star hbt 30 aug 2001mike lisa - acs nuclear division - chicago 1 characterizing the freezeout at...

30 Aug 2001 Mike Lisa - ACS Nuclear Division - Chicago

1STARHBT

Characterizing the freezeout at RHIC:

HBT, spectra, and elliptic flow

U.S. Labs: Argonne, Lawrence Berkeley National Lab, Brookhaven National Lab

U.S. Universities: Arkansas, UC Berkeley, UC Davis, UCLA, Carnegie Mellon, Creighton, Indiana,Kent State,MSU, CCNY, Ohio State,Penn State, Purdue, Rice,Texas A&M, UT Austin,Washington, Wayne State, Yale

Brazil: Universidade de Sao Paolo

China: IHEP - Beijing, IPP - Wuhan

England: University of Birmingham

France: Institut de Recherches Subatomiques Strasbourg, SUBATECH - Nantes

Germany: Max Planck Institute – Munich, University of Frankfurt

Poland: Warsaw University, Warsaw University of Technology

Russia: MEPHI – Moscow, LPP/LHE JINR–Dubna, IHEP-Protvino

Mike Lisa, Ohio State UniversitySTAR Collaboration


2STARHBT

Schematic goal and method - soft physics

Goal: EoS of dense matter - relationship b/t bulk properties (P,T,…)• evidence for phase transition?

Method:• Full characterization of freezeout distribution f(x,p)

• Consistent characterization for several observables• Use measurements to constrain EoS via a model (hydro?),

which connects early time to freezeout

This talk:• Focus on transverse observables: dN/dpT, v2(pT,m), HBT(pT,)• Consistent picture within “hydro-inspired” parameterization?

(is the data telling a consistent story, and what does it mean?)• identify features of “real” model needing attention


3STARHBT

An analogous situation…


4STARHBT

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

( )

( ) νμπ

πνμ

νμ

π

πμ

μ

−⋅⋅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


5STARHBT

mT distribution from Hydrodynamics type model

)r(tanh 1β=ρ −

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


6STARHBT

• 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


7STARHBT

STAR HBT data for central collisions- further info? conflicting info?

STAR Collab., PRL 87 082301 (2001)

π-

π+

R(pT) probes interplay b/t space-timegeometry and temperature/flow


8STARHBT

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+=


9STARHBT

Implications for HBT: radii vs pT

STAR data

model: R=13.5 fm, =1.5 fm/c T=0.11 GeV, ρ0 = 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


10STARHBT

Joint view of π freezeout: HBT & spectra

spectra (π)

HBT

• common model/parameterset describes different aspects of f(x,p) for central collisions

• 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


11STARHBT

Non-central collisions:coordinate and momentum-space anisotropies

Equal energy density lines

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


12STARHBT

Elliptic flow (momentum-space anisotropy):

sensitive to early pressure / thermalization φ= 2cosv2

in-plane enhancement

P. Kolb, et al., PLB 500 232 (2001)

v2 @ SPS:between hydro and LDL

Hydro describes flow quantitatively @ RHIC


13STARHBT

HBT: (transverse) spatial anisotropy

•Source in b-fixed system: (x,y,z)•Space/time entangled in

pair system (xO,xS,xL)

U. Wiedemann, PRC 57, 266 (1998)

( )( )( ) ( ) p

2221

ppT2os

pp22

p22

pT2s

22pp

22p

22pT

2o

2sinx~y~2cosy~x~,pR

2siny~x~cosy~sinx~,pR

t~2siny~x~siny~cosx~,pR

φ−+φ⋅=φ

φ⋅−φ+φ=φ

β+φ⋅+φ+φ=φ ⊥

large flow @ RHIC induces space-momentum

correlations

p-dependent homogeneity lengths

sensitive to more than “just” anisotropic geometry

( )pT ,px~x~ φνμ

out

b

K

x

yside


14STARHBT

Reminder: observations for Au(2 AGeV)Au

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)

p=0°

p=90°

out-of-planeextended source

interesting physics, but not currenly accessible in STARwith 2nd-order reaction plane

Lines are global fitOscillation magnitude eccentricityOscillation phases orientation


15STARHBT

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 Collab, submitted to PRL

( ) ( ) ( ) ( )( ) ( )∫

∫π ρρ

π ρρ

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 ρa is clear how to interpret s2?

hydro-inspiredblast-wave modelHouvinen et al (2001)


16STARHBT

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

≅


17STARHBT

STAR HBT

“Out”

“Side”

“Long”

1.0

1.3

1.0

1.3

1.0

1.3

0 0.1 0.2

C(Q

)

Q (GeV/c)

Correlation function: p=45º

RO

2 (fm

2 )R

S2 (

fm2 )

RO

S2 (

fm2 )

π- from semi-peripheral events

raw

corrected forreactionplane resolution

data fit

• only mix events with “same” RP

• retain relative sign between q-components• HBT radii oscillations similar to AGS• curves are not a global fit• RS almost flat

STAR preliminary


18STARHBT

Out-of-plane elliptical shape indicated

case 1

using (approximate) values ofs2 and ρa from elliptical flow

case 2

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


19STARHBT

s2 dependence dominates HBT signal

error contour fromelliptic flow data

color: 2 levelsfrom HBT data

STAR preliminary

s2=0.033, T=100 MeV, ρ0ρaR=10 fm, =2 fm/c


20STARHBT

Time-averaged freezeout shape

3

2

2

x

y

s21

s21

R

R

−+

=≡η

• close to circular @ RHIC• info on evolution duration?

STAR preliminary

(E895)


21STARHBT

Hydro predictions

0

0.8

-0.8

10

5

15

20

40

60

0 90 180p (º)

RO

2 (fm

2 )R

OS2 (

fm2 )

RS2 (

fm2 )

• phases and ~ magnitude of HBT radii oscillations OKRO too largeRS too small


22STARHBT

Summary - a consistent picture

parameter spectra elliptic flow HBTTemperature T ≈11MeV √ √ √

Radialflowvelocity

ρ≈. √ √ √

Oscillationinradialflow

ρa≈.4 √ √

Spatialanisotropy

s2≈.4 √ √

Radiusiny Ry≈1-1fm(dependsonb)

√

Natureofxanisotropy

* √

Emissionduration

≈2fm/c √main sourceof discrepancy?

( )( ) ( ) 22ps

T

2/ty

222cossinhT

pT

1 eR/xy1ecoshT

mKp,xf τφ−φρ

η+−θ⎟⎠⎞

⎜⎝⎛ ρ=

rr


23STARHBT

Summary• Spectra, elliptic flow, and HBT measures consistent with a freeze-out

distribution including strong space-momentum correlations

• In non-central collisions, v2 measurements sensitive to existence of spatial anisotropy, while HBT measurement reveals its nature

• Systematics of HBT parameters:• flow gradients produce pT-dependence (consistent with spectra and v2(pT,m))

•anisotropic geometry (and anisotropic flow boost) produce -dependence

• (average) out-of-plane extension indicated• however, distribution almost “round,” --> more hydro-like evolution as

compared to AGS

While data tell consistent story within hydro-inspired parameterization, hydro itself tells a different story - likely point of conflict is timescale


24STARHBT

Hydro reproduced spectra well

star hbt 30 aug 2001mike lisa - acs nuclear division - chicago 1 characterizing the freezeout at...

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