HBT Dan Magestro, The Ohio State University Overview of HBT interferometry Overview of HBT...

HBTHBTDan Magestro, The Ohio State University

• Overview of HBT interferometry Overview of HBT interferometry

• The SPS & RHIC HBT programThe SPS & RHIC HBT program

• Recent “standard” HBT resultsRecent “standard” HBT results

• The RHIC HBT puzzleThe RHIC HBT puzzle

• New directions: New directions: dependence, pp vs. AuAu, non-Id, dependence, pp vs. AuAu, non-Id, HBT HBT

: : A (mostly) experimental A (mostly) experimental overviewoverview

Quark Matter 2004 2 Dan Magestro, Ohio State University

qout

qside

qlong

Hanbury Brown-Twiss Hanbury Brown-Twiss interferometryinterferometry

Rsi

de

R long

Rout

x1

x2

12 ppq

p1

p2

q

12 pp2

1k

• Two-particle interferometry: p-space separation Two-particle interferometry: p-space separation space-time separation space-time separation

• HBT: Quantum interference between identical particlesHBT: Quantum interference between identical particles

pairsevent mixed

pairsevent real

)(P)(P

),(P),(

21

2121

pp

ppppC

2long

2long

2side

2side

2out

2out)(1),(

RqRqRqekkqC

q (GeV/c)q (GeV/c)

C (

q)C

(q)

11

22R

1~

• Final-state effects (Final-state effects (CoulombCoulomb, strong) also can cause , strong) also can cause correlations, need to be accounted forcorrelations, need to be accounted for

Gaussian model (3-d):


The HBT program at SPS and The HBT program at SPS and RHICRHIC

• Technique: Study interferometry as Technique: Study interferometry as differentiallydifferentially as possible as possible

• RHIC: Fertile ground for correlations studiesRHIC: Fertile ground for correlations studies

beam energybeam energy onset effects, transition phenomenaonset effects, transition phenomena

transverse momentum (ktransverse momentum (kTT)) dynamics, collective expansiondynamics, collective expansion

particle speciesparticle species differences in emissiondifferences in emission

collision systemcollision system origins of correlations, phase space origins of correlations, phase space

azimuthal angleazimuthal angle spatial anisotropies, constrain system evolutionspatial anisotropies, constrain system evolution

• HBT in HI collisions: Explore space-time evolution of systemHBT in HI collisions: Explore space-time evolution of system

• Geometry: Geometry: spatial distribution of emission pointsspatial distribution of emission points

• Dynamics: Dynamics: hot & dense early stages reflected in freeze-out patternhot & dense early stages reflected in freeze-out pattern

• Lifetime: Lifetime: sensitive to nature of phase transitionsensitive to nature of phase transition


HBT excitation functionHBT excitation function

STAR, PRL 87 (2001) 082301


The kThe kT T (m(mTT) dependence) dependence

• x-p correlations arise mostly x-p correlations arise mostly due to collective expansiondue to collective expansion

• Radial flow pushes higher-pRadial flow pushes higher-pTT

particles more at surfaceparticles more at surface

Kolb & Heinz, QGP3 (nucl-th/0305084)

• Analytical expressionsAnalytical expressions

• System lifetime (Sinyukov)System lifetime (Sinyukov)

• Transverse flow velocity, system sizeTransverse flow velocity, system size

21 fT

geomside

Tm

RR

expansion duration

transverse rapidity

)(

)(

1

20

T

T

Tlong mK

mK

m

TR


• Little difference from SPS to RHICLittle difference from SPS to RHIC

• Consistent lifetimes: Consistent lifetimes: ff ~ 8-10 fm/c ~ 8-10 fm/c

CERES, Nucl.Phys. A 714 (2003) 124

kT (GeV/c)

NA49, Phys.Lett. B 557 (2003) 157

• mmTT scaling ~ holds up to 1 GeV at SPS scaling ~ holds up to 1 GeV at SPS


HBT at √s = 200 GeVHBT at √s = 200 GeV

• PHENIX PHENIX -HBT: k-HBT: kTT , centrality , centrality

dependence at 200 GeVdependence at 200 GeV(nucl-ex/0401003)(nucl-ex/0401003)

• New Coulomb treatment causes New Coulomb treatment causes ~ 10-15% change in R~ 10-15% change in Routout/R/Rsideside

• STAR STAR -HBT:-HBT: kkTT , centrality and , centrality and

dependence at 200 GeV (later) dependence at 200 GeV (later)(nucl-ex/0312009)(nucl-ex/0312009)

• Sufficient statistics for triple-Sufficient statistics for triple-differential analysis!differential analysis!


A highlight from this weekA highlight from this week

Burt Holzman, PHOBOS


The RHIC HBT Puzzle - 1The RHIC HBT Puzzle - 1• Hydrodynamics at RHICHydrodynamics at RHIC

Can describe soft pCan describe soft pTT spectra and v spectra and v22

consistently, for several particle speciesconsistently, for several particle species• Fast thermalization in partonic phase Fast thermalization in partonic phase

(~(~½½ fm/c), lives for ~15 fm/c fm/c), lives for ~15 fm/c

Underpredicts RUnderpredicts Rsideside and its k and its kTT dependence dependence

Overpredicts ROverpredicts Routout and R and Rlonglong by factor ~2 by factor ~2


• Hydro doesn’t work. Why is this a Hydro doesn’t work. Why is this a puzzle?puzzle?

• Expanding fireball, undergoing phase Expanding fireball, undergoing phase transition, should transition, should at leastat least cause R cause Routout > R > Rsideside

RRsideside

RRoutout

STARPHENIX

hydro onlyhydro+hadronic rescatt

Soff, Bass Dumitru

Hadronic rescattering phase makes it worse


The RHIC HBT Puzzle - 2The RHIC HBT Puzzle - 2

1.1. Default initial conditions (fit pDefault initial conditions (fit pTT & v & v22))


√s = 130 GeV STAR PHENIX

4

8

4

8

4

8

0.2 0.4 0.6 0.8kT (GeV/c)

3.3. Thermalize faster, or initialize Thermalize faster, or initialize Hydro with non-zero flowHydro with non-zero flow

2.2. Freeze-out directly at hadronizationFreeze-out directly at hadronization

• Conflicts with fits to particle spectraConflicts with fits to particle spectra

Can HBT puzzle be resolved in Hydro?

4.4. Hydro + partial chemical equilibriumHydro + partial chemical equilibriumHirano and Tsuda, PRC 66 (2002) 054905Hirano and Tsuda, PRC 66 (2002) 054905

• Chemical potentials maintain proper Chemical potentials maintain proper abundances through hadronic evolutionabundances through hadronic evolution

• Smaller RSmaller Rlonglong, but fails R, but fails Routout , R , Rsideside

1.2.3.4.

Ro

ut (

fm)

Rsi

de (

fm)

Rlo

ng (

fm)



5.5. Parton cascade with opacityParton cascade with opacityMolnar and Gyulassy, nucl-th/0211017Molnar and Gyulassy, nucl-th/0211017

• Pion freeze-out distribution sensitive to Pion freeze-out distribution sensitive to transport opacity transport opacity


4

8

0.2 0.4 0.6 0.8kT (GeV/c)

6.6. Positive xPositive xoo-t correlation ?!-t correlation ?!Lin, Ko and Pal, PRL 89 (2002) 152301Lin, Ko and Pal, PRL 89 (2002) 152301

Alternative approaches

4

8

4

8

2222

22

2222

~)(

~)(

~2~)(

tzKR

xKR

ttxxKR

l

ss

oToo T

Ro

ut (

fm)

Rsi

de (

fm)

Rlo

ng (

fm)

= 7.73 = 3.01 = 0.60

Lin, Ko and Pal, PRL 89 (2002) 152301



• Blast-wave parametrizationBlast-wave parametrizationRetiere and Lisa, nucl-th/0312024Retiere and Lisa, nucl-th/0312024

• Longitudinal boost invarianceLongitudinal boost invariance

• Relative particle abundances not fixedRelative particle abundances not fixed

• Constant parameters at freeze-outConstant parameters at freeze-out


4

8

0.2 0.4 0.6 0.8kT (GeV/c)

• Buda-Lund Hydro parameterizationBuda-Lund Hydro parameterizationCsorgo et al, nucl-th/0311102Csorgo et al, nucl-th/0311102

• Not boost invariant (Hubble flow)Not boost invariant (Hubble flow)

• Freeze-out smeared in temperatureFreeze-out smeared in temperature

4

8

4

8

Hinting at the solution

Ro

ut (

fm)

Rsi

de (

fm)

Rlo

ng (

fm)

Retiere, Lisa

Csorgo et al

TTff 104 104 3 MeV 3 MeV

ff 8.9 8.9 0.3 fm/c 0.3 fm/c

TToo 214 214 7 MeV 7 MeV

ff 6.0 6.0 0.2 fm/c 0.2 fm/c


Azimuthally sensitive Azimuthally sensitive HBT HBT• HBT(HBT(): probe spatial anisotropy at freeze-out): probe spatial anisotropy at freeze-out

Wiedemann, PRC 57 (1998) 266Wiedemann, PRC 57 (1998) 266

• Freeze-out shape probes nature & timescale of system evolutionFreeze-out shape probes nature & timescale of system evolution

• How much (if any) initial spatial deformation survives system expansion?How much (if any) initial spatial deformation survives system expansion?

Initial geometry → aniosotropies in pressure gradients

Preferential in-plane expansion → decreases spatial anisotropy

Freeze-out source shape via HBT → measure of pressure, expansion time

(model-dependent)

late rescatteringhydrodynamic expansion

time

x

beam into screen

Rside2

reactionplane

qoutqside

qlong

= 0°

= 90°

Rside (large)

Rside (small)


HBT(HBT(): Centrality & k): Centrality & kTT dependencedependence

STAR Collaboration, nucl-ex/0312009Au+Au, √s = 200 GeV


Fourier coefficients of HBT(Fourier coefficients of HBT() ) oscillationsoscillations

• 00thth-order FC: centrality & k-order FC: centrality & kTT

dependence mirrors dependence mirrors -integrated -integrated analyses; quantitatively consistentanalyses; quantitatively consistent

• Relative amplitudes increase from Relative amplitudes increase from central to peripheral collisionscentral to peripheral collisions

means relative amplitudes

STAR Collaboration, nucl-ex/0312009

• Freeze-out eccentricity can be estimated from relative amplitudes

• Blast-wave: rel. amplitudes sensitive to spatial anisotropy, depend weakly on collective flowRetiere and Lisa, nucl-th/0312024

• Freeze-out eccentricity can be estimated from relative amplitudes

• Blast-wave: rel. amplitudes sensitive to spatial anisotropy, depend weakly on collective flowRetiere and Lisa, nucl-th/0312024

20,s

22,o

20,s

22,os

20,s

22,s

2x

2y

2x

2y

R

R2

R

R2

R

R2

RR

RR

no temporal component


Fourier coefficients of HBT(Fourier coefficients of HBT() ) oscillationsoscillations

Rx

Ry

initi

al =

final

STAR Collaboration, nucl-ex/0312009

• Out-of-plane sources at Out-of-plane sources at freeze-outfreeze-out

• Pressure and/or expansion Pressure and/or expansion time was not sufficient to time was not sufficient to quench initial shapequench initial shape

• From vFrom v22 we know... we know...

• Strong in-plane flow → Strong in-plane flow → significant pressure build-up in significant pressure build-up in systemsystem

Short expansion time plays dominant role in out-of-plane freeze-out source shapes

• Evolution of eccentricity Evolution of eccentricity → consistent with → consistent with ~ 9 fm ~ 9 fm from Rfrom Rlonglong Sinyukov fit Sinyukov fit


Universal pion freeze-outUniversal pion freeze-out

• Use HBT radii to estimate freeze-out Use HBT radii to estimate freeze-out volume Vvolume Vff

Vf

N

CERES, PRL 90 (2003) 022301

2sidelong

2/3)2( RRV f

i

NNii NNNN

• Fold Fold -- and and -N cross sections with -N cross sections with experimentally-measured dN/dy’sexperimentally-measured dN/dy’s

fm 1~

N

V fff

• Mean free path can be estimated Mean free path can be estimated from these two relations:from these two relations:

• CERES proposed a simple ansatz to investigate if critical mean free CERES proposed a simple ansatz to investigate if critical mean free path for pions path for pions ff drives freeze-out drives freeze-out

• Does this work for lighter systems?Does this work for lighter systems?


HBT in p+p collisions at RHICHBT in p+p collisions at RHIC

• RHIC: HBT for 3 very different RHIC: HBT for 3 very different systems at same c.m. energy & with systems at same c.m. energy & with same detectorsame detector

• kkTT dependence of HBT radii dependence of HBT radii

presumably arises in different ways presumably arises in different ways

p+pMultistring fragmentation

Au+AuCollective expansion

transverse plane

T. Gutierrez for STAR Coll, poster

Rout

Rside

Rlong

p+p


p+p p+p →→ d+Au d+Au →→ Au+Au Au+Au

• All three systems exhibit similar kAll three systems exhibit similar kTT dependence (?!) dependence (?!)

• Systematic study underway to assess “Gaussian-ness” of correlationSystematic study underway to assess “Gaussian-ness” of correlation

T. Gutierrez for STAR Coll, poster

Rout (fm) Rside (fm)

Rlong (fm)

Rout / Rout(pp) Rside / Rside(pp)

Rlong / Rlong(pp)

preliminary


Same universal freeze-out in p+p, Same universal freeze-out in p+p, d+Au ?d+Au ?

Vf

N

CERES, PRL 90 (2003) 022301

10

20

30

40

50

60

70

80

90

10

20

30

40

50

60

70

80

90

Vf (

fm3 )

d+Au

p+p

√s=200 GeV

0

N

(fm

2 ) ff ~ 1 fm seems to hold for light systems as well (!) ~ 1 fm seems to hold for light systems as well (!)

• Why are p+p, d+Au and Au+Au so similar?Why are p+p, d+Au and Au+Au so similar?

• Check CERES’ ansatz using dN/dy’s and HBT radii for p+p and d+AuCheck CERES’ ansatz using dN/dy’s and HBT radii for p+p and d+Au

• dN/dy’s taken from power-law fits to STAR pdN/dy’s taken from power-law fits to STAR pTT spectra (nucl-ex/0309012) spectra (nucl-ex/0309012)


Non-identical particle correlationsNon-identical particle correlations• Study emission asymmetries with final-state interactionsStudy emission asymmetries with final-state interactions

• Strong radial flow induces species-dependent x-p correlationsStrong radial flow induces species-dependent x-p correlations

Case 1Particle emitted closer

to center is slower

Case 2Particle emitted closer

to center is faster

• Effective interaction time Effective interaction time largerlarger

• Stronger correlationStronger correlation

• Effective interaction time Effective interaction time shortershorter

• Weaker correlationWeaker correlation

• The two cases can be discriminatedThe two cases can be discriminated

• Two correlation functions: “lighter particle faster”, “lighter particle slower”Two correlation functions: “lighter particle faster”, “lighter particle slower”

• Compare correlation strength of two CF’sCompare correlation strength of two CF’s


Non-identical particle correlationsNon-identical particle correlations

• ““pion faster” shows stronger correlationpion faster” shows stronger correlation

pions on average emitted nearer to source centerpions on average emitted nearer to source center

• Arises naturally in collective expansion pictureArises naturally in collective expansion picture

• Similar studies are underway for many particle combinationsSimilar studies are underway for many particle combinations

• Exotic correlations like Exotic correlations like -- can yield information about nature of can yield information about nature of flow flow

C(pion faster) / C(pion slower)

K

pion faster

PRELIMINARY

pion slower

A. Kisiel for STAR

• Blast-wave picture • Blast-wave picture

pions

protonslow high

Au+Au, √s = 200 GeV


HBT of direct photonsHBT of direct photons

• Photon interferometry in heavy ion collisionsPhoton interferometry in heavy ion collisions• Probes initial state, not final-state interactionsProbes initial state, not final-state interactions

Srivastava and Kapusta; Timmerman Srivastava and Kapusta; Timmerman et alet al; Peressounko PRC 67 (2003) 014905; Peressounko PRC 67 (2003) 014905

• A major challenge experimentally!A major challenge experimentally!

• Low relative direct photon yieldLow relative direct photon yield

• Many sources of small-QMany sources of small-Qinvinv pairs: pairs:

photon conversions, photon conversions, 00 HBT, HBT, mis-id mis-id ’s, resonance decays, etc.’s, resonance decays, etc.

• WA98: First WA98: First -HBT in R.H.I.C. -HBT in R.H.I.C.

• RRinvinv quantitatively similar to quantitatively similar to

HBT in same k HBT in same kTT region region

• →→ Soft photons arise in lateSoft photons arise in latestages of collision stages of collision

WA98 Collaboration, nucl-ex/0310022

0.1 < kT < 0.2 GeV/c

0.2 < kT < 0.3 GeV/c

fm (sys.)9.0(stat.)8.04.5 invR

fm (sys.)2.1(stat.)8.08.5 invR

0 peak

WA98 Collaboration, nucl-ex/0310022

• Direct photon yield can be accessed with Direct photon yield can be accessed with

2TotalDirect NN


ConclusionsConclusions• Identical-meson HBT interferometryIdentical-meson HBT interferometry

• HBT is HBT is thethe observable that doesn’t fit into dynamic picture at low p observable that doesn’t fit into dynamic picture at low p t t

• p+p, d+Au and Au+Au exhibit similar kp+p, d+Au and Au+Au exhibit similar kTT dependence, similar dependence, similar

freeze-out pion mean free pathfreeze-out pion mean free path

• Azumithally sensitive HBTAzumithally sensitive HBT• Evidence for out-of-plane extended sources at freeze-outEvidence for out-of-plane extended sources at freeze-out

• Short-lived system “remembers” its initial spatial anisotropyShort-lived system “remembers” its initial spatial anisotropy

• Non-identical particle correlationsNon-identical particle correlations• Lighter particles emitted closer to centerLighter particles emitted closer to center

• Direct photon interferometryDirect photon interferometry• Similar RSimilar Rinvinv for for - and - and -HBT; access to low-p-HBT; access to low-pTT direct photon yield direct photon yield


“HBT brings us from enlightenment to tragedy, and back to enlightenment, on a time scale of four years.”

Reinhard Stock

The HBT puzzle is three years old. 2004 is looking promising!


BACK-UPSBACK-UPS


Recent “standard” HBT results - Recent “standard” HBT results - SPS SPS

• NA44: High mNA44: High mTT - and p-HBT - and p-HBT ((nucl-ex/0305014)nucl-ex/0305014)

TmppR

102

1


Recent “standard” HBT results - Recent “standard” HBT results - SPS SPS

• NA49: Kaon HBT NA49: Kaon HBT ((Phys.Lett. B 557 (2003) 157)Phys.Lett. B 557 (2003) 157)

• Less influence from resonances & feeddownLess influence from resonances & feeddown

• New results shown this weekNew results shown this week

• HBT @ 20, 30, 40, 80, 158 AGeV (!)HBT @ 20, 30, 40, 80, 158 AGeV (!)

T = 120 12 MeV → f ~ 9.5 1 fm, T ~ 0.55


A highlight from this weekA highlight from this week

preliminary0-30%

PHENIX Preliminary

Mike Heffner, PHENIX Selemon Bekele, STAR


Refined Coulomb treatmentRefined Coulomb treatment• Final-state interactions (Coulomb, strong) influence correlation signalFinal-state interactions (Coulomb, strong) influence correlation signal

• Traditionally, all pairs in CF corrected for CoulombTraditionally, all pairs in CF corrected for Coulomb

• This over-corrects the CF This over-corrects the CF → increases width, decreases radii→ increases width, decreases radii

)()()(

)(qGqK

qB

qA

22

1 ii Rqe

• CERES: Apply Coulomb correction only to pairs participating in B-ECERES: Apply Coulomb correction only to pairs participating in B-E((Nucl. Phys. A 714 (2003) 124)Nucl. Phys. A 714 (2003) 124)

First proposed in: Bowler PLB 270 (1991) 69

)()(1)(

)(qGqK

qB

qA

fraction of non-participating pairs

• Adopted by in recent papers by STAR, PHENIXAdopted by in recent papers by STAR, PHENIXSTAR Coll, nucl-ex/0312009; PHENIX Coll, nucl-ex/0401003STAR Coll, nucl-ex/0312009; PHENIX Coll, nucl-ex/0401003

PHENIX Coll, nucl-ex/0401003

Coulomb-corrected uncorrected


Collision timescaleCollision timescale

0 5 10 15

Evolution time (fm/c)

Hydrodynamical model

Blast-wave fit

Rlong Sinyukov fit

ceq

HBT()

Buda-Lund


HBT(HBT() predictions from ) predictions from hydrodynamicshydrodynamics

• Hydro: Freeze-out shape sensitive to lifetime, initial conditionsHydro: Freeze-out shape sensitive to lifetime, initial conditions

• kkTT dependence probes different regions of space-time source dependence probes different regions of space-time source

• Realistic hydro parameters: Source orientation reflected in HBT(Realistic hydro parameters: Source orientation reflected in HBT() ) oscillations oscillations

Heinz & Kolb, PLB 542 (2002) 216

Hydro calculations initialized with fits to RHIC spectra & v2


HBT(HBT() experimental technique) experimental technique

1.1. Construct correlation functions for Construct correlation functions for discrete bins w.r.t. reaction plane anglediscrete bins w.r.t. reaction plane angle

2.2. Apply HBT formalism to extract RApply HBT formalism to extract Rijij22 vs. vs.

• Additional out-side cross-term Additional out-side cross-term

reactionplane

qoutqside

qlong

3.3. Oscillations of ROscillations of Rijij22 reflect spatial reflect spatial

anisotropies in systemanisotropies in system

• Oscillations governed by geometrical symmetriesOscillations governed by geometrical symmetries

Rside2

Out-of-plane

In-plane

= 0°

= 90°

Rside (large)

Rside (small)


A simple estimate – A simple estimate – 00 from from initinit and and finalfinal

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

HBT Dan Magestro, The Ohio State University Overview of HBT interferometry Overview of HBT...

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