dynamic timescales from star year1

3 Apr 2002 malisa - colloquium at Duke 1

STARHBT

Dynamic timescales from STAR Year1

Mike Lisa, Ohio State University, STAR Collaboration


STARHBT

Overview

• ~ 1.5 year from initial data-taking in new energy regime (s=130 GeV)• overall picture / underlying driving physics not fully clear

Outline• Ultrarelativistic heavy ion collisions• STAR at RHIC• Collective (radial and elliptic) flow measurements

• Initial quantitative success of hydrodynamics• Blast-wave parameterization

• Two-particle correlations (HBT) • STAR HBT and the “HBT Puzzle”

• Data/fit-driven extraction of dynamical timescales - consistent description of data?• azimuthally-sensitive HBT• K- correlations• short-lived resonance yields• balance functions

• Summary


STARHBT

Why heavy ion collisions?

• Bulk properties of strongly-interacting matter

• Extreme conditions (high density/temperature): expect a transition to new phase of matter…

• Quark-Gluon Plasma (QGP)• partons are relevant degrees of freedom over large

length scales (deconfined state)

• believed to define universe ~ s after BB

• Study of QGP crucial to understanding QCD• low-q (nonperturbative) behaviour

• confinement (defining property of QCD)

• nature of phase transition

• Heavy ion collisions ( “little bang”): the only way to experimentally probe the deconfined state

The “little bang”


STARHBT

Stages of the collision - several timescales

initial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronic phaseand freeze-out

PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM1 fm/c 5 fm/c 10 fm/c 50 fm/c time

dN/dt

Chemical freeze outKinetic freeze out

“end result” looks very similar whether a QGP was formed or not!!!

low-pT hadronic observables

hadronization


STARHBT

uRQMD simulation of Au+Au @ s=200 GeV

pure hadronic & stringdescription (cascade)

~OK at lower energies

applicability @ very high density (RHIC) unclear

produces too little collective flow at RHIC

courtesy uRQMD collaboration


STARHBT

Achieving the collision experimentally

STAR


STARHBT

Measuring the ashes:

Geometry of STAR

ZCal

Barrel EM Calorimeter

Endcap Calorimeter

Magnet

Coils

TPC Endcap & MWPC

ZCal

FTPCs

Vertex Position Detectors

Central Trigger Barrel or TOF

Time Projection Chamber

Silicon Vertex Tracker

RICH

a midrapidity, large-acceptance hadron detector


STARHBT

Peripheral Au+Au Collision at 130 AGeV

Data Taken June 25, 2000.

Pictures from Level 3 online display.


STARHBT

Au on Au Event at CM Energy ~ 130 AGeV

Data Taken June 25, 2000.


STARHBT

First RHIC spectra - an explosive source

data: STAR, PHENIX, QM01model: P. Kolb, U. Heinz

• various experiments agree well

• different spectral shapes for particles of differing mass strong collective radial flow

mT1/m

T d

N/d

mT

light

heavyT

purely thermalsource

explosivesource

T,mT1/

mT d

N/d

mT

light

heavy• very good agreement with hydrodynamic

prediction


STARHBT

Hydrodynamics: modeling high-density scenarios

• Assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles)

• Equations given by continuity, conservation laws, and Equation of State (EOS)

• EOS relates quantities like pressure, temperature, chemical potential, density– direct access to underlying physics

• Works qualitatively at lower energybut always overpredicts collectiveeffects - infinite scattering limitnot valid there

• freezeout when energy density fallsbelow some threshold

lattice QCD input


STARHBT

Hydro time evolution of non-central collisions

Equal energy density linesP. Kolb, J. Sollfrank,and U. Heinz

• entrance-channel aniostropy in x-space pressure gradients (system response) p-space anisotropy (collective elliptic flow)

• correlating observations with respect to event-wise reaction plane allows much more detailed study of reaction dynamics

self-quenching effect - sensitive to early pressure


STARHBT

Data: Azimuthal-angle distributionversus reaction plane

v2:

• quantifies anisotropy

• increases from central to peripheral collisions

• sensitive to EoS @ lower s

φ= 2cosv2

particle-reaction plane

( )φ+φ

2cosv21~d

dN2or


STARHBT

Very large event anisotropies seen by STAR, PHENIX, PHOBOS

v2

centrality

• space-momentum connection clear in multiplicity dependence

• different experiments agree well

• finally, we reach regime of quantitative hydro validity evidence for early thermalization

• AGS & lower energies: magnitude described by hadronic cascade models

• RHIC; Hydro description for central to mid-central collisions

– 26% more particles in-plane than out-of-plane (even more at high pT)!!


STARHBT

Local thermal equilibrium versus Low Density Limit

SPS (s=17 GeV); Low-Density-Limit and Hydro bracket pT dependence

RHIC; pt dependence quantitatively described by Hydro

pt dependence sensitive to early thermalization

p

Charged particles


STARHBT

Blastwave parameterization - “hydrolike source”

R

t

( )

( )

( )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


STARHBT

Spectra and v2 from blast wave

-

K-

p

1/m

T d

N/d

mT

(a

.u.)

mT - m [GeV/c2]

STAR preliminary

• Transverse momentum spectra– T 110 MeV 0.6

• PID Elliptic flow

STAR, PRL 87 182301 (2001)

– T=101 24 MeV– = 0.61 0.05

– a = 0.04 0.01

– s2 = 0.04 0.01


STARHBT

• Momentum-space characteristics of freeze-out appear well understood• “real” model (hydro)• parameterization of real model (blastwave)

• What about space-time degrees of freedom ?• Probe with two-particle intensity interferometry (“HBT”)

The other half of the story…


STARHBT

“HBT 101” - probing source geometry

12 ppqrrr −=

2

21

2121 )q(~1

)p(P)p(P)p,p(P

)p,p(C +== C (Qinv)

Qinv (GeV/c)

1

2

0.05 0.10

Width ~ 1/R

Measurable! F.T. of pion source

( ))xx(iq2

*21

*1T

*T

21e1UUUU −⋅+⋅⋅=ψψ

Creation probability (x,p) = U*U

222111 p)xr(i22

p)xr(i11T e)p,x(Ue)p,x(U

rrrrrr rrrr ⋅−⋅−=ψ

5 fm

1 m source(x)

r1

r2

x1

x2

{2

1

}e)p,x(Ue)p,x(U 212121 p)xr(i21

p)xr(i12

rrrrrr rrrr ⋅−⋅−+

p1

p2


STARHBT

“HBT 101” - probing the timescale of emission

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

4

RoutRside ( ) ( )y,xx,x sideout ≠

Decompose q into components:qLong : in beam directionqOut : in direction of transverse momentumqSide : qLong & qOut

(beam is into board)( )22

s2o RR τ⋅β+=

beware this “helpful” mnemonic!

( )2l2l

2s

2s

2o

2o RqRqRq

lso e1)q,q,q(C ++−⋅λ+=


STARHBT

Large lifetime - a favorite signal of “new” physics at RHIC

• hadronization time (burning log) will increase emission timescale (“lifetime”)

• magnitude of predicted effect depends strongly on nature of transition

• measurements at lower energies (SPS, AGS) observe ~3 fm/c

“”

withtransition

c

Rischke & GyulassyNPA 608, 479 (1996)

3D 1-fluid Hydrodynamics

~

…but lifetime determination is complicated by other factors…


STARHBT

First HBT data at RHIC

STAR Collab., PRL 87 082301 (2001)

( )2l2l

2s

2s

2o

2o RqRqRq

lso e1)q,q,q(C ++−⋅λ+=

Data well-fit by Gaussian parametrization

Coulomb-corrected(5 fm full Coulomb-wave)

“raw” correlation function projection

1D projections of 3D correlation functionintegrated over 35 MeV/c in unplotted components


STARHBT

World HBT excitation function

STAR Collab., PRL 87 082301 (2001)

•decreasing parameter partially due to resonances

•saturation in radii

•geometric or dynamic (thermal/flow) saturation

•the “action” is ~ 10 GeV (!)

•no jump in effective lifetime

•NO predicted Ro/Rs increase(theorists: “data must be wrong”)

•Lower energy running needed!?

midrapidity, low pT -

from central AuAu/PbPb


STARHBT

Hydro attempts to reproduce data

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/emits too long in models

• Right dynamic effect / wrong space-time evolution??? the “RHIC HBT Puzzle”

generichydro


STARHBT

“Realistic” afterburner not enough

pure hydro

hydro + uRQMD

STAR data

1.0

0.8

explosive space-time scenario suggested by observation not reproduced by realistic models

RO/R

S


STARHBT

Now what?

• “Realistic” dynamical models cannot adequately describe 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 (e.g. flow and HBT)• Isolate features generating discrepancy with “real” physics models• focus especially on timescales


STARHBT

Blastwave parameterization:Implications for HBT: radii vs pT

Assuming , T obtained from spectra fits strong x-p correlations, affecting RO, RS differently

pT=0.2

pT=0.4

( )22S

2O RR τ⋅β+=

K

KRS

RO

“whole source” not viewed


STARHBT

Blastwave: 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

Four parameters affect HBT radii

pT=0.4

pT=0.2

K

K


STARHBT

Pion source geometry in peripheral events

• In peripheral events– Start out-of-plane– Evolve towards in-plane source

• Source shape: a measure of the freeze-out time scale

Time

Out-of-plane Circular In-plane

Typical evolution in the hydro world


STARHBT

Measuring the anisotropic shape: HBT with respect to reaction plane

• Anisotropic geometry leads to oscillations of the radii– For example Rside

Rsi

de2

(fm

2 )

Out-of-plane In-planeCircular

(degree)p=0°

p=90°

Rside (large)Reactionplane

Rside (small)

Naïve view with no flow


STARHBT

Out-of-plane extended source~ short system evolution time

STAR preliminary

• Same blastwave parameters as required to describe v2(pT,m), plus two more:

– Ry = 10 fm = 2 fm/c

• Both p-space and x-space anisotropies contribute to R()

– mostly x-space: definitely out-of-plane

• calibrating with hydro, freezeout ~ 7 fm/c

Ros2 - new “radius” important for

azimuthally asymmetric sources


STARHBT

Kaon – pion correlation:dominated by Coulomb interaction

Smaller source stronger (anti)correlation

K-p correlation well-described by:

• Static sphere (no radial flow):

– R= 7 fm

• Blast wave with same parameters as spectra, HBT

But with non-identical particles, we can access more information…

STAR preliminary


STARHBT

Initial idea: probing emission-time ordering

• Catching up: cos0• long interaction time• strong correlation

• Ratio of both scenarios allow quantitative study of the emission asymmetry

• Moving away: cos0• short interaction time• weak correlation

Crucial point:kaon begins farther in “out” direction(in this case due to time-ordering)

purple K emitted firstgreen is faster

purple K emitted firstgreen is slower


STARHBT

measured K- correlations - natural consequence of space-momentum

correlations• clear space-time asymmetry observed

• C+/C- ratio described by:– static (no-flow) source w/ tK- t=4 fm/c

– “standard” blastwave w/ no time shift

• We “know” there is radial flow further evidence of very rapid freezeout

• Direct proof of radial flow-induced space-momentum correlations

Kaon <pt> = 0.42 GeV/c

Pion <pt> = 0.12 GeV/c

STAR preliminary


STARHBT

A consistent picture within blastwave

parameter spectra v2(m,pT) HBT(pT,φ) K-

T au T≈110MV √ √ √ √

Radiaowvociψ

0≈0.6 √ √ √ √

Osciaioninadiaow

a≈0.04( inias)

√ √

Saiaanisooψ

s2≈0.04( inias)

√ √

Radiusinψ Ry≈10-13(dndson)

√ √

E issionduaion

≈2 /c √ √

i daψ <K>-<>=0 √

( )( ) ( ) 22ps

T

2/ty

222cossinhT

pT

1 eR/xy1ecoshT

mKp,xf τφ−φρ

η+−θ⎟⎠⎞

⎜⎝⎛ ρ=

rr


STARHBT

Consistency with other probes?

• Focussing on transverse plane, consistent picture within simple parameterization

• explosive freezeout - short duration of kinetic freezeout kinetic

• out-of-plane-extended shape: “short” evolution time to kinetic freezeout tkinetic

• Other probes of timescales:

• RL(mT): tkinetic

• short-lived resonance survival: tkinetic - tchemical (kinetic ?)

• Balance Functions:tkinetic - tcharge creation (kinetic ??)tkinetic


STARHBT

RsideRout

Kt = pair Pt

Rlong from HBT

• R.H.I.C. - strong longitudinal expansion

• Rlong probes longitudinal homogeneity lengths

size of region emitting a given pZ

• In Bjorken picture: probe emission time tkinetic

– How wide does the cell become after evolving during tkinetic?

t

l l

Rlong


STARHBT

From Rlong: tkinetic = 8-10 fm/c(compare ~7 fm/c from anisotropic shape)

Simple Sinyukov formula (S. Johnson)

– RL2 = tkinetic2 T/mT

tkinetic = 10 fm/c (T=110 MeV)

B. Tomasik (~3D blast wave) tkinetic = 8 fm/c (++)

tkinetic = 9.2 fm/c (--)


STARHBT

Resonance survival rate

timechemical freeze out T~170 MeV

thermal freeze outT~110MeV

d1R

d2d1

Rd2

UrQMD: signal loss in invariant mass reconstruction

K*(892) (1520)

SPS (17 GeV) [1] 66% 50% 26%

RHIC (200GeV) [2] 55% 30% 23%

• short-lived resonances

– K*(892) = 3.9 fm/c (1520) = 12.8 fm/c

• Rescattering of daughters between chemical and kinetic freeze-out washes out the resonance signal

– Sensitive to tkinetic - tchemical

kinetic rescattering


STARHBT

Resonance reconstruction (via combinatorics):

K* and (1520) from STAR

K*0 K+ + - K*0 K- + +

multiplicity for |y| <0.5 K*0 |y|<0.5 = 10.0 0.8 25%

Upper limit estimation: dN/dy preliminary

(1520) |y|<1 < 1.2 at 95% C. L.

(1520) p + K-

minv (GeV/c2)


STARHBT

Resonance survival rate:Rafelski’s picture

Upper limit

• Combining both K* and (1520):

• Caveats:

– partial “quenching” (width broadening) allows for higher T, still small

– Tchem~100 MeV ?!?

• Thermal fit: T ~ 170 MeV

– no evidence of low-pT suppression

– Possible K* regeneration?

=tkinetic - tchemical ~ 0-3 fm/c


STARHBT

Summary• Strong collective flow at RHIC

– clear from p-space observables

• well-described by hydro

– important implications for x-space observables (HBT, balance functions)

• Problem! - HBT systematics not reproduced by hydro

– right dynamic effects, but wrong evolution?

– analysis tools “miscalibrated,” or something wrong in model, or…

– systematics point to timescale

• Try to provide feedback to modelers...

• Blastwave parameterization– incorporates implicitly x-p correlations

– consistent picture of several observables

• central: dN/dpT, HBT(pT), K-– 3 views of radial flow

• peripheral: v2(m,pT), HBT()

– out-of-plane extended source!

– just a “toy,” but consistency suggests the x-p interplay and basic description is right

• useful feedback to modelers (?)

– short evolution time, ~”instant” freezout!

• Other estimators of timescales– RL(mT), resonance yields**, balance fctns**

– suggest timescales ~consistent with blastwave estimates

** rather different analysis/models, with several open issues


STARHBT

Summary:Collision time scale from STAR data

1 fm/c 5 fm/c 10 fm/c 20 fm/ctime

dN/dt

Chemical freeze outKinetic freeze out

Balance function (require flow)

Resonance survival

Rlong (and HBT wrt reaction plane)Rout, Rside

~1 fm/cexplosive!!

~7-10 fm/crapid!!


STARHBT

The End


STARHBT

Some speculative ideas

• Super-cooling of the QGP phase

• Many bubble system (M. Gyulassy)– Bubble carry flow

– Each bubble break very rapidly

– Product of bubble don’t reinteract with each other

– Dynamical fluctuations?

• Brutal breaking of the chiral symmetry (A. Dumitru)– Pion become off-shell and can

freeze out

– If system has evolve long enough: no re-interaction

• Short emission duration

– Caveat:

• Too long lifetime?

• Dynamical fluctuations?

• Back to back - correlations


STARHBT

Speculation:A. Dumitru

• A way to get short emission duration

• pions take a long time to become on-shell and freeze-out– Freeze-out a low density: no

reinteractions, short emission duration

– Wouldn’t the system live too long?– Imply back to back -

correlations?– Dynamical fluctuations?


STARHBT

SummarySpectra• Very strong radial flow field superimposed on thermal motion• T saturates rapidly ~ 140 MeV higher at RHIC

•space-momentum correlations important•“stiffer” system response?

• consistent with hydro expectation

Momentum-space anisotropy• sensitive to EoS and early pressure and thermalization• significantly stronger elliptical flow at RHIC, compared to lower

energy• indication of coordinate-space anisotropy as well as flow-field

anisotropy (v2 cannot distinguish its nature, however)• for the first time, consistent with hydro expectation


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- correlations

• most likely cause of discrepancy is extremely rapid emission timescale suggested by data - more work needed!


STARHBT

Can we learn from blasphemy?

• purely hadronic model, even at T = 300 MeV, ~ 6 GeV/fm3

• details of elliptic flow and HBT

~well-reproduced• worked similarly well at SPS (impt!)

T. Humanicnucl-th/0203004

HB

T R

,

centrality mT (GeV/c2)


STARHBT

A “typical” emissiontime distribution

hydro+RQMDD. Teaney

dN/d

t


STARHBT

K*(892)

• Tchem ~ 170 MeV describes K* and

other ratios consistently• No need for in-medium effects

• Tslope ~ 300-400 MeV consistent with

mass systematics

• No extra suppression at low pT due to

in-medium effects


STARHBT

more recent HBT wrt RP


STARHBT

K0-K0 interferometry in year-2

C(Q

inv)

• K0s identified topologically

(not combinatorically)• S/N ~ 5• No issues with Coulomb correction• Trackmerging essentially a non-issue• Full 3D treatment possible with Y2 statistics

preliminary


STARHBT

Minv distribution from topological cuts


STARHBT

Balance functions: How they work

For each charge +Q, there is one extra balancing charge –Q.

Charges: electric, strangeness, baryon number


STARHBT

Balance functions:basic idea

• Early hadronization• Large

• Delayed hadronization

• Small


STARHBT

Balance functions:Preliminary data on +- pairs

*No electrons


STARHBT

Balance functions:Summary plot

PionsCharged Particles

Something fundamentally different from p-p is happening


STARHBT

Balance functions:Quantitative results

• Bjorken + thermal model– Ti ~ Tchemical

– Tf ~ Tthermal

– ti ~ tchemical

– tf ~ tthermall

• To reproduce data f = 15 fm/c > from

Rlong (8-10)

– Extremely low Tf


STARHBT

Balance functions:Using “known” parameters

• Parameters– Ti = 175 MeV

• From particle ratios i = 9-10 fm/c

• From HBT RL

– Tf = 100-110 MeV

• From spectra f-i = = 2-4 fm/c

• From HBT RO/RS

• Too large width0.5

0.55

0.6

0.65 Central DataT

f=110,

i=10,

f=13, =5.42, =1rate ncoll

Tf=100,

i=9,


Tf=110,

i=9,


0 0.2 0.4 0.6 0.8 1/b b

max100 , k Bjorken simulations fast TPC ,filter ,no flow T

i=175 , MeV other parameters as given

pairs


STARHBT

Balance functions: Add radial flow

• Adding transverse flow – We “know” it is there

– narrows balance function

– highly sensitive (more than to T)

0.5

0.55

0.6

0.65 DataBjorken, fast TPCi,T0=175MV,T

f=110MV,

i=10/c,

f=13/c,

cooinga=5.42,nco=1sawiowsia

0 0.2 0.4 0.6 0.8 1/b b

max


STARHBT

Already producing QGP at lower energy?

J. Stachel, Quark Matter ‘99

Thermal model fits to particle yields (& strangeness enhancement, J/ψ suppression) approach QGP at CERN (s=17 GeV)?

lattice QCD applies

Must go beyond chemistry: study dynamics of system well into deconfined phase (RHIC)

• is the system really thermal?• dynamical signatures? (no)• what was pressure generated?• what is Equation of State of strongly-interacting matter?

warning: e+e- yields fall on similar line!!


STARHBT

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


STARHBT

Emergence of a Consistent Picture from First Results of STAR at RHIC?

Mike Lisa, Ohio State UniversitySTAR Collaboration

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,Michigan State,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


STARHBT

The “little bang”Stages of the collision

• pre-equilibrium (deposition of initial energy density)• rapid (~1 fm/c) thermalization (?)

QGP formation (?)

hadronic rescattering

hadronization transition (very poorly understood)

freeze-out: cessation of hard scatterings

• low-pT hadronic observables probe this stage

“end result” looks very similar whether a QGP was formed or not!!!


STARHBT

Joint view of freezeout: HBT & spectra

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

• Increasing T has similar effect on a spectrum as increasing

• But it has opposite effect on R(pT) opposite parameter correlations in

the two analyses tighter constraint on parameters

spectra ()

HBT

STAR preliminary


STARHBT

Topological Strangeness Measurements

−+ +→0sK

++→ p

−− +→Ξ−+→ p

a

p TA

rm

K+n


STARHBT

Determining the reaction plane

( )

( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

φ⋅

φ⋅=

∑

∑−

iii

iii

1B,A2 2cosw

2sinwTan

2

1


STARHBT

Sub events

A

A

B

B-1<<-0.05 0.05<<1

2nd order event plane of independent sub-events A&B


STARHBT

Reaction plane resolution

))(cos( rn

obsn

n n

vv

−= ))(cos())(cos( b

nanrn nCn −×=−

A.M. Poskanzer and S.A. Voloshin, Phys. Rev. C 58 (1998) 1671


STARHBT

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

STAR Collab., PRL 87 082301 (2001)

-

+

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


STARHBT

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


STARHBT

Particle Identification via dE/dx in TPC - June 2000

Approaching expectedresolution in dE/dx

Preliminary


STARHBT

Measurements at AGS; E895 and E877 (Protons)

• At low beam energies negative v2 (“squeeze-out”)

• Balancing energy around 4 AGeV, sensitive to EOS

Elab (AGeV)

0.04

-0.08

-0.04

0

1 10

v 2

E895, Phys. Rev. Lett. 83 (1999) 1295

P. Danielewicz, Phys. Rev. Lett. 81 (1998) 2438


STARHBT

Probing f(x,p) from different angles

∫ ∫ ∫

⋅⋅⋅φφ=2

0

2

0

R

0Tps2

T

)p,x(fmdrrdddm

dN

Transverse spectra: number distribution in mT

∫ ∫ ∫∫ ∫ ∫

⋅⋅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

( )

( ) n

n

n

−⋅⋅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


STARHBT

mT distribution from Hydrodynamics-inspired model

)r(tanh 1= −

E.Schnedermann et al, PRC48 (1993) 2462

R

s

( ) ( )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,) fit to mT distribution

)r(g)r( s ⋅=


STARHBT

• c2 contour maps for 95.5%CL

T th [

GeV

]

s [c]

- K-p

T th [

GeV

]

s [c]

T th [

GeV

]

s [c]

Tth =120+40-30MeV

<r >=0.52 ±0.06[c]

tanh-1(<r >) = 0.6

<r >= 0.8s

Fits to STAR spectra; r=s(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


STARHBT

Excitation function of spectral parameters

• Kinetic “temperature” saturates ~ 140 MeV already at AGS

• Explosive radial flow significantly stronger than at lower energy

• System responds more “stiffly”?

• Expect dominant space-momentum correlations from flow field


STARHBT

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

Equal energy density lines

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


STARHBT

More detail: identified particle elliptic flow

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)

STAR, in press PRL (2001)

( ) ( ) ( ) ( )( ) ( )∫

∫

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)


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≡

1

1

2

1s

3

3

2 +−

≅


STARHBT

Out-of-plane elliptical shape indicated

case 1

using (approximate) values ofs2 and a from elliptical flow

case 2

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


STARHBT

s2 dependence dominates HBT signal

error contour fromelliptic flow data

color: c2 levelsfrom HBT data

STAR preliminary

s2=0.033, T=100 MeV, 0=0.6a=0.033,R=10 fm, =2 fm/c

dynamic timescales from star year1

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