Femtoscopy in heavy ion collisions
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Transcript of 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 !
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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
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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
Motivation Formalism Experiment Trends Models
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
Motivation Formalism Experiment Trends Models
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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
Motivation Formalism Experiment Trends Models
source sp(x) = homogeneity region [Sinyukov(95)]
connections with “whole source” always model-dependent
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10Motivation Formalism Experiment Trends Models
Measurable substructureSize, shape, and orientation of homogeneity regions
€
Sr P (r r ) ~ e
−ri ⋅rj
2R i ,j2
i ,j
∑Gaussian parameterization
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11Motivation Formalism Experiment Trends Models
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
Motivation Formalism Experiment Trends Models
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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
“Real” pairs formsignal or numerator B(ab)
ab
“Mixed” pairs formbackground ordenominator
b ba a
Motivation Formalism Experiment Trends Models
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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
“Real” pairs formsignal or numerator B(ab)
ab
“Mixed” pairs formbackground ordenominator
C(ab)
ab
ratio C=A/B“only” correlations
Motivation Formalism Experiment Trends Models
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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
Motivation Formalism Experiment Trends Models
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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
A()
high unlikely
a b a ba b
B()
high likely
• in vertex position
event 1 event 2 …
• in reaction plane orientation
Motivation Formalism Experiment Trends Models
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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
• in vertex position
• 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)
Motivation Formalism Experiment Trends Models
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
Motivation Formalism Experiment Trends Models
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
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
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
track-crossing points “hits”too close in 2D spacecannot be resolved
track merging likelihood quantified by relative hit positions
“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
track-crossing points “hits”too close in 2D spacecannot be resolved
track merging likelihood quantified by relative hit positions
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
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
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”
Motivation Formalism Experiment Trends Models
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”
Motivation Formalism Experiment Trends Models
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)
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)
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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
QuickTime™ and aTIFF (LZW) decompressor
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
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
STAR PRC71 044906 (2005)
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
• 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”
Motivation Formalism Experiment Trends Models
‘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
Motivation Formalism Experiment Trends Models
‘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)
May 2005 The Berkeley School - Femtoscopy - malisa
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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)]
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
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37Motivation Formalism Experiment Trends Models
ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s φr
NA44 ZPC (2000)
SPS: NA44/NA49 S+S / S+Pb / Pb+Pb• b0• A,B increase size; neither is scaling variable
May 2005 The Berkeley School - Femtoscopy - malisa
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ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s φr
•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)
?
Motivation Formalism Experiment Trends Models
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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
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STAR, PRL93 012301 (2004)Measured final source* shape
Motivation Formalism Experiment Trends Models
* model-dependent. Discussed next time
R2out-side<0
when pair=135º
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φr
ever see that symmetry at ycm ?
May 2005 The Berkeley School - Femtoscopy - malisa
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STAR, PRL93 012301 (2004)
centralcollisions
mid-centralcollisions
peripheralcollisions
Motivation Formalism Experiment Trends Models
* model-dependent. Discussed next time
Measured final source* shape
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φr
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
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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