Femtoscopy in heavy ion collisions: Wherefore, Whence, & Whither?

mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 1

Femtoscopy in heavy ion collisions:

Wherefore, Whence, & Whither?

Mike Lisa

Ohio State University

MAL, Pratt, Soltz, WiedemannAnn Rev Nucl Part Sci 55 (2005)

• Wherefore (=“why?”)• motivation & (basic) formalism

• Whence (=“from where?”) • systematics over 2 decades

• Whither (=“to where?”) • or “wither”...?

http://www-rnc.lbl.gov/TBS


Spacetime - The characteristic of H.I.C.

• Non-trivial space-time - the hallmark of R.H.I.C.• Initial state: dominates further dynamics• Intermediate state: impt element in exciting signals•Final state:

• Geometric structural scale is THE defining feature of QGP

STAR, PRC66 (2002) 034904 STAR, PRL93 (2004) 252301

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Ann.Rev.Nucl.Part.Sci. 46 (1996) 71

• Temporal scale sensitive to deconfinement transition (?)


Extraction of length scales

€

C r P

ab(r q ) = d3 ′

r r ⋅Sr

P

ab( ′ r r )∫ ⋅ φ(

r ′ q ,r ′ r )

2

Gaussian parameterization of a-b separation

€

Sr P

ab( ′ r r ) ~ exp −

′ r i − X i[ ] ⋅ ′ r j − X j[ ]

4γ iγ jR i, j2

i, j= o,s,l

∑ ⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪

X i ≡ ′ x a,i − ′ x b,i ; i, j = out,side,long( )

usually used(even for non-id)

maximum-likelihood fit to

€

Cr q ( ) = λ ⋅F Q inv( ) ⋅ 1+ exp − qiq jR ij

2

ij

∑ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥+ 1− λ( ) for identical pions

• F(Qinv) = integrated squared Coulomb wavefunction

• “contamination” included via • NB: Gaussian source: not Gaussian CF

xa

xb

xa

xb

pa

pbxa

xb

pa

pb


qout

qside

qlong

Reminder

Rsi

de

R long

Rout

x1

x2

12 ppqrrr −=

p1

p2

qr

( )12 pp2

1k

rrr+=

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

RRsideside

RRoutout

Pratt-Bertsch (“out-side-long”) decomposition designed to help disentangle space & time

source sp(x) = homogeneity region [Sinyukov(95)]

connections with “whole source” always model-dependent


Disintegration timescale - INITIAL expectation

3D 1-fluid HydrodynamicsRischke & Gyulassy, NPA 608, 479 (1996)

withtransition

“” “”

Long-standing favorite signature of QGP:

• increase in , ROUT/RSIDE due to deconfinement confinement transition

• hoped-for “turn on” as QGP threshold is reached


A.D. Chacon et al, Phys. Rev. C43 2670 (1991)G. Alexander, Rep. Prog. Phys. 66 481 (2003)

R = 1.2 (fm)•A1/3

Two decades of systematics

•Pion HBT @ Bevalac: “largely confirming nuclear dimensions”•Since 90’s: increasingly detailed understanding and study w/ high stats

)s(HBT

‘85 ‘90 ‘95 ‘00 ‘05

5

10

15

20AGS/SPS/RHIC HBT papers (expt)

Bo

al/

Je

nn

ing

s/G

elb

ke

Heinz/JacakWiedemann/Heinz

Csorgo

To

ma

sik

/Wie

de

ma

nn

“R = 5 fm”

Lis

a,

Pra

tt,

So

ltz,

Wie

de

ma

nn


Two decades of systematics

•Pion HBT @ Bevalac: “largely confirming nuclear dimensions”•Since 90’s: increasingly detailed understanding and study w/ high stats

T 1 2 sysˆHBT( ;p , y, b ,b,ms ,m ,A )

r

y

|b|

pT

‘85 ‘90 ‘95 ‘00 ‘05

5

10

15

20AGS/SPS/RHIC HBT papers (expt)

Bo

al/

Je

nn

ing

s/G

elb

ke

Heinz/JacakWiedemann/Heinz

Csorgo

To

ma

sik

/Wie

de

ma

nn

Lis

a,

Pra

tt,

So

ltz,

Wie

de

ma

nn


Forget homogeneity regions or fancy stuff.

Do femtoscopic length scales increase when they “should?”

Also• SPS [NA44(‘99),NA49(‘00)]• RHIC [STAR(‘05)]

Repeating most basic sanity check at relativistic energies...

p-p correlations

* big bump small source


ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s φr

•Generalize A1/3 Npart1/3

•not bad @ RHIC!•connection w/ init. size?

Varying initial “source size”

Fixed A+B : vary b

Fixed b : vary A (& B!)

Likely scaling variable: Npart

b

PHENIX, PRL 2004

Au+Au sNN =200 GeV


•Generalize A1/3 Npart1/3

•not bad @ RHIC!•connection w/ init. size?

•Heavy and light data from AGS, SPS, RHIC•~s-ordering in “geometrical” Rlong, Rside

•Mult ~ K(s)*Npart

•source of residual s dep?

•...Yes! common scaling•final state drives radii, not init. geometry

•(breaks down s < 5 GeV)

ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s φr

PHOBOS

LPSW nucl-ex/0505014

NB: not constant density


We are not alone...

H. Caines (STAR) QM05

Tounsi, Mischke, RedlichNPA715 565 (2003)

H. Caines (STAR) QM05

NA57 (open)STAR (filled)

NA57 (open)STAR (filled)

S. Manly (PHOBOS) QM05

Entropy determines “everything” at bulk level (soft sector) ?c.f. Helen’s talk

NB: scaling violated s < 4 GeV(as with femtoscopy)


Refinement: chemical effects

• different behaviour below/above AGS

•violates “universal” scaling

•baryon meson dominance

• neglect time/dynamics: gross F.O.

geometry appears determined by

•chemistry

• “universal” mean free path ~ 1 fm (!?)

fm 1~ ⇒==σσ

ρ

NVff

fm.f.p

2sidelong

2/3)2( RRV f π≡~ FO volume

∑ +=≡i

NNii NNNN πππππ σσσσx-section:

Vf

Nσ

CERES, PRL 90 (2003) 022301


Messages from systematics• AB, |b|, Npart systematics

•sanity check on overall size dependence • final state multiplicity/chemistry determines rough geometry...

c.f. Chajecki - lighter systems

collective/flow-like expansion? probe anisotropically!

...and that geometry is ~2x initial size


Strongly-interacting 6Li released from an asymmetric trapO’Hara, et al, Science 298 2179 (2002)

T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φr

What can we learn?

in-plane-extended

out-of-plane-extended

Teaney, Lauret, & Shuryak nucl-th/0110037

transverse FO shape+ collective velocity evolution time estimate

check independent of RL(pT)

?


• observe the source from all angles

with respect to RP• expect oscillations in HBT radii

big RS

small RS



• observe the source from all angles

with respect to RP• expect oscillations in HBT radii

(including “new” cross-terms)

out

side

R2out-side<0

when pair=135º


out

side


STAR, PRL93 012301 (2004)Measured final source* shape

* model-dependent, but see Retiere & MAL PRC70 044907 2004

R2out-side<0

when pair=135º


ever see that symmetry at ycm ?


STAR, PRL93 012301 (2004)

centralcollisions

mid-centralcollisions

peripheralcollisions

Measured final source* shape


* model-dependent, but see Retiere & MAL PRC70 044907 2004

Expected evolution:


Evolution of size and shape - “the rule of two”

€

R s;pT ,y,r b ,AB,φˆ b

,m1,m2( )

initi

al= fin

al

STAR PRL93 012301 (2004)

Initial size/shape estimated by Glauber calculationFinal config according to Retiere & MAL PRC70 044907 2004

~ x2 size increase ~ 1/2 shape reduction

c.f. Chajecki - lighter systems

2x

2y

2x

2y

RR

RR

+−

≡


• non-trivial excitation function• does it make sense? Is it

related to bulk dynamics? YES

sNN (GeV)

(approximately same centrality)

AGS: FO init

RHIC: FO < init

“Anisotropic sanity check”

€

Δ ≈β ⊗ v2 ⊗ τ ???

is relation b/t final and near quantitatively sensible?

(in a toy model yes - fordiscusison if asked)


Messages from systematics• AB, |b|, Npart systematics

•sanity check on overall size dependence • final state multiplicity/chemistry determines rough geometry...

, |b|, s systematics•sanity check on shape evolution •geometric evolution ~ consistent with collective bulk dynamics (flow)

look for dynamic signatures & substructure

• more than T versus mass• more than spectral shapes• more than v2

• ...flow is defined by space-momentum correlations

only femtoscopy can probe substructureof dynamic bulk behaviour


Geometric substructure?

random (non-)system:

all observers measure the

“whole source”


Specific predictions ofbulk global collective flow:

• space-momentum (x-p) correlations

• faster (high pT) particles come from

•smaller source

•closer to “the edge”

Flow-generated substructure

random (non-)system:

all observers measure the

“whole source”


Strong flow confirmed by all expts...

€


,m1,m2( )

LPSW(05)

what agreement!! (what agreement?)


Spectra

v2

HBT

Flow-dominated“Blast-wave” modelPRC70 044907 (2004)


ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps φr

Decreasing R(pT)

• usually attributed to collective flow

• flow integral to our understanding of R.H.I.C.; taken for granted

• femtoscopy the only way to confirm x-p correlations – impt check

Non-flow possibilities• cooling, thermally (not collectively)

expanding source

• combo of x-t and t-p correlationsearly times: small, hot source

late times: large, cool source



Decreasing R(pT)





expanding source

• combo of x-t and t-p correlations

MAL et al, PRC49 2788 (1994)



Decreasing R(pT)





expanding source


• hot core surrounded by cool shell

• important ingredient of Buda-Lund hydro picturee.g. Csörgő & LörstadPRC54 1390 (1996)



Decreasing R(pT)





expanding source


• hot core surrounded by cool shell

• important ingredient of Buda-Lund hydro picturee.g. Csörgő & LörstadPRC54 1390 (1996)

t

Each scenario generatesx-p correlations but…

x2-p correlation: yesx-p correlation: yes

x2-p correlation: yesx-p correlation: no

x2-p correlation: yesx-p correlation: no


Spectra

v2

HBT

Flow-dominated“Blast-wave” modelPRC70 044907 (2004)

π

K

R (

fm)

mT (GeV/c)

STAR PRL 91 262301 (2003)

space-momentum substructure mapped in detail


RHIC femtoscopy with wide variety of particle species

π+ π- K+ K- K0S p p

π+

π-

- K+

K-

- - K0S

p

p

R(√SNN, b, Npart, A, B, mT, y, , PID1, PID2)

= prelim or final result available


Trends, soft sector, and RHI history

A. Wetzler (2005)

M Gyulassy ‘95

Just oneevent!

Finally, weunderstand it!

Then: p-dependent potentials, surface effects, hard-cores, absoption...

• unlike hard and “intermediate” sectors, soft sector has “decades” of systematics


model comparisons

• unlike hard and “intermediate” sectors, soft sector has “decades” of systematics

• single-point agreement a bit unsatisfying...

• femtoscopic model comparisons: mostly “HBT radii” in b=0 collisions

• RHIC models only expected to work at highest energies...


Comparison to “perfect” hydro calculations

LPSW(05)

• model sensitivity (not just R=5) •Rout too big (too long emission time?)

• Rlong too big (too long evolution time?)

• Rside too small (?)


Comparison to Boltzmann/cascade models

better! (better than “perfect”...?)


What’s the difference? freeeze-out........ EoS............viscosity

€

Ro2 = ˜ x 2 − 2βT ˜ x ⋅ ˜ t + βT

2 ˜ t 2

RS2 = ˜ y 2 ; RL

2 = ˜ z 2

“HBT radii” from variancesfit calculated* 3D C(q)to Gaussian functional form:

€

C(r q ) =1+ λ ⋅e−q o

2 R o2 −q s

2R s2 −q l

2R l2

*later: how it is calculated

should be the same IF source is Gaussian

hydro cascade


Non-Gaussian Effects and Model Comparisons - Hydro/BW

C2

qs (GeV/c)

C2

qs (GeV/c)

RO

RS

RL

C2

qs (GeV/c)

KT (GeV/c) KT (GeV/c)

Frodermann, Heinz, MAL PRC63 (2006)Hydrodynamics - CE EOS

Frodermann, Heinz, MAL PRC63 (2006)


Hydrodynamics - NCE EOS

Frodermann, Heinz, MAL PRC63 (2006)


Blast Wave

Depending on model (& parameters, like EoS),non-Gauss effects may be important, (also, Hirano, Ko/Li, Rischke)• BW - no big effect• “perfect” hydro - pushes results into “right” direction. NCE EoS close


Wherefore & Whence

• size & shape; timescale estimate• space-momentum substructure of a flowing system;

dynamics and evolution of• radial flow (size and shift)•elliptic flow (shape and timescale)•directed flow (shape and tilt) [did not show due to time]

• hadronic particle potentials / phase shifts

• Femtoscopy:•well-calibrated, well-established tool• the one most directly connected to space-time - THE defining feature of R.H.I.C.•huge set of systematics of consistent measurements•sensitive to physics in models

• with care: the femtoscope is a precision tool to apply to new systemsLHC, p+p, etc

R(√SNN, b, Npart, A, B, mT, y, , PID1, PID2)


Whither?

• non-id correlations for b≠0 [Retiere & Lisa PRCPRC70 044907 (2004)]

• invert the problem : low-energy phaseshifts from exotic pairs (e.g. π-)

[talk of H. Gos] & [P. Chaloupta QM05]

• space-time substructure in p+p ?? - “direct comparison] [talk of Z. Chajecki][Chajecki et al, WW05]

• imaging - beyond sizes and shifts [Brown, Danielewicz, Pratt, & others]

• first-order azimuthally-sensitive femtoscopy - spacetime aspects of v1[Lisa et al, PLB489 287; PLB496 1]

• relative jets, spin.... (?)

• continue/expand rich program @ ALICE/LHC


THEEND


€


,m1,m2( )

€

R i mT( ) =′ R i

mTα i

Strong flow confirmed by all expts...

Central (~10%) AuAu (PbPb) collisions at y~0


A simple estimate – 0 from init and final

0Y,XY,X

t.)O.F()t(

ββ ⋅=→

“radial flow”

P. Kolb, nucl-th/0306081

• BW → βX, βY @ F.O. (βX > βY)

• 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

• too short to account for expansion??

• Need a real model comparison→ asHBT workable “evolutionary clock” constraint for models MAL ISMD03


“Gaussian fit”(remember: notGaussian CF)

Motivation Formalism Experiment Trends Models

• Usually, quality of data and fit shown in 1D projections

• Narrow integration best

• limited view of data• see talks of Adam, Scott, Sandra• tomorrow: a better way

1D projections: a limited view

out

side long

STAR PRC71 044906 (2005)


The perennial non-GaussiannessMotivation Formalism Experiment Trends Models

• Source has never been fully Gaussian. c.f. J. Sullivan @ SPS

• periodically re-discovered, with little change; information condensation needed to observe systematic data trends

• non-Gaussianness @ RHIC reported in first and subsequent HBT measurements

• imaging is probably best solution (but even then...)


The perennial non-Gaussianness


are needed to see this picture.RO (

fm)

RS (fm

)

Rl (

fm) R

O /RS

Motivation Formalism Experiment Trends Models

CF is “mostly” GaussianSTAR tried “Edgeworth” functional expansion (Csorgo 2000)

among few quantitative estimatesof non-Gaussian shape



STAR PRC71 044906 (2005)



• 20% effect in Rlong! systematic error...?

• appears fit captures dominant length scale


Another implication of strong flow: ~ mT scaling

€


,m1,m2( )


1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs φr

2x

2y

2x

2y

RR

RR

+−

≡

sNN (GeV)

(approximately same centrality)

AGS: FO init

RHIC: FO < init

• transverse shape:• non-trivial excitation function• increased flow*time rounder

FO geometry @ RHIC• insufficient [flow]x[time] to

become in-plane

using four of the six “radii”

€

Sr P

ab( ′ r r ) ~ exp −

′ r i − X i[ ] ⋅ ′ r j − X j[ ]

4γ iγ jR i, j2

i, j= o,s,l

∑ ⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪



Au+Au sNN = 2.3 GeV; b5 fm

E895, PLB496 1 (2000)

using ALL of the six “radii”

€

Sr P

ab( ′ r r ) ~ exp −

′ r i − X i[ ] ⋅ ′ r j − X j[ ]

4γ iγ jR i, j2

i, j= o,s,l

∑ ⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪




(o

)

sNN (GeV)

(Beam)

x

y

z

s

? ?

STAR: soon



become in-plane

• Spatial orientation:• another handle on flow & time• HUGE tilts @ AGS!!• RHIC?• QGP-induced orientation?

AGS


v1 predictions (QGP invoked)

J. Brachmann et al., Phys. Rev. C. 61 024909 (2000)

L.P. Csernai, D. Rohrich: Phys. Lett. B 458 (1999) 454

x-p transverse-longitudinal coupling may be affected in early (v1) stage



(o

)

sNN (GeV)

(Beam)

x

y

z

s

? ?

STAR: soon ?



become in-plane

• Spatial orientation:• another handle on flow & time• HUGE tilts @ AGS!!• RHIC?• QGP-induced orientation?• requires true 3D dynamical

model (explicitly non-B.I.)

AGS

Documents

Femtoscopy in heavy ion collisions: Wherefore, Whence, & Whither?