femtoscopy in heavy ion collisions

May 2005 The Berkeley School - Femtoscopy - malisa

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Femtoscopy in heavy ion collisions

Mike Lisa

The Ohio State University

! “School” lecture !


2

Outline

Lecture I - basics and sanity check

• Motivation (brief)• Formalism (brief reminder)

– accessible geometric substructure

• Some experimental details• 2 decades* of data systematics

– system size: AB, |b|, Npart...

– system shape: (P,b)

Lecture II - dynamics (insanity check?)

• data systematics [cnt’d]

– boost-invariance?: Y

– transverse dynamics: kT, mT

– new substructure: m1≠m2

• Interpretations (& puzzles)– Messages from data itself– Model comparisons– Prelim. comparison: pp, dA

• Summary

* in time and in sNN


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First, a word from our sponsor…

Workshop on femtoscopy at RHIC21 June 2005 @ BNL

RHIC/AGS Users’ Meetinghttp://www.star.bnl.gov/~panitkin/UsersMeeting_05/

Femtoscopy in Relativistic Heavy Ion CollisionsMAL, S. Pratt, R. Soltz, U. WiedemannAnn. Rev. Nucl. Part. Sci. 2006; nucl-ex/0505014

http://www.star.bnl.gov/~panitkin/UsersMeeting_05/


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“RHIC Month One”


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Spacetime - an annoying bump on the road (to Stockholm?)

• 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

Motivation Formalism Experiment Trends Models

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 (?)


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Disintegration timescale - expectation3D 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


time

dN/dt

PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM


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“Short” and “long” – in seconds

Today’s lecture

100 106 1012 1018 102410-610-1210-1810-24

as many yoctoseconds (10-24 s ~ 3 fm/c) in a secondas seconds in 10 thousand trillion years



8Motivation Formalism Experiment Trends Models

Correlation function b/t particles a,b

€

C r P

ab(r q ) =

d6Nab /(dpa3dpb

3)

d3Na /dpa3

( ) d3Nb /dpb3

( )

€

rP =

r p a +

r p b

q =r p a −

r p b( ) /2

€

C r P

ab(r q ) = d3 ′

r r ⋅Sr

P

ab( ′ r r )∫ ⋅ φ(

r ′ q ,r ′ r )

2prime:pair frame

pa

pb

xa

xb

pa

pbxa

xb

€

Sr P

ab(r ′ r ) =

d4xad4xbsa (p a,xa )sb(p b,xb)δ

r ′ r −

r ′ x a +

r ′ x b( )∫

d4xad4xbsa (p a,xa )sb(p b,xb)∫

Separationdistribution


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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



Measurable substructureSize, shape, and orientation of homogeneity regions

€

Sr P (r r ) ~ e

−ri ⋅rj

2R i ,j2

i ,j

∑Gaussian parameterization



Measurable substructureAverage separation between homogeneity regions

also rside , rlong

€

Sr P ( ′ r r ) ~ exp −

′ r out − X out[ ]2

4γ⊥2Rout

2−

′ r side2

4R side2

−′ r long2

4R long2

⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪

X out ≡ ′ x a,out − ′ x b,out

Gaussian parameterization


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Experimental definition of CFMotivation Formalism Experiment Trends Models

€

C r P

ab(r q ) =

d6Nab /(dpa3dpb

3)

d3Na /dpa3

( ) d3Nb /dpb3

( )

€

rP =

r p a +

r p b

q =r p a −

r p b( ) /2

how to access this rich substructure...

€

C r P

ab(r q ) =

Ar P

ab(r q )

Br P

ab(r q )⋅ξ r

P

ab(r q )

A() = “signal” s.p. p.s. s.p. acceptance correlations

B() = “reference” s.p. p.s. s.p. acceptance

() = corrections


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event 1 event 2 event 3 event n

…

Collection of selected particles within selected events:

A(ab)

ab

The Pairwise distributions

a b a b a ba

b

“Real” pairs formsignal or numerator



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…


A(ab)

ab


a b

“Real” pairs formsignal or numerator B(ab)

ab

“Mixed” pairs formbackground ordenominator

b ba a



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…


A(ab)

ab


“Real” pairs formsignal or numerator B(ab)

ab

“Mixed” pairs formbackground ordenominator

C(ab)

ab

ratio C=A/B“only” correlations



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Caution: mix “similar” events

• Allow range of event-wise characteristics into analysis

• Particles in “Real” pairs (obviously) come from similar events

• must be similar for “mixed” pairs

event 1 event 2 …

A(y)

y

high y unlikely

a b a ba b

B(y)

y

high y likely

• in vertex position



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A()

high unlikely

a b a ba b

B()

high likely


event 1 event 2 …

• in reaction plane orientation



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• in reaction plane orientation

event 1 event 2 …

• detector configuration (run/time) Alternatives to event-mixing *• singles (Lisa 1991)• unlike-sign (Abreu 1992)

• pb -pb (Stavinskiy 2004)

• Monte Carlo (Duque 2003)

* (Kopylov 1974)


Properly-constructed background cancellation of noncorrelated (single-particle) effects

in A(), B() due to s.p. phasespace and acceptance physical* and detector-induced correlations remain

* femtoscopic and nonfemtoscopic


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Common correlated* detector effects

* increased/decreased likelihood of finding a track, due to the presence of another track


Splitting: confused tracker finds 2 tracks due to one particle

Merging: two particles overlap & become indistinguishable

Both usually small enough (<%) to be ignored in all except femtoscopic analyses


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Identifying likely splitsMotivation Formalism Experiment Trends Models

Example: quantity based onpairwise relative topology

“better” than Nhits cutor Q-cut

Used by STAR

LOW

GUARDED

ELEVATED

HIGH

SEVERE

LOW

GUARDED

ELEVATED

HIGH

SEVERE

LOW

GUARDED

ELEVATED

HIGH

SEVERE

LOW

GUARDED

ELEVATED

HIGH

SEVERE


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Pairwise cut removes splitting effectMotivation Formalism Experiment Trends Models

SL = “splitting likelihood”

“all” gone


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Track merging due to hit mergingMotivation Formalism Experiment Trends Models



STARNote 238

track-crossing points “hits”too close in 2D spacecannot be resolved

track merging likelihood quantified by relative hit positions


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Pairwise cut removes merging effectMotivation Formalism Experiment Trends Models



“all” gone

anti-merging cut

Wait-- how do you cut pairs you don’t see?


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Pairwise cut removes merging effectMotivation Formalism Experiment Trends Models



anti-merging cut

Wait-- how do you cut pairs you don’t see?

cut works mostly on background distribution- which tracks would merge?

A()

B()

Before: A() shows merging

After: B() loses bathwater and some babyA() loses some baby

Cancellation in ratio

Similarly, splitting cut in B()


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Corrections 1: Finite Resolution EffectsMotivation Formalism Experiment Trends Models



pT/p

T

(ra

d)

(ra

d)

0.01

0.01

0.01

p (GeV/c)1

1a) Momentum Resolution

iterative correction of C(q) via convolution of single-particle dp (~1%) with assumed correlation

≤ 5% effect on sizes

STAR. PRL 86 (2001) 402

1b) Event Plane Resolution

for azimuthally-sensitive analyses:correct 1000’s of Fourier coefficients a la Poskanzer&Voloshin

~ 10% effect on shape


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Corrections 2a:Uncorrelated “contamination”


correlation strength diluted (~x3) by “white” noise from

• random false tracks• mis-PID• weak decay daughters*

may be corrected or included in fit

* not strictly uncorrelated noise

€

Cmeas(q) =Ameas(q)

B(q)=λ ⋅Atrue(q) + (1− λ ) ⋅B(q)

B(q)= λ ⋅

Atrue(q)

B(q)−1

⎛

⎝ ⎜

⎞

⎠ ⎟+1

Ctrue(q) =Atrue(q)

B(q)=

Cmeas(q) −1

λ+1

Assuming identical junk and real s.p. p.s.

= “good” pair fraction

Ctrue

Cmeas


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Corrections 2b:Correlated “contamination”


e.g. correlated -p feeddown into p-p correlations

• non-trivial : requires model & Monte Carlo• not commonly done (but will become more common)• not discussed further here


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Extraction of length scalesMotivation Formalism Experiment Trends Models

€

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


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Cross-check Coulomb with non-idMotivation Formalism Experiment Trends Models

a = - ; b = +

F(Qinv)

“contaminated”F(Qinv)

STAR PRC71 044906 (2005)


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“Gaussian fit”(remember: notGaussian CF)


• 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)


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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...)


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The perennial non-Gaussianness


are needed to see this picture.RO (

fm)

RS (fm

)

Rl (

fm) R

O /RS


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


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Trends, soft sector, and RHI historyMotivation Formalism Experiment Trends Models

Art’s talk. Compiled byA. Wetzler (2005)

6 decades of E/A(2 decades of sNN)Gyulassy 1995

Just oneevent!

Finally, weunderstand it!


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

R = 1.2 (fm)•A1/3

Systematic decades (years and energy)

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

)s(HBT

“R = 5 fm”


‘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/P

ratt

/So

ltz/

Wie

de

ma

nn


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• 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/P

ratt

/So

ltz/

Wie

de

ma

nn

Systematic decades (years and energy)



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

Most basic sanity check:

Forget homogeneity regions or fancy stuff.

Do femtoscopic length scales increase as• b0• A,B ?

Nucleon scales clearly larger for more central collisions

• AGS [E877(‘99)]• SPS [NA44(‘99)]






NA44 ZPC (2000)

SPS: NA44/NA49 S+S / S+Pb / Pb+Pb• b0• A,B increase size; neither is scaling variable




•Heavy and light data from AGS, SPS, RHIC

•Generalize A1/3 Npart1/3

•not bad !•connection w/ init. size?

•~s-ordering in “geometrical” Rlong, Rside

•Mult = K(s)*Npart

•source of residual s dep?

• ...Yes! common scaling•common density (?) drives radii, not init. geometry

•(breaks down s < 5 GeV)


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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)

?



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• observe the source from all angles with respect to RP

• expect oscillations in HBT radii

big RS

small RS

T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φrMotivation Formalism Experiment Trends Models


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• observe the source from all angles with respect to RP

• expect oscillations in HBT radii (including “new” cross-terms)

out

side

out

side

R2out-side<0

when pair=135º

T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φrMotivation Formalism Experiment Trends Models


42

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


* model-dependent. Discussed next time

R2out-side<0

when pair=135º


ever see that symmetry at ycm ?


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STAR, PRL93 012301 (2004)

centralcollisions

mid-centralcollisions

peripheralcollisions


* model-dependent. Discussed next time

Measured final source* shape


no message here so far.Passes sanity check


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Summary of Lecture I• Non-trivial space-time evolution/structure: Defining feature of

our field. p-space = 1/2 the story (and not the best half)

• Rich substructure accessible via femtoscopy

• size, shape, orientation, displacement

• “only” homogeneity regions probed

connections to “whole source” model-dependent

• source size sanity check pans out

• reveals scaling with dN/dy; “explains” larger source at RHIC

• refutes periodic suggestion that HBT radii dominated by nonfemtoscopic scales

• broken symmetry (b≠0)--> more detailed information

• source shape sanity check pans out

• next time: more asHBT and y≠0 and a≠b


45

Outline

Lecture I - basics and sanity check

• Motivation (brief)• Formalism (brief reminder)

– accessible geometric substructure

• Some experimental details• 2 decades* of data systematics

– system size: AB, |b|, Npart...

– system shape: (P,b)

Lecture II - dynamics (insanity check?)

• data systematics [cnt’d]

– boost-invariance?: Y

– transverse dynamics: kT, mT

– new substructure: m1≠m2

• Interpretations (& puzzles)– Messages from data itself– Model comparisons– Prelim. comparison: pp, dA

• Summary

* in time and in sNN

femtoscopy in heavy ion collisions

Documents

dynamicsintermediate

initial state

exciting signalsfinal

wise characteristics

homogeneity regionsalsorside

qgp threshold

nontrivial spacetime

geometric structural