Femtoscopy in heavy ion collisions
Mike Lisa
The Ohio State University
!
“School” lecture
May 2005
!
The Berkeley School Femtoscopy - malisa
1
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
May 2005
The Berkeley School - Femtoscopy - malisa
First, a word from our sponsor…
Workshop on femtoscopy at RHIC
21 June 2005 @ BNL
RHIC/AGS Users’ Meeting
http://www.star.bnl.gov/~panitkin/UsersMeeting_05/
Femtoscopy in Relativistic Heavy Ion Collisions
MAL, S. Pratt, R. Soltz, U. Wiedemann
Ann. Rev. Nucl. Part. Sci. 2006; nucl-ex/0505014
May 2005
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3
4
“RHIC Month One”
May 2005
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
Spacetime - an annoying bump on the road
(to Stockholm?)
STAR, PRC66 (2002) 034904
STAR, PRL93 (2004) 252301
Ann.Rev.Nucl.Part.Sci. 46 (1996) 71
QuickTime™ and a
TIFF (L ZW) d eco mpres sor
are nee ded to s ee this picture.
• 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
• Temporal scale sensitive to deconfinement transition (?)
May 2005
The Berkeley School - Femtoscopy - malisa
5
Motivation
Formalism
Experiment
Trends
Models
6
Disintegration timescale - expectation
3D 1-fluid Hydrodynamics
Rischke & Gyulassy, NPA 608, 479 (1996)
dN/dt
with
transition
CYM & LGT
PCM & clust. hadronization
NFD
NFD & hadronic TM
string & hadronic TM
PCM & hadronic TM
time
“”
Long-standing favorite signature of QGP:
• increase in , ROUT/RSIDE due to deconfinement  confinement transition
• hoped-for “turn on” as QGP threshold is reached
May 2005
The Berkeley School - Femtoscopy - malisa
“”
Motivation
Formalism
Experiment
Trends
Models
7
“Short” and “long” – in seconds
10-24
10-18
10-12
10-6
100
106
1012
as many yoctoseconds (10-24 s ~ 3 fm/c) in a second
as seconds in 10 thousand trillion years
Today’s lecture
May 2005
The Berkeley School - Femtoscopy - malisa
1018
1024
Motivation
Formalism
Experiment
Trends
Models
Correlation function b/t particles a,b
6 ab
3
3
d
N
/(dp
dp
ab
a
b)
C P (q)  3 a
d N /dp3a d3N b /dp3b 

C (q) 
ab
P
prime:
pair frame
Sab
( r ) 
P

q  p a  p b /2
ab
P
( r )   (q, r )
2
4
4
d
x
d
 a xbsa (pa ,xa )sb (pb,xb )r  xa  xb 
Separation
distribution
May 2005
 d r S
3
P  pa  pb

4
4
d
x
d
 a xbsa (pa ,xa )sb (pb,xb )
pa
pa
pb
x
x
xba
xb a
The Berkeley School - Femtoscopy - malisa
pb
8
Motivation
Formalism
Experiment
Trends
Models
Reminder
• Two-particle interferometry: p-space separation  space-time separation
x1
p1

q
qside
p2
Rside
x2
qout
  
q  p2  p1
 1  
k  p 2  p1 
2
qlong
Rout
source sp(x) = homogeneity region [Sinyukov(95)]
 connections with “whole source” always model-dependent
Rside
Pratt-Bertsch (“out-side-long”)
decomposition designed to
help disentangle space & time
Rout
May 2005
The Berkeley School - Femtoscopy - malisa
9
Motivation
Formalism
Experiment
Trends
Models
Measurable substructure
Size, shape, and orientation of homogeneity regions
Gaussian parameterization

SP (r ) ~ e
ri rj
 2R 2
i,j

May 2005
The Berkeley School - Femtoscopy - malisa
i,j
10
Motivation
Formalism
Experiment
Trends
Models
11
Measurable substructure
Average separation between homogeneity regions
Gaussian parameterization
2

  X out 
 rout
2 

rlong
2
rside
SP ( r ) ~ exp 



2 2
2
2
4R side 4R long 

 4   R out

X out  x
a,out  x 
b,out

May 2005
The Berkeley School - Femtoscopy - malisa
alsorside , rlong
Motivation
Formalism
Experiment
Trends
Models
Experimental definition of CF
how to access this rich substructure...
6 ab
3
3
d
N
/(dp
dp
ab
a
b)
C P (q)  3 a
d N /dp3a d3N b /dp3b 
Cab
(q) 
P

P  pa  pb
q  p a  p b /2
Aab
(q)
P
ab
P
  ab (q)
B (q)
P
A() = “signal”
s.p. p.s.  s.p. acceptance  correlations
B() = “reference”
s.p. p.s.  s.p. acceptance
() = corrections

May 2005
The Berkeley School - Femtoscopy - malisa
12
Motivation
Formalism
Experiment
Trends
Models
13
The Pairwise distributions
Collection of selected particles within selected events:
event 1
event 2
event 3
event n
…
a
b
a
b
a
b
“Real” pairs form
A(ab) signal or numerator
ab
May 2005
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a
b
Motivation
Formalism
Experiment
Trends
Models
14
The Pairwise distributions
Collection of selected particles within selected events:
event 1
event 2
event 3
event n
…
a
a
“Real” pairs form
A(ab) signal or numerator
ab
May 2005
b
b
a
b
“Mixed” pairs form
B(ab) background or
denominator
ab
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
15
The Pairwise distributions
Collection of selected particles within selected events:
event 1
event 2
event 3
event n
…
“Real” pairs form
A(ab) signal or numerator
ab
May 2005
C(ab)
“Mixed” pairs form
ratio C=A/B
B(ab) background or
“only” correlations
denominator
ab
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ab
Motivation
Formalism
Experiment
Trends
Models
16
Caution: mix “similar” events
event 2
event 1
…
• 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
b a
a
A(y)
high y unlikely
B(y)
y
May 2005
The Berkeley School - Femtoscopy - malisa
a
b
b
high y likely
y
Motivation
Formalism
Experiment
Trends
Models
17
Caution: mix “similar” events
event 2
event 1
…
• 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
A()
b a
a
high  unlikely
B()

May 2005
The Berkeley School - Femtoscopy - malisa
a
b
b
high  likely

Motivation
Formalism
Experiment
Trends
Models
18
Caution: mix “similar” events
event 1
event 2
…
• 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
Alternatives to event-mixing *
• singles
(Lisa 1991)
Properly-constructed background
• unlike-sign
 cancellation of noncorrelated (single-particle)
effects(Abreu 1992)
• pacceptance
in A(), B() due to s.p. phasespace and
b  -pb (Stavinskiy 2004)
 physical* and detector-induced correlations
• Monteremain
Carlo (Duque 2003)
• detector configuration (run/time)
* femtoscopic and nonfemtoscopic
May 2005
* (Kopylov 1974)
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
Common correlated* detector effects
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
* increased/decreased likelihood of finding a track, due to the presence of another track
May 2005
The Berkeley School - Femtoscopy - malisa
19
Motivation
Formalism
Experiment
Trends
Models
20
Identifying likely splits
Example: quantity based on
pairwise relative topology
“better” than Nhits cut
or Q-cut
Used by STAR
May 2005
SEVERE
SEVERE
SEVERE
SEVERE
HIGH
HIGH
HIGH
HIGH
ELEVATED
ELEVATED
ELEVATED
ELEVATED
GUARDED
GUARDED
GUARDED
GUARDED
LOW
LOW
LOW
LOW
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
Pairwise cut removes splitting effect
 “all” gone
SL = “splitting likelihood”
May 2005
The Berkeley School - Femtoscopy - malisa
21
Motivation
Formalism
Experiment
Trends
Models
Track merging due to hit merging
STARNote 238
track-crossing points “hits”
too close in 2D space
cannot be resolved
track merging likelihood
quantified by relative hit
positions
May 2005
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
The Berkeley School - Femtoscopy - malisa
22
Motivation
Formalism
Experiment
Trends
Models
23
Pairwise cut removes merging effect
track-crossing points “hits”
too close in 2D space
cannot be resolved
track merging likelihood
quantified by relative hit
positions
anti-merging cut
Wait-- how do you cut pairs you don’t see?
May 2005
The Berkeley School - Femtoscopy - malisa
 “all” gone
Motivation
Formalism
Experiment
Trends
Models
24
Pairwise cut removes merging effect
A()
B()
track-crossing points “hits”
too close in 2D space
cannot be resolved
track merging likelihood
quantified by relative hit
positions


Before: A() shows merging
anti-merging cut
After: B() loses bathwater and some baby
A() loses some baby
Cancellation in ratio
Wait-- how do you cut pairs you don’t see?
Similarly, splitting cut in B()
cut works mostly on background distribution
- which tracks would merge?
May 2005
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
25
1a) Momentum Resolution
iterative correction of C(q) via
convolution of single-particle
dp (~1%) with assumed correlation
pT/pT
Corrections 1: Finite Resolution Effects
0.01
1b) Event Plane Resolution
for azimuthally-sensitive analyses:
correct 1000’s of Fourier coefficients
a la Poskanzer&Voloshin
 (rad)
≤ 5% effect on sizes
QuickTime™ and a
TIFF (LZW) decompressor
STAR. PRL 86 (2001) 402
0.01needed to see this picture.
are
 (rad)
~ 10% effect on shape
0.01
1
May 2005
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p (GeV/c)
Motivation
Formalism
Experiment
Trends
Models
Corrections 2a:
Uncorrelated “contamination”
correlation strength diluted (~x3)
by “white” noise from
• random false tracks
• mis-PID
• weak decay daughters*
Ctrue
Cmeas
may be corrected or included in fit
Assuming identical junk and real s.p. p.s.
* not strictly
uncorrelated
noise
May
2005
C
meas
C
true
Atrue (q) 
Ameas (q)   Atrue(q)  (1 )  B(q)
(q) 

   
1 1
B(q)
B(q)
 B(q)

Atrue (q) C meas (q) 1
(q) 

1
B(q)

 = “good” pair fraction
The Berkeley School - Femtoscopy - malisa
26
Motivation
Formalism
Experiment
Trends
Models
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
May 2005
The Berkeley School - Femtoscopy - malisa
27
Motivation
Formalism
Experiment
Trends
Models
28
Extraction of length scales
maximum-likelihood fit to
C (q) 
ab
P
 d r S
3
ab
P
( r )   (q, r )
2
usually used
(even for non-id)
Gaussian parameterization of a-b separation





r

X

r

X






i
i
j
j
ab
SP ( r ) ~ exp  

2
4 i jR i, j


 i, j o,s,l

X i  x
a,i  x
b,i
;
i, j = out, side, long 



2
Cq    FQ inv   1 exp

q
q
R

i j ij

 1 

 ij



• F(Qinv) = integrated squared Coulomb wavefunction
• “contamination” included via 
• NB: Gaussian source:
not Gaussian CF
May 2005
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for identical pions
29
Various Coulomb “Corrections”
A(q)
 N  (1    G (q))
B(q)  K coul (q)
account for Coulomb suppression
in all background pairs
A(q)
 N  (1    G (q))  K coul (q)
B(q)
*
K coul (q)  K coul
(q)  1    1    K coul (q)
A(q)
 N  (1    G (q))
*
B(q)  K coul (q)
“Standard Correction”
only Coulomb-suppress the
fraction of pairs () which are
direct pions
A(q)
 N  (1    G (q))  1   ( K coul (q)  1) 
B(q)
“Diluted Correction”
a pair either participates
A(q)
in both BE and Coulomb,
 N  (1   ) 1    K coul (q)  1  G (q)
B(q)
or neither
A(q)
Bowler-Sinyukov method

 N  1    K coul (q)  1  G (q) 1
(not a “correction”)
B(q)
G (q)  exp( qi q j Rij2 )
May 2005
K coul (q)   coul x, q 
The Berkeley School - Femtoscopy - malisa
2
x
Motivation
Formalism
Experiment
Trends
Models
Cross-check Coulomb with non-id
a = - ; b = +
STAR PRC71 044906 (2005)
F(Qinv)
“contaminated”
F(Qinv)
May 2005
The Berkeley School - Femtoscopy - malisa
30
Motivation
Formalism
Experiment
Trends
Models
1D projections: a limited view
STAR PRC71 044906 (2005)
• Usually, quality of data and
fit shown in 1D projections
• Narrow integration best
out
“Gaussian fit”
(remember: not
Gaussian CF)
• limited view of data
– see talks of Adam,
Scott, Sandra
– tomorrow: a better way
side
May 2005
The Berkeley School - Femtoscopy - malisa
long
31
Motivation
Formalism
Experiment
Trends
Models
The perennial non-Gaussianness
• 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...)
May 2005
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32
Motivation
Formalism
Experiment
Trends
Models
33
The perennial non-Gaussianness
CF is “mostly” Gaussian
STAR tried “Edgeworth”
functional expansion
(Csorgo 2000)
STAR PRC71 044906 (2005)
Rl (fm)
• 20% effect in Rlong! systematic error...?
• appears fit captures dominant
length scale
May 2005
The Berkeley School - Femtoscopy - malisa
RO/RS
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and
QuickTime™
and aa
TIFF (LZW)
(LZW) decompressor
decompressor
TIFF
are needed to see this picture.
are needed to see this picture.
RS (fm)
RO (fm)
among few quantitative estimates
of non-Gaussian shape
Motivation
Formalism
Experiment
Trends
Models
Trends, soft sector, and RHI history
Finally, we
understand it!
Just one
event!
Gyulassy 1995
May 2005
6 decades of E/A
(2 decades of sNN)
The Berkeley School - Femtoscopy - malisa
Art’s talk. Compiled by
A. Wetzler (2005)
34
Motivation
Formalism
Experiment
Trends
Models
Systematic decades (years and energy)
AGS/SPS/RHIC HBT papers (expt)
10
Lisa/Pratt/Soltz/Wiedemann
15
Heinz/Jacak
Wiedemann/Heinz
Csorgo
HBT ( s )
Tomasik/Wiedemann
Boal/Jennings/Gelbke
20
A.D. Chacon et al, Phys. Rev. C43 2670 (1991)
G. Alexander, Rep. Prog. Phys. 66 481 (2003)
R = 1.2 (fm)•A1/3
“R = 5 fm”
5
‘85
‘90
‘95
‘00
‘05
• Pion HBT @ Bevalac: “largely confirming nuclear dimensions”
• Since 90’s: increasingly detailed understanding and study w/ high stats
May 2005
The Berkeley School - Femtoscopy - malisa
35
Motivation
Formalism
Experiment
Trends
Models
36
Systematic decades (years and energy)
ˆ
HBT( s ;p T , y, b ,b,m
1 ,m2 ,Asys )
15
10
Heinz/Jacak
Wiedemann/Heinz
Csorgo
Tomasik/Wiedemann
Boal/Jennings/Gelbke
20
Lisa/Pratt/Soltz/Wiedemann
AGS/SPS/RHIC HBT papers (expt)
y
|b|
5
pT
‘85
‘90
‘95
‘00
‘05
• Pion HBT @ Bevalac: “largely confirming nuclear dimensions”
• Since 90’s: increasingly detailed understanding and study w/ high stats
May 2005
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
Most basic sanity check:
Forget homogeneity regions or fancy stuff.
Do femtoscopic length scales increase as
• b0
• A,B
?
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
 Nucleon scales clearly larger
for more central collisions
• AGS [E877(‘99)]
• SPS [NA44(‘99)]
May 2005
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37
Motivation
Formalism
Experiment
Trends
Models
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
NA44 ZPC (2000)
SPS: NA44/NA49 S+S / S+Pb / Pb+Pb
• b0
increase size; neither is scaling variable
• A,B
May 2005
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38
Motivation
Formalism
Experiment
Trends
Models
39
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
• 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
May 2005
•(breaks
The Berkeley School - Femtoscopy - malisa
down s < 5 GeV)
Motivation
Formalism
Experiment
Trends
Models
40
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
Strongly-interacting 6Li released from an asymmetric trap
O’Hara, et al, Science 298 2179 (2002)
What can we learn?
?
in-planeextended
transverse FO shape
+ collective velocity
 evolution time estimate
check independent of RL(pT)
out-of-plane-extended
May 2005
Teaney,
TheLauret,
Berkeley
& School
Shuryak- nucl-th/0110037
Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
small RS
• observe the source from all angles
with respect to RP
• expect oscillations in HBT radii
big RS
May 2005
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41
Motivation
Formalism
Experiment
Trends
Models
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
• observe the source from all angles
with respect to RP
• expect oscillations in HBT radii
(including “new” cross-terms)
R2out-side<0
when pair=135º
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Motivation
Formalism
Experiment
Trends
Models
43
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
STAR, PRL93 012301 (2004)
Measured final source* shape
R2out-side<0
when pair=135º
ever see that symmetry at ycm ?
* model-dependent. Discussed next time
May 2005
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Motivation
Formalism
Experiment
Trends
Models
44
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
STAR, PRL93 012301 (2004)
Measured final source* shape
central
collisions
mid-central
collisions
peripheral
collisions
no message here so far.
Passes sanity check
* model-dependent. Discussed next time
May 2005
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45
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
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End Lecture I
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48
start lecture 2 with
• connect overall SIZE and SHAPE of source at F.O. with
dynamics/evolution (x2 expansion, rounder source; also include
whether these facts are consistent with 9 fm/c -- could be...)
• then go into more direct femtoscopic signatures of dynamics
(pT, mT dep, YKP, etc...)
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Formalism
Experiment
Trends
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Models
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Motivation
Formalism
Experiment
Trends
Models
50
Measured final source shape
STAR, PRL93 012301 (2004)
central
collisions
mid-central
collisions
peripheral
collisions
Expected evolution:
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Motivation
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Formalism
Experiment
Trends
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Models
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Motivation
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Formalism
Experiment
Trends
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Models
52
Motivation
Formalism
Experiment
Ri
R i mT    i
mT

May 2005
Trends
Models
Ri
R i mT  
mT

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Motivation
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Experiment
Trends
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Models
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Motivation
Formalism
Experiment
Trends
Models
also pix of
• k-pi slide of fabrice
• piplus-piminus
• pi-Xi (plus a comment on “thermal emission” and femtoscopy
relationship?)
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Interpretation /
Messages /
Model
Comparisons
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Motivation
Formalism
Experiment
Trends
“zeroth puzzle”
it is always this plot
which is pointed to as
the proof that HBT is
“invariant,” but we’ve
seen it in much richer
detail.
1) it is disturbingly invariant
2) but not totally! (e.g. asHBT)
N.B. At any one energy, we’d probably say
we could work it out, screwing around
with models. But even at generic level (no
theory) this zeroth puzzle is maybe the worst
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Models
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Motivation
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Experiment
Trends
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Motivation
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Experiment
Trends
Models
Cascade models
LPSW(05) - DATA in color-- experimentalist’s plot
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60
v2 and HBT from AMPT?
σ < 6 mb (~ 3 mb?)
May 2005
σ ~ 10 mb
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Motivation
Formalism
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Trends
Models
Hydrodynamical calculations
LPSW(05) - DATA in color-- experimentalist’s plot
NOT insensitive to physics
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General
comments for
discussion day
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General comments / gripes for the
end or the discussion day
• experimental effort into measuring spacetime huge. “Professional”
(to borrow a phrase from Edward).
• theoretical effort has not been to same “professional” standard
– v2 to 30% acceptable? [Edward says HBT only 30% off] v2(pT)
~30% different from SPS to RHIC. v2[HadronicSystem] ~30%
different from v2[QGP]. Indeed, many (most?) plots showing
“hydro limit” use v2 without 15% nonflow removed.
• Consider (takes some imagination-- remove yourself from present
paradigm in which v2 = New York Times announcements): what if
very large Rlong and Rout/Rside had been observed? In that case,
the New York Times would have been notified. And if v2 were off,
then THAT would have been “an annoying artifact,” saying well, it
was never reproduced by hydro anyway at any sqrt(s), and anyway
long-lived signal is generic expectation, not dependent on hydro
model, blah blah blah
– how this reflects on “professional” nature of our field?
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64
Non-gaussianness
•
•
•
popular issue every few years
CF is NEVER Gaussian
sometimes confusion: nobody expects Gaussian CF. It is Gaussian
S(Dx,p) which is assumed.
– source characterized by 2 params (in each direction): average and
variance
– true also for non-id CF results thus far
•
Practical issue: each modern paper contains typically 100’s of CFs,
each with ~60K bins in q.
– to observe source systematics, obviously ned to reduce the
information.
• Information is always lost in such a procedure.
• is it crucial information? Not clear (for large systems)
– comparing full 3D CFs with models: not practical-- insight unlikely to
be gained.
– similar for imaging
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Questions for Miller / Cramer
• obvious to expect agreement/consistency between “all” particle
types?
• what’s about zero-th HBT puzzle?
• expect “trivial” centrality dependence? (Geometry and potential
change in “lock-step”?)
May 2005
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Extra
slides
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Motivation
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Experiment
Trends
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Motivation
Formalism
Experiment
Trends
Models
“Big” and “Small” – in meters
68
1,000,000,000,000,000,000,000,000 m
10-18
10-12
10-6
100
106
1012
0.000000000000000001 m
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1018
1024
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69
Scales accessible to modern measurement
The group hopes ... to achieve sensitivity in the yoctogram
(10-24 g) range-- about the mass of a single hydrogen atom.
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Motivation
Formalism
Experiment
Trends
Models
Motivation
Formalism
Experiment
Trends
Models
Motivation
Formalism
Experiment
Trends
Models
Motivation
Formalism
Experiment
Trends
Models
Motivation
Formalism
Experiment
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Models
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Motivation
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The 20 accepted SI prefixes
Why?!
Why?!
May 2005
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deca
deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto
[Y] 1 000
[Z] 1 000
[E] 1 000
[P] 1 000
[T] 1 000
[G] 1 000
[M] 1 000
[k] 1 000
[h] 100
[da]10
1
[d] 0.1
[c] 0.01
[m] 0.001
[µ] 0.000
[n] 0.000
[p] 0.000
[f] 0.000
[a] 0.000
[z] 0.000
[y] 0.000
000
000
000
000
000
000
000
001
000
000
000
000
000
000
000
000
000
000
000
000
001
000
000
000
000
000
000
000
000
000
000
000 000 000 000
000 000 000
000 000
000
= 10^24
= 10^21
= 10^18
= 10^15
= 10^12
(a billion)
(a million)
(a thousand)
(a hundred)
(ten)
(a
(a
(a
(a
(a
001
000
000
000
000
001
000 001
000 000 001
000 000 000 001
The Berkeley School - Femtoscopy - malisa
tenth)
hundredth)
thousandth)
millionth)
billionth)
= 10^-12
= 10^-15
= 10^-18
= 10^-21
= 10^-24
71
Motivation
Formalism
Experiment
Trends
Two-track resolution
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
STAR, NIM A499, 659 (2003)
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Motivation
Formalism
Experiment
Trends
Models
Outline
•
•
•
•
•
•
•
May 2005
Why SYSTEMATICS matter: to those “newbies” coming in during the RHIC era.
Beware! The history of heavy ion physics is littered with “successful theories”
and claims of understanding fundamental physics (e.g. multifragmentation/liquidgas or dense-phase EoS) due to coincidence of theory and data at ONE (or
small range) of energy or centrality or whatever.
– Since this is a historical conference in its way: Who can identify the author
of this claim? “Give me the first 5 Au+Au collisions at the Bevalac, and I’ll
tell you the nuclear Equation of State!”
• Sounds like Nobel Prize stuff, no? But where is this person today? Oh,
there he is! Right there on the heels of ANOTHER Nobel Prize!
And systematics matters AT LEAST as much for femtoscopy, because:
1) it is affected by “everything”
2) it has actually been measured over a large range (what a concept!!)
3) it presents “puzzles” so need lots of cross-checks and consistency checks
4) it is so dependent upon models for interpretation. (True of all HI observables,
but perhaps even more so for HBT).
5) related: one needs to continually assure oneself that it DOES WORK!
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Data
Trends
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