azimuthally-sensitive hbt in star

oct 2002 Mike Lisa - XXXII ISMD - Alushta, Ukraine

1

STARHBT

Azimuthally-sensitive HBT in STARMike Lisa

Ohio State University

• Motivation

• Noncentral collision dynamics

• Azimuthally-sensitive interferometry & previous results

• STAR results

• Hydrodynamic predictions for RHIC and “LHC”

• Summary


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


3

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?


• Turn to richer dynamics of non-central collisions for more detailed information


4

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


5

STARHBT

hydro evolution later hadronic stage?




Effect of dilute stage

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

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


6

STARHBT






• 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


7

STARHBT







• related to timescale? - need more info



8

STARHBT







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

• important piece of the puzzle!

in-plane-extended

out-of-plane-extended



9

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


10

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+=


11

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).


12

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


13

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


14

STARHBT

xout

xside

K

Anisotropic HBT results @ AGS (s~2 AGeV)

p (°) 0 180

0

0 180 0 180

10

-10

20

40

R2 (

fm2 ) out side long

ol os sl

Au+Au 2 AGeV; E895, PLB 496 1 (2000)

• strong oscillations observed• lines: predictions for static (tilted) out-of-plane extended source

consistent with initial overlap geometry

p = 0°


15

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

Au+Au 2 AGeV; E895, 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

eK

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

No access to 1st-orderoscillations in STAR Y1


16

STARHBT

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 0.02βa (c)

0.04 0.01 0.0S2

0.54 0.030.52 0.02β0(c)

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

anisotropy of flow boost

spatial anisotropy (out-of-plane extended)


17

STARHBT

STAR data Au+Au 130 GeV

minbias

2OR

2OSR

2SR

2LR

preliminary

• significant oscillations observed

• blastwave with ~ same parameters as used to describe spectra & v2(pT,m)

• additional parameters:

•R = 11 fm = 2 fm/c !!

full blastwave

consistent with R(pT), K-π


18

STARHBT

2OR

2OSR

2SR

2LR

preliminary

full blastwave

STAR data Au+Au 130 GeV

minbias• significant oscillations observed

• blastwave with ~ same parameters as used to describe spectra & v2(pT,m)

• additional parameters:

•R = 11 fm = 2 fm/c !!

consistent with R(pT), K-π

no spatial anisotropy

no flow anisotropy

• both flow anisotropy and source shape contribute to oscillations, but…

• geometry dominates dynamics

• freezeout source out-of-plane extended fast freeze-out timescale !


19

STARHBT

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)


20

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



21

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


22

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


23

STARHBT

Backup slides follow


24

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

a new angle

elliptic flow data suggest x-space anisotropyHBT R() confirm out-of-plane extended source

• 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


25

STARHBT

RHIC AGS

• Current experimental access only to second-order event-plane• odd-order oscillations in p are invisible

• cannot (unambiguously) extract tilt (which is likely tiny anyhow)• cross-terms Rsl

2 and Rol2 vanish @ y=0

concentrate on “purely transverse” radii Ro2, Rs

2, Ros2

• 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


26

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!!


27

STARHBT

hydro: time evolution of anisotropies at RHIC and “LHC”



28

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


29

STARHBT

Sensitivity to 0 within blast-wave

“Reasonable” variations in radial flow magnitude (0)parallel pT dependence

for transverse HBT radii

0


30

STARHBT

Sensitivity to within blast-wave

RS insensitive to

RO increases with pT as increases


31

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


32

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)


33

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


34

STARHBT

First look at centrality dependence!

Hot off the presses PRELIMINARYc/o Dan Magestro


35

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


36

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)


37

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

≅


38

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


39

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)


40

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 ?


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


42

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


43

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


44

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.


45

STARHBT


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


47

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


48

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)


49

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


50

STARHBT

2D contour plot of the pair emission angle CF….


51

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


52

STARHBT

Effect of dilute stage (RQMD) on v2SPS and RHIC:



53

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


54

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


55

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


56

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


57

STARHBT

Characterizing the freezeout: An analogous

situation


58

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


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


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


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


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


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


64

STARHBT

Non-central collisions: coordinate- and momentum-space anisotropies

Equal energy density lines

P. Kolb, J. Sollfrank, and U. Heinz


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


b = boost direction




66

STARHBT



( )( )

( ) ( )rR2cosR

rs21ecosh

T

mKp,xf s2

cossinhT

pT

1ps

T

−θ⎟⎠⎞

⎜⎝⎛ φ+⎟

⎠⎞

⎜⎝⎛ ρ=

φ−φρrr


RMSx > RMSy

RMSx < RMSy

( )( ) ( )y222cossinh

T

pT

1 R/xy1ecoshT

mKp,xf

psT

η+−θ⎟⎠⎞

⎜⎝⎛ ρ=

φ−φρrr


x

y

R

R≡η

1

1

2

1s

3

3

2 +η−η

≅


67

STARHBT

case 1


case 2

opposite R() oscillations would lead to opposite conclusion

Out-of-plane elliptical shape indicated


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


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


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)


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


72

STARHBT

xout

xside

K



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)



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°




73

STARHBT


74

STARHBT


75

STARHBT


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


77

STARHBT


78

STARHBT

xout

xside

K



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)



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°




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?


80

STARHBT

v2(pT) for “early time” parameters

• “saturation” of v2 @ high pT

• mass - dependence essentially gone


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


b = boost direction




82

STARHBT



( )( )

( ) ( )rR2cosR

rs21ecosh

T

mKp,xf s2

cossinhT

pT

1ps

T

−θ⎟⎠⎞

⎜⎝⎛ φ+⎟

⎠⎞

⎜⎝⎛ ρ=

φ−φρrr


RMSx > RMSy

RMSx < RMSy

( )( ) ( )y222cossinh

T

pT

1 R/xy1ecoshT

mKp,xf

psT

η+−θ⎟⎠⎞

⎜⎝⎛ ρ=

φ−φρrr


x

y

R

R≡η

1

1

2

1s

3

3

2 +η−η

≅


83

STARHBT

Out-of-plane elliptical shape indicated

case 1


case 2

opposite R() oscillations would lead to opposite conclusion STAR preliminary


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!

azimuthally-sensitive hbt in star

Documents