NPA698, 177c (2002)

• Y2 data: dilution effect vs pT, centrality• RO/RS ~ 10-15% increase when f = λ ≈ 0.5

f

{ }( )[ ] 1qqRexp(1)q(K1N)q(B)q(A

ji2ijcoul −−+⋅⋅+⋅= λ

• More correct CC method of Bowler (’91) & Sinyukov (’98), used by CERES (’02)

• Similar effect on radii as dilution with f = λ In “right” direction, but does not solve RO/RS problem


“Traditional” HBT results ~ stable

• So what’s the problem with theory?– Timescale too long?– Hadronic phase overestimated?– HBT technique not understood?

• Can (HBT and other) data be consistently understood?– What are characteristics of freezeout source @ RHIC?

• Parameterization of freezeout• Explore with further systematics– non-central collisions

– Azimuthally-sensitive HBT


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



hydro evolution later hadronic stage?


Effect of dilute stage

• dilute hadronic stage (RQMD):• little effect on v2 @ RHIC

Teaney, Lauret, & Shuryak, nucl-th/0110037





• 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






• related to timescale? - need more info







• related to timescale? - need more info• qualitative change of freezeout shape!!

• important piece of the puzzle!

in-plane-extended

out-of-plane-extended



Indirect indications of x-space anisotropy @ RHIC

• v2(pT,m) globally well-fit by hydro-inspired “blast-wave”

STAR, PRL 87 182301 (2001)

soliddashed

0.04 0.010.09 0.02a (c)

0.04 0.01 0.0S2

0.54 0.030.52 0.020(c)

100 24135 20T (MeV) temperature, radial flowconsistent with fits to spectra

anisotropy of flow boost

spatial anisotropy (out-of-plane extended)


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


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

( ))2cos(~),( 0 bas rr φρρφρ +=

• coordinate space• transverse extents RX, RY

RY

RX

• freezeout in proper time • evolution duration 0

• emission duration

( )⎟⎟⎠⎞

⎜⎜⎝⎛

−

− 2

20

2exp~

τττ

τddN

7 parameters describing freezeout


BlastWave fits to published RHIC data

• pT spectra constrain (mostly) T, 0

• (traditional) HBT constrains R, 0,

– (fit to STAR-HBT only)

• v2(pT,m) constrains a, RX/RY

centralmidcentralperipheral

Central Midcentral Peripheral

T (MeV) 108 3 106 2 95 3

0 0.88 0.01 0.87 0.01 0.81 0.02

a 0.06 0.01 0.05 0.01 0.04 0.01

RX (fm) 12.9 0.4 10.2 0.5 8.0 0.1

RY (fm) 12.8 0.4 11.8 0.6 10.0 0.2

0 (fm/c) 8.9 0.3 7.4 0.7 6.5 0.4

(fm/c) 0.0 9.0 0.8 1.8 0.09 0.6

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


“raw”

after RP/binningcorrection

2OR

2OSR

2SR

2LR

preliminaryλ flat within errors• Significant (& “allowed”) oscillations

observed in HBT radii• RP/binning correction* significant

• produces RL2 oscillation from

“nowhere”? – is it real?

Minbias observations at 130 GeV

(*) [Heinz, Hummel, MAL, Wiedemann PRC 044903 (2002)]

R. Wells, PhD thesis, Ohio State, 2002


• Minbias asHBT well-reproduced with same BlastWave from minbias v2(pT,m)

• Ry = 11.4 fm

• Rx = 10.8 fm0 = 8.3 fm/c = 0 ( → ~1.5 fm/c w/ Bowler CC))

• Consistent picture – convincing argument for flow scenario

• Saturation ????

s2 = 0.045

Au+Au 130 GeVminbias

asHBT versus BlastWave

• asHBT: geometry dominates dynamics• Source out-of-plane extended


Azimuthal HBT: hydro predictionsRHIC (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)


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: flow sign 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



Further systematics in Au+Au 200 GeV

• Oscillation phases: out-of-plane extended source• Source size increases, oscillations decrease with increasing centrality• 0th and 2nd harmonics only• Average size (0th harmonic) falls with kT

• Mild evolution of 2nd harmonic with kT

Centrality cutskT-integrated12 bins

kT cutsMid-central4 bins

Centrality cutskT-integrated12 bins


“Grand summary”

Fourier Coefficients

• Centrality- and kT- dependence of the -dependence summarized concisely by Fourier coefficients

( )( ) ( ) ( )( ) ( ) ( )⎪⎩

⎪⎨⎧

=⋅

=⋅=

osnsin,pR

l,s,oncos,pRpR

T2

T2

T2

n, μφφ

μφφ

μ

μμ


n = 0 n = 2


“Grand summary”

Fourier Coefficients

• Centrality- and kT- dependence of the -dependence summarized concisely by Fourier coefficients

( )( ) ( ) ( )( ) ( ) ( )⎪⎩

⎪⎨⎧

=⋅

=⋅=

osnsin,pR

l,s,oncos,pRpR

T2

T2

T2

n, μφφ

μφφ

μ

μμ


n = 0 n = 2

• Hydro predictions (*): b = 6 fm

(*) Heinz & Kolb, hep-ph/0204061

“RHIC” source“LHC” (IPES) source

• Scale of homogeneity lengths off• Phase/magnitude of oscillations

from “RHIC” source in the ballpark• significance ?


Evolution of spatial anisotropy

• Extraction of full freezeout scenario underway

• Timescales short, flow dominant• Out-of-plane-extended freezeout

geometry for all centralities– further constraint on evolution

timescale (and dynamic models!!)


• HBT systematics from 200 GeV similar to 130 GeV– New, more correct CC ~ 10-15% effect on Ro

• Dynamic models (hydro, hydro+RQMD)– soft p-space signals – soft x-space signals X– worse agreement with hadronic stage included

• BlastWave – toy model, but…– consistent framework to extract main features of freezeout– can initial state effects describe all signals as consistently?– in particular, short timescales 0, -- perhaps the problem

• asHBT– probes details of anisotropic geometry/flow interplay– consistent w/ BW expectations (& further constrains f.o. picture)

• (ditto for non-identical particle correlations)– f.o. source out-of-plane extended

• (model-dependent in principle, but robust in fact)• another constraint on evolution duration

– detailed systematics from 200 GeV run• hydro suggests this can reveal important physics• tighter model constraints• new level of presentation (FCs) for asHBT


Backups follow


Next slides

• Show Fabrice’s BW fits of published data• Show BW vs Randy’s stuff

– Rx=Ry and rho_a = 0 cases too• Show Dan’s 3 centrality bins with 12 phi bins

– 2nd order harmonics only• Show Dan’s centrality/kT dependence• Show “1-page summary,” with Heinz/Kolb on top• Show Dan’s figure 4


Symmetries of the emission functionI. Mirror reflection symmetry w.r.t. reactionplane (for spherical nuclei):

),,;,,,(S),,;,,,(S Φ−−=Φ TT KYzyxKYzyx

),,(~~),,(~~1 Φ−⋅θ=Φ νμνμ TT KYxxKYxx

with 22)1(1νμ δ+δ−=θ

II. Point reflection symmetry w.r.t. collision center (equal nuclei):

),,;,,,(S),,;,,,(S +Φ−−−−=Φ TT KYzyxKYzyx

),,(~~),,(~~2 +Φ−⋅θ=Φ νμνμ TT KYxxKYxx

with 00)1(2νμ δ+δ−=θ

Heinz, Hummel, MAL, Wiedemann, PRC66 044903 (2002)


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

nRRnRRnRRRnRRnRRRnRRR

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, PRC66 044903 (2002)


Bowler CoulombCorrection vs +-

Low kT High kT

Work in progress: finalizing resolution effects, etc.


“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)

( )2l

2l

2s

2s

2o

2o RqRqRq

lso e1)q,q,q(C ++−⋅λ+=


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

φ−−φ−=

+−φ−+φ−=

φ−φ+φ−+φ=

+−=

φ−φ−φ−+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 (xμxν()) dependence on

xxx~ −≡

∫∫

⋅⋅⋅

≡)K,x(fxd

)x(q)K,x(fxdq 4

4

Wiedemann, PRC57 266 (1998).


Recent analysis developments II

Quick slide on pT vs kT cutsif Mercedes gets me a plot…

Otherwise, forget it..Not that important


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

( ))2cos(~),( 0 bas rr φρρφρ +=

• coordinate space• transverse extents RX, RY

[ ]s

Y

s

X

s

arr

Rr

Rrr

/)1~(exp11)~(

sincos~22

−+=Ω

⎟⎟⎠⎞

⎜⎜⎝⎛

+⎟⎟⎠⎞

⎜⎜⎝⎛

≡ φφ

RY

RX

• freezeout in proper time • evolution duration 0

• emission duration

( )⎟⎟⎠⎞

⎜⎜⎝⎛

−

− 2

20

2exp~

τττ

τddN

7 parameters describing freezeout

star hbt 13 february 2003winter workshop - breckenridge co1 hbt in star mike lisa*, ohio state...

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