Femtoscopy in heavy ion collisions - Part 2
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
Motivation
Formalism
Experiment
Trends
Models
3
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
Blast wave : the truth, or something like it
F. Retière , QM04
RY
QuickTime™ and a
TIFF (LZW) decompressor
Spectra
are needed to see this picture.
RX
v2
F. Retière & MAL PRC70 044907 (2004)
• generalized anisotropic BW in
ubiquitous use
• consistent picture capturing
essence of data
• homo. region  “whole source”
with realistic flow gradients
May 2005
QuickTime™ and a
HBT
TIFF (LZW)
decompressor
are needed to see this picture.
The Berkeley School - Femtoscopy - malisa
4
Motivation
Formalism
Experiment
Extracting FO shape/size
Trends
out
Models
side
• 2nd - order oscillations in radii (n>2 negligible)
• characterize each kT bin with 7 numbers:
2

 R  pT ,   cosn 
R  ,n pT    2
R p ,   sin n 

  T
2
  o, s, l
  os
R2os,0 = 0 by symmetry
[Heinz, Hummel, MAL, Wiedemann PRC66, 044903]
out-side
in no-flow scenario...

R 2y  R 2x
R 2y

R 2x
2
R s2, 2
R s2,0
2
2
R os
,2
R s2,0
 2
R o2, 2
R s2,0
U. Wiedemann PR C57 266 (1998)
MAL, U. Heinz, U. Wiedemann PL B489 287 (2000)
May 2005
F. Retière &The
MAL
Berkeley
PRC70School
044907 -(2004)
Femtoscopy - malisa
long
5
Motivation
Formalism
Experiment
Trends
Models
Extracting FO shape/size
• 2nd - order oscillations in radii (n>2 negligible)
• characterize each kT bin with 7 numbers:
2

 R  pT ,   cosn 
R  ,n pT    2
R p ,   sin n 

  T
2
  o, s, l
  os
R2os,0 = 0 by symmetry
[Heinz, Hummel, MAL, Wiedemann PRC66, 044903]
/2
in no-flow scenario...

R 2y  R 2x
R 2y

R 2x
2
R s2, 2
R s2,0
2
2
R os
,2
R s2,0
 2
R o2, 2
R s2,0
U. Wiedemann PR C57 266 (1998)
MAL, U. Heinz, U. Wiedemann PL B489 287 (2000)
continues to be good approximation
even with flow! (~30%)
May 2005
F. Retière &The
MAL
Berkeley
PRC70School
044907 -(2004)
Femtoscopy - malisa
6
Motivation
Formalism
Experiment
Trends
Models
Extracting FO shape/size
• 2nd - order oscillations in radii (n>2 negligible)
• characterize each kT bin with 7 numbers:
2

 R  pT ,   cosn 
R  ,n pT    2
R p ,   sin n 

  T
2
  o, s, l
  os
R2os,0 = 0 by symmetry
[Heinz, Hummel, MAL, Wiedemann PRC66, 044903]
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
in no-flow scenario...

R 2y  R 2x
R 2y

R 2x
2
R s2, 2
R s2,0
2
2
R os
,2
R s2,0
 2
R o2, 2
R s2,0
U. Wiedemann PR C57 266 (1998)
MAL, U. Heinz, U. Wiedemann PL B489 287 (2000)
continues to be good approximation
even with flow! (~30%)
May 2005
F. Retière &The
MAL
Berkeley
PRC70School
044907 -(2004)
Femtoscopy - malisa
7
Motivation
Formalism
Experiment
Trends
Models
Measured final source shape
STAR, PRL93 012301 (2004)
central
collisions
mid-central
collisions
peripheral
collisions
Expected evolution:
May 2005
The Berkeley School - Femtoscopy - malisa
8
Motivation
Formalism
Experiment
Trends
Models
Evolution of size and shape
R
 s;p ,y, b ,AB, ,m ,m 
bˆ
T
1
2
@RHIC
STAR PRC71 044906 (2005)
STAR PRL93 012301 (2004)
Rfinal/Rinitial
2.5

QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
2
1.5
1
0
100
200
300
~ x2 size increase
Npart
400
~ 1/2 shape reduction
Initial size/shape estimated by Glauber calculation
May 2005
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9
10
Evolution
ahead
Detour
May 2005
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
asHBT systematics (1/100 * sNN)
R
•  = 0-2 (not 0-)
first-order plane used
 s;p ,y, b ,AB, ,m ,m 
T
bˆ
1
2
Au+Au sNN = 2.3 GeV; b5 fm
• similar oscillations
in

purely transverse radii
• out-long & side-long?
• new symmetry!
E895, PLB496 1 (2000)
May 2005
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11
Motivation
Formalism
Experiment
Trends
out-side-long versus x-y-z
side
•Source in b-fixed system: (x,y,z)
•Space/time entangled in
pair system (xO,xS,xL)

   y˜
   y˜

 y˜
cos2   y˜
sin 2
R 2o   12 y˜ 2  x˜ 2 cos2 
R 2s
R 2os
1
2
1
2
2
2
 x˜ 2
 x˜ 2
Models
y
12
K
out

x


1
2
2
 x˜ 2   2 ˜t 2
1
2
2
 x˜ 2
b
R 2l  z˜ 2   L2 ˜t 2
R 2ol  x˜  z˜ cos 
R 2sl   x˜  z˜ sin 
May 2005
(several terms vanish @ pT = y = 0)
U. Wiedemann, PRC 57, 266 (1998)
MAL, U. Heinz, U. Wiedemann PLB 489, 287 (2000)
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13
First-order information in HBT()
y
2nd-harmonic oscillations from
elliptical transverse shape
~
x2
~y 2
b

   y˜
   y˜

 y˜
cos2   y˜
sin 2
R 2o   12 y˜ 2  x˜ 2 cos2 
R 2s
R
2
os
1
2
1
2
2
2
 x˜ 2
 x˜
2
x

-harmonic oscillations:
 1spatial
tilt angle q
1
2
2
 x˜ 2   2 ˜t 2
1
2
2
 x˜ 2
st
S
y
R 2l  z˜ 2   L2 ˜t 2
x
R 2ol  x˜  z˜ cos 
qs
R 2sl   x˜  z˜ sin 
z
(Beam)
May 2005
Coordinate
space!
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- malisa
14
Data: - correlation functions
Au(4 AGeV)Au, b4-8 fm
2D projections 
C(q)
1D projections, =45°
out
side
long
lines: projections of 3D Gaussian fit

 q i q j R ij2  
C(q, )  1     e
• 6 components to radius tensor: i, j = o,s,l
E895, PLB 496 1 (2000)
May 2005
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Cross-term radii Rol, Ros, Rsl
quantify “tilts” in correlation functions
 fit results to correlation functions
Lines: Simultaneous fit to HBT radii
to extract underlying geometry
May 2005
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15

16
Images of --emitting sources (scaled ~ x1014)
~y 2
 1.35
2
~
x
y
similar to naïve
overlap: b~5 fm
y
x’
2 AGeV
3 fm
z
y
qS=47°
z
x’
x’
4 AGeV
6 AGeV
qS=37°
z
qS=33°
Large, positive
tilt angles
x
May 2005
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x
x
17
Opposing average tilts in p, x & the physics of  flow
+ 6 AGeV
z (fm)
•  “antiflow” (negative tilt in p-space)
• x-space tilt in positive direction
 non-hydro nature of  flow (@ AGS)
B. Caskey, E895
May 2005
RQMD
The Berkeley School - Femtoscopy
- malisa Au(2GeV)Au
x (fm)
18
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )

R 2y  R 2x
R 2y  R 2x
• transverse shape:
• non-trivial excitation function
• increased flow*time  rounder
FO geometry @ RHIC
• insufficient [flow]x[time] to
become in-plane
AGS: FO  init
RHIC: FO < init
(approximately same centrality)
sNN (GeV)
May 2005
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19
q ( o)
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
AGS
• transverse shape:
• non-trivial excitation function
• increased flow*time  rounder
FO geometry @ RHIC
• insufficient [flow]x[time] to
become in-plane
• Spatial orientation:
• another handle on flow & time
• HUGE tilts @ AGS!!
• RHIC?
• QGP-induced orientation?
May 2005
STAR: soon
?
?
sNN (GeV)
y
The Berkeley School - Femtoscopy - malisa
x
qs
z
(Beam)
20
v1 predictions (QGP invoked)
x-p transverse-longitudinal coupling may be affected in early (v1) stage
J. Brachmann et al., Phys. Rev. C. 61 024909 (2000)
May 2005
L.P. Csernai, D. Rohrich:
Phys. Lett. B 458 (1999)
454
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21
q ( o)
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
AGS
• transverse shape:
• non-trivial excitation function
• increased flow*time  rounder
FO geometry @ RHIC
• insufficient [flow]x[time] to
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.)
May 2005
STAR: soon ?
?
?
sNN (GeV)
y
The Berkeley School - Femtoscopy - malisa
x
qs
z
(Beam)
22
x2 size increase & decreasing deformation
-- ?collective expansion? --
Spectra
Evolution
ahead
v2
Resume
legal
speed
May 2005
HBT
The Berkeley School - Femtoscopy - malisa
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
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
May 2005
& -Heinz,
QGP3
nucl-th/0305084
The BerkeleyKolb
School
Femtoscopy
- malisa
23
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
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 correlations
early times: small, hot source
late times: large, cool source
May 2005
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24
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
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 correlations
May 2005
MAL
et al, School
PRC49
2788 (1994)
The
Berkeley
- Femtoscopy
- malisa
25
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
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 correlations
• hot core surrounded by cool shell
• important ingredient of Buda-Lund
hydro picture
e.g. Csörgő & Lörstad
PRC54 1390 (1996)
May 2005
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26
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
Each scenario generates
x-p correlations but…
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
x2-p correlation: yes
x-p correlation: yes
Non-flow possibilities
• cooling, thermally (not collectively)
expanding source
• combo of x-t and t-p correlations
t
• hot core surrounded by cool shell
• important ingredient of Buda-Lund
hydro picture
e.g. Csörgő & Lörstad
PRC54 1390 (1996)
May 2005
27
The Berkeley School - Femtoscopy - malisa
x2-p correlation: yes
x-p correlation: no
x2-p correlation: yes
x-p correlation: no
28
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
• flow-dominated “models” can reproduce
soft-sector x-space observables
• imply short timescales
• however, are we on the right track? [flow]
• puzzles?  check your assumptions!
• look for flow’s “special signature”
x-p correlation
• In flow pictures, low-pT particles emitted
closer to source’s center (along “out”)
• non-identical particle correlations
(FSI at low v) probe:
• (x1-x2)2 (as does HBT)
• x1-x2

T
K
pT
p
[click for more details on non-id correlations]
May 2005F.
Retiere & MAL,Csanád,
nucl-th/0312024
Csörgő,
Lörstad
nucl-th/0311102
and nucl-th/0310040
The Berkeley
School
- Femtoscopy
- malisa
29
HBT( s ;p T , y, b , bˆ , m1,m2 ,Asys )
QM02
T
x (fm)
T
x (fm)
QuickTime™ and a
TIFF
• extracted shift in emission point
x1(LZW)
-x2 decompressor
areblastwave
needed
to see this picture.
w/ flow-dominated
• consistent
In flow pictures,
low-pT particles
emitted
closer to source’s center (along “out”)
• non-identical particle correlations
(FSI at low v) probe:
• (x1-x2)2 (as does HBT)
• x1-x2
May 2005
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A. Kisiel (STAR) QM04
Motivation
Formalism
Experiment
Trends
Models
Strong flow confirmed by all expts...
R
 s;p ,y, b ,AB, ,m ,m 
T
bˆ
1
2
LPSW(05) - DATA in color-- experimentalist’s plot

what agreement!! (what agreement?)
May 2005
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30
Motivation
Formalism
Experiment
Trends
Models
Strong flow confirmed by all expts...
R
 s;p ,y, b ,AB, ,m ,m 
T
bˆ
1
2
Ri
R i mT    i
mT


Central (~10%) AuAu (PbPb) collisions at y~0
May 2005
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31
Motivation
Formalism
Experiment
Trends
Models
Another implication of strong flow: ~mT scaling
R
 s;p ,y, b ,AB, ,m ,m 
T
bˆ
1

May 2005
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2
32
Motivation
Formalism
Experiment
Trends
Models
Some longitudinal systematics
R
 s;p ,y, b ,AB, ,m ,m 
T
bˆ
1

QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
May 2005 PHOBOS nucl-ex/0410022
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2
33
34
“Dynamic” BI without “Chemical” BI ?
Only femtoscopy can tell!
beam
May 2005
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35
“Dynamic” BI without “Chemical” BI ?
Only femtoscopy can tell!
beam
May 2005
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
Experiment
Trends
Models
Greater detail - -p correlations @ AGS
R
bˆ
T
1
2
sizes and offsets in impact parameter
and longitudinal
E877, Miskowiec
CRIS’98 directions
nucl-ex/9808003
C

 s;p ,y, b ,AB, ,m ,m 
p-10 fm
QuickTime™ and a
TIFF (LZW) decompressor
QuickTime™ and a
are TIFF
needed
see thissorpicture.
(LZW)to
decompres
are needed to see this picture.
b
qX (GeV/c)
qY (GeV/c)
z
May 2005
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qZ (GeV/c)
36
Summary - very brief.
More in Friday’s discussion
May 2005
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37
Summary - very brief.
More in Friday’s discussion
HBT ( s )
• Part I
– space-time THE special aspect of our field
– systematics pass sanity check
• Data show remarkable consistency
R = 1.2 (fm)•A
• HUGE range of systematics, b (mag and direction),
pT, m11/3
m2, y, AB
–
–
–
–
size
shape
orientation in 3D space
detailed dynamic substructure in all directions including shifts
• At a given s, flow-dominated scenario strongly indicated. Can work
(Blast Wave)
• (Unfortunately?) 2 decades of experimental effort over 2 decades of s
– very little changes
– scaling with final multiplicity, not A... progress?
May 2005
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38
39
final words (for today)
• We are measuring system geometry
• Space and time geometry (in detail) hardly changes
AGS RHIC
• This astounding fact is the 0th HBT Puzzle, and much more
important/troubling than the 1st Puzzle (model failures)
– generic expectation: entropy & latent heat / “softest point”
• Given the importance of spacetime to RHI and QGP, this
deserves our attention, despite its being a wart on otherwise
“perfect” story
May 2005
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40
The end
May 2005
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41
pion-proton @ AGS
E877, Miskowiec CRIS’98 nucl-ex/9808003
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
May 2005
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Extra from
Lecture II
May 2005
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42
43
Consistency of timescales & evolution?
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
maybe barely
STAR PRC71 044906 (2005)
May 2005
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44
A simple estimate – 0 from init and final
• BW → X, Y @ F.O. (X > Y)
• hydro: flow velocity grows ~ t
  X ,Y ( t )   X ,Y (F.O.) 
t
0
• From RL(mT): 0 ~ 9 fm/c
consistent picture
• Longer or shorter evolution times
X inconsistent
toy estimate: 0 ~ 0(BW)~ 9 fm/c
• But need a real model comparison
→ asHBT valuable “evolutionary clock”
constraint for models
May 2005
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P. Kolb, nucl-th/0306081
Stuff from
End of
Lecture I
follows this
May 2005
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45
Motivation
Formalism
Experiment
Trends
Models
46
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
47
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
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Experiment
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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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48
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
May 2005
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49
Motivation
Formalism
Experiment
Trends
Models
50
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
51
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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52
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
May 2005
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End Lecture I
May 2005
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53
54
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...)
May 2005
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Motivation
May 2005
Formalism
Experiment
Trends
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55
Motivation
May 2005
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Experiment
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Models
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Motivation
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Models
Ri
R i mT  
mT
Ri
R i mT    i
mT


May 2005
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Motivation
May 2005
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Models
58
Motivation
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also pix of
• k-pi slide of fabrice
• piplus-piminus
• pi-Xi (plus a comment on “thermal emission” and femtoscopy
relationship?)
May 2005
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59
Interpretation /
Messages /
Model
Comparisons
May 2005
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60
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
May 2005
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Models
61
Motivation
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Models
62
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Cascade models
LPSW(05) - DATA in color-- experimentalist’s plot
May 2005
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64
v2 and HBT from AMPT?
σ < 6 mb (~ 3 mb?)
May 2005
σ ~ 10 mb
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Motivation
Formalism
Experiment
Trends
Models
Hydrodynamical calculations
LPSW(05) - DATA in color-- experimentalist’s plot
NOT insensitive to physics
May 2005
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65
General
comments for
discussion day
May 2005
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66
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?
May 2005
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68
Non-gaussianness
•
•
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
May 2005
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69
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”?)
• what’s about similar (but just scaled) behaviour of pp, dA
collisions?
May 2005
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An alternate universe...
• v2 as expected; HBT ~ 40%
–  Announcement of success !
• HBT as expected (hoped); v2 ~ 40%
–  Announcement of success ?
– my guess: yes.
May 2005
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Extra
slides
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Motivation
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Experiment
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Models
72
73
May 2005
Motivation
Formalism
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Motivation
Formalism
Experiment
Trends
Models
Motivation
Formalism
Experiment
Trends
Models
Motivation
Formalism
Experiment
Trends
Models
Motivation
Formalism
Experiment
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Models
The Berkeley School - Femtoscopy - malisa
Motivation
Formalism
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Trends
Models
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
74
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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75
Data
Trends
May 2005
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77
May 2005
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