Femtoscopy in relativistic heavy ion collisions:
a (too-universal) dynamical picture
Mike Lisa
Ohio State University
* femtoscopy (fem-ta-skö-pee) noun
Measurement of spatial scales at the fermi level with 2-particle correlations
Non-trivially related to the “HBT effect” invented to measure stellar scales
mike lisa - austin texas - 10 sept 2007
1
Femtoscopy in relativistic heavy ion collisions:
a (too-universal) dynamical picture
• Reminder: why heavy ions (@ RHIC & beyond)
mike lisa - austin texas - 10 sept 2007
2
Femtoscopy in relativistic heavy ion collisions:
a (too-universal) dynamical picture
• Reminder: why heavy ions (@ RHIC & beyond)
• femtoscopy: relevance and method
mike lisa - austin texas - 10 sept 2007
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Femtoscopy in relativistic heavy ion collisions:
a (too-universal) dynamical picture
• Reminder: why heavy ions (@ RHIC & beyond)
• femtoscopy: relevance and method
• detailed systematics & what it tells us
• pT, mT, y, 
• s, dN/dy, A+B
• “exotic beam factory”
mike lisa - austin texas - 10 sept 2007
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Femtoscopy in relativistic heavy ion collisions:
a (too-universal) dynamical picture
• Reminder: why heavy ions (@ RHIC & beyond)
• femtoscopy: relevance and method
• detailed systematics & what it tells us
• pT, mT, y, 
• s, dN/dy, A+B
• “exotic beam factory”
• excitation function, comparison to “simpler” (?) systems
• in progress
• Summary
mike lisa - austin texas - 10 sept 2007
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Nuclear
Particle
PHOBOS
PHENIX
RHIC
BRAHMS
STAR
AGS
TANDEMS
mike lisa - austin texas - 10 sept 2007
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Nuclear
Why heavy ion collisions?
Particle
STAR ~500 Collaborators
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2 types (?) of collisions...
looks like fun...
looks like a mess...
mike lisa - austin texas - 10 sept 2007
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A dynamical but crude view of the collision
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
c/o UrQMD Collaboration, Frankfurt
In this model, insufficient re-interactions
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A dynamical but crude view of the collision
In this model, insufficient re-interactions
mike lisa - austin texas - 10 sept 2007
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R.H.I.C. defined...
• collision of nuclei sufficiently large that nuclear details unimportant
• distinct from nuclear or particle physics
• “Geranium on Linoleum”
• sufficiently large for
meaningful bulk &
thermodynamic quantities
• non-trivial spatial scales &
geometry drive bulk dynamics
(e.g. flow)
• how big is “sufficient” ?
• important reference issue
mike lisa - austin texas - 10 sept 2007
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phase structure of bulk system:
• driving symmetries
• long-range collective behaviour
• “new” physics [superfluidity in l-He]
•mike
relevance
meaningful
lisa - austin of
texas
- 10 sept 2007EoS
13
The four elements from 400 BC to 2000AD
400 BC : all creation
Air
Water
?
Earth
Fire
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RHIC energies: the first quantitative success of hydro
• direct access to EoS (phase transitions, lattice, etc.)
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
EoS: P versus  versus n
(Heinz et al)
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mike lisa - austin texas - 10 sept 2007
Microexplosions
Femtoexplosions
• energy quickly deposited
1017 phase
J/m3
5 GeV/fm3 = 1036 J/m3
•enter plasma
•sexpand hydrodynamically
0.1 J
1 J
• cool back to original
phase
T
106 K
200 MeV = 1012 K
• do geometric “postmortem” & infer momentum
rate
1018 K/sec
1035 K/s
16
mike lisa - austin texas - 10 sept 2007
Microexplosions
Femtoexplosions
• energy quickly deposited
0.1phase
J
1 J
•senter plasma
•expand hydrodynamically
1017 J/m3
5 GeV/fm3 = 1036 J/m3
•Tcool back to
phase 200 MeV = 1012 K
6 K
10original
• do geometric “postmortem” & infer momentum
rate
1018 K/sec
1035 K/s
17
Impact parameter & Reaction plane
Impact parameter vector b :
 beam direction
connects centers of colliding nuclei
b = 0  “central collision”
many particles produced
“peripheral collision”
fewer particles produced
b
mike lisa - austin texas - 10 sept 2007
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Impact parameter & Reaction plane
Impact parameter vector b :
 beam direction
connects centers of colliding nuclei
Reaction plane:
spanned by beam direction and b
b = 0  “central collision”
many particles produced
“peripheral collision”
fewer particles produced
b
mike lisa - austin texas - 10 sept 2007
b
19
How do semi-central collisions evolve?
1) Superposition of independent p+p:
momenta pointed at random
relative to reaction plane
b
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How do semi-central collisions evolve?
1) Superposition of independent p+p:
high
density / pressure
at center
momenta pointed at random
relative to reaction plane
2) Evolution as a bulk system
Pressure gradients (larger in-plane)
push bulk “out”  “flow”
“zero” pressure
in surrounding vacuum
more, faster particles
seen in-plane
b
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How do semi-central collisions evolve?
1) Superposition of independent p+p: N
momenta pointed at random
relative to reaction plane
0
/4
/2
0
/4
/2
3/4

3/4

-RP (rad)
2) Evolution as a bulk system
Pressure gradients (larger in-plane)
push bulk “out”  “flow”
more, faster particles
seen in-plane
mike lisa - austin texas - 10 sept 2007
N
-RP (rad)
22
Azimuthal distributions at RHIC
STAR, PRL90 032301 (2003)
b ≈ 6.5 fm
b ≈ 4 fm
“central” collisions
midcentral
collisions
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Azimuthal distributions at RHIC
STAR, PRL90 032301 (2003)
b ≈ 10 fm
b ≈ 6.5 fm
b ≈ 4 fm
peripheral collisions
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Wow ! Sensitivity to early EoS!
Hydro: P. Huovinen, P. Kolb,
U. Heinz
mike lisa - austin texas - 10 sept 2007
STAR, PRL90 032301 (2003)
25
It’s not just good, it’s... perfect!
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Hydromania - careful...
• single-point agreement red flag in H.I. physics
STAR, PRL86 402 (2001)
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Beyond press releases
ature of EoS unde
estigation ; agreement wi
data might be accidental ;
viscous hydrodynamics under
development ; assumption
of thermalization in question
sensitivity to modeling of
initial state, under
intense study
The detailed work now underway is what can probe & constrain sQGP properties
It is probably not press-release material...
(...but, hey, you’ve already got your coffee mug)
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More direct access to geometric substructure?
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Simple picture: probing source geometry through interferometry
The Bottom line…
p1
r1
x1
  
  to
  i( r  x )p
if a pion is emitted, itis more
i ( r emit
x )p another
1 { likely
U(x1, p1)e
U(x 2 , p2 )e
 source
T
2
source
  
 
1 m momentum
(x) pion with very similar
 if the
is small
i ( r  x )p
i ( r  x )p
 U(x 2 , p1)e
p2
5 fm
r2
1
1
1
2
1
2
U(x1, p2 )e

2
2
1
*TT  U1*U1  U*2 U 2  1  eiq( x1  x 2 )
experimentally measuring
this enhanced
Creation probability
(x,p) =probability:
U*U
quite challenging
P(p1, p 2 )
2
C(p1, p 2 ) 
 1 ~
 (q )
P(p1 )P(p 2 )
C (Qinv)
x2
1
2
2
}

Width ~ 1/R
2
1
Measurable!
F.T. of pion source
  
q  p 2  p1
mike lisa - austin texas - 10 sept 2007
0.05
0.10
Qinv (GeV/c)
31
C2(Qinv)
Correlation functions for
different sized systems
STAR
p+p
R ~ 1 fm
d+Au
R ~ 2 fm
Au+Au
R ~ 6 fm
Qinv (GeV/c)
Different colliding systems studied at RHIC
nucl-ex/0505014
Interferometry probes the smallest
scales ever measured !
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High-statistics: beyond simple scales
• Two-particle interferometry: p-space separation  space-time separation
q  p2  p1
p1
x1
qside
p2
Rside
x2
qlong
Rout
qout
k  12 p2  p1 


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
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Femtoscopic information
STAR Collab PRC 2004
Sab
( r )
P
= x a - x b  distribution
Au+Au: central collisions
C(Qout)
 (q, r ) = (a,b) relative wavefctn
pa
pb
xa
xa
xb
pa
pb
xb
C (q)   d r S ( r)   (q, r )
ab
P
C(Qside)
3
ab
P
2
C(Qlong)
Koonin ‘77; Pratt ‘84
• Distillation of ~105 datapoints in correlation
function into ~5 numbers
• often: S(r) assumed 3D Gaussian
mike lisa - austin texas - 10 sept 2007
3 “radii” by using
3-D vector q
34
R(√SNN) – simple signal ?
Rout/Rside
Generic expectation pre-RHIC turnon
“”
Rischke, Gyulassy, NP A 608 (1996) 479
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R(√S
– simple
R(√SNN), b,
Npart, A,signal
B, mT,?y, , PID)
Generic expectation pre-RHIC turnon
No glaring signal in simple
measures
Rout/Rside
The „real” (experimentalist’s)
„puzzle”
mass
|b|
“”
Rischke, Gyulassy, NP A 608 (1996) 479
mike lisa - austin texas - 10 sept 2007
pT
36
Why do the radii fall
with increasing momentum ??
(3 "radii" corresponding to the three components of
mike lisa - austin texas - 10 sept 2007
q)
38
measure explosive pattern of the thermalized bulk matter (low-pT)
collective pT component: m*vT
Spectra
v2
HBT
hydro expectation
(off-center collision)
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measure explosive pattern of the thermalized bulk matter (low-pT)
Spectra
v2
HBT
“elliptic flow”
mike lisa - austin texas - 10 sept 2007
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measure explosive pattern of the thermalized bulk matter (low-pT)
Spectra
“homogeneity
regions”
v2
HBT
femtoscopy probes
x-p substructure
Amount of flow consistent with p-space nucl-th/0312024
Huge,
diverse
consistent with this substructure nucl-ex/0505014
mike
lisa - austin
texas -systematics
10 sept 2007
41
Comparison to “perfect” hydro calculations
LPSW(05)
• “embarrassing” experimental consistency
• considerable physics/model sensitivity
• Rout too big (too long emission time?)
• Rlong too big (too long evolution time?)
• Rside too small (?)
mike lisa - austin texas - 10 sept 2007
BlastWave ~9 fm/c
hydro: ~15 fm/c
42
Time, (isotropic) pressure gradients and (isotropic) flow
dv flow
dt

dv
radial flow   dt  flow
dt
0
pressure gradient 
old figures
femtoscopy  
(model-dep)

mike lisa - austin texas - 10 sept 2007
hydro models:
pressure too low & time too long??
• impacts EoS / “soft point”
• need more info to confirm
43
Time, (anisotropic) pressure gradients and (anisotropic) flow
Strongly-interacting 6Li released from an asymmetric trap
O’Hara, et al, Science 298 2179 (2002)
What can we learn?
?
Hydro:Huovinen, Kolb, Heinz
momentum only
(  dt )
space! (& time)
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HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
small RS
big RS
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HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
central
collisions
mid-central
collisions
peripheral
collisions
mike lisa - austin texas - 10 sept 2007
46
The rule ofangle-differential
2
angle-integrated
@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
dv
pressure gradient  flow
dt
100
200
300

dv
radial flow   dt  flow
dt
0
~ x2 size increase
RL  

400
P P
dv x dv y



x y
dt
dt
dv x dv y 
v 2   dt  


dt
dt


~ 01/2 shape reduction

f
  calculation
Initial size/shape estimated by Glauber
i
harder EoS (no latent heat) likely required
mike lisa - austin texas - 10 sept 2007

47
Global picture should include more than ...
• K0s- K0s
mike lisa - austin texas - 10 sept 2007
STAR PRC74 054902
48
Global picture should include more than ...
• K0s- K0s
• -p
mike lisa - austin texas - 10 sept 2007
STAR PRC 74 (2006) 064906
49
Global picture should include more than ...
• K0s- K0s
• -p
• p(bar)-p(bar)
• centrality dependence ok
• but more...
Typically one considers “contamination”
in terms of uncorrelated pairs (mid-id,
weak decays, ...)
Fits are kernel-filtered Gaussian sources
30-80%
0-10%
" "
Cmeasq  f corr  Ctrue q  1 f corr 
measured CF is just “diluted” true CF
(e.g. “”)
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Crucial to extract
reliable source
estimates
H. Gos
STAR, PRC74 (2006) 064906
Correlated ‘contamination’ in (anti-)baryon correlations
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51
Global geometric substructure of explosive source
• All signatures of explosive flow
observed
• momentum-space-only
(spectra, v2)
Spectra
• falling pion “radii” with mT
v2
HBT
slow  emission
fast  emission
mike lisa - austin texas - 10 sept 2007
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Global geometric substructure of explosive source
• All signatures of explosive flow
observed
• falling pion “radii” with mT
• falling other “radii” with mT
 emission region
K emission region
mike lisa - austin texas - 10 sept 2007
R (fm)
• momentum-space-only
(spectra, v2)
mT (GeV/c)
But there is something more...
53
Beyond size-momentum correlations
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
• hot core surrounded by cool shell
• important ingredient of Buda-Lund
hydro picture
e.g. Csörgő & Lörstad
PRC54 1390 (1996)
mike lisa - austin texas - 10 sept 2007
t
x2-p correlation: yes
x-p correlation: no
x2-p correlation: yes
x-p correlation: no
54
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
• In flow pictures (BlastWave), low-pT
particles emitted closer to source’s center
• non-identical particle correlations
(FSI at low v) probe:
• (x1-x2)2 (as does HBT)
• x1-x2

T
K
pT
p
F.
Retiere
& MAL,
PRC70
044907
mike
lisa - austin
texas
- 10 sept
2007 (2004)
55
Kaon – pion correlations:
dominated by Coulomb interaction
Smaller source  stronger
(anti)correlation
K-p correlation well-described by:
• Blast wave with same parameters
as spectra, HBT
But with non-identical particles, we
can access more information…
STAR PRL91 (2003) 262302
mike lisa - austin texas - 10 sept 2007
56
Initial idea: probing emission-time ordering
purple K emitted first
green  is faster
• Catching up: cos 0
•
•
long interaction time
strong correlation
• Moving away: cos 0
purple K emitted first
green  is slower
•
•
Crucial point:
kaon begins farther in “out” direction
(in this case due to time-ordering)
short interaction time
weak correlation
• Ratio of both scenarios
allow quantitative study of
the emission asymmetry
e.g. Lednicky et al Phys. Lett. B373:30–34, 1996
mike lisa - austin texas - 10 sept 2007
57
Initial idea: probing emission-time ordering
purple K emitted first
green  is faster
• Catching up: cos 0
•
•
long interaction time
strong correlation
Mass-ordering observed in
Moving away: cos 0
agreement with blast• substructure
purple K emitted first
green  is slower
•
short interaction time
weak correlation
STAR PRL91 (2003) 262302
•
Crucial point:
kaon begins farther in
“out” direction
 emission
region
(in this case due to time-ordering)
• Ratio of both scenarios
allow quantitative study of
the emission asymmetry
K emission region
e.g. Lednicky et al Phys. Lett. B373:30–34, 1996
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+
-
K+
K-
p
p










+







-

-





-
-




p



p
K 0S

central vs peripheral
Systematic mapping


!!!
K+
KK 0S




mike lisa - austin texas - 10 sept 2007
60
+
-
K+
K-
p
p










+







-

-


K+



K-
-
-
K 0S




p



p
K 0S

“exotic beams”



Parallel focus - vary
kernel parameters, too



xa
pa
pa
pb
pb
xb
mike lisa - austin texas - 10 sept 2007
xa
xb
= x a - x b  distribution
Sab
( r )
P
 (q, r ) = (a,b) relative wavefctn
C (q)   d r  Sab
( r )   (q, r )
P
ab
P

3
2
61
Parallel focus - vary kernel parameters, STAR,
too PRC 2006
• First-ever p-, p-, p correlations
• Consistency from baryon sector for
flow-generated x-p correlations
• Extraction of real/imaginary p-,
p- scattering lengths from CF !!
• similarly for K0S
• important new physics direction
xa
pa
pa
pb
pb
xb
mike lisa - austin texas - 10 sept 2007
xa
xb
= x a - x b  distribution
Sab
( r )
P
 (q, r ) = (a,b) relative wavefctn
C (q)   d r  Sab
( r )   (q, r )
P
ab
P

3
2
62
F. Retiere WPCF05
see talk of M. Bysersky / M. Sumbera
mike lisa - austin texas - 10 sept 2007
63
p+p: A clear reference system?
mike lisa - austin texas - 10 sept 2007
65
Zbigniew Chajecki QM05
R Z(fm)
1. Heisenberg
uncertainty?
Z0 decay @ LEP
•2.e.g.
G. fragmentation?
Alexander
String
(Lund)
••3.“plausible”
ineffects?
z-direction
pResonance
maybe (??)
T dependence
•• unlikely
in transvrseprobably no
dependence
• mass
e.g. Wiedemann
& DELPHI
Heinz ‘97
[Andersson,
Moriond 2000]
• maybe,
but presumably
 different effect
significantly
femtoscopy in p+p @ STAR
p+p and A+A measured in same
experiment
• great opportunity to compare physics
• what causes pT-dependence in p+p?
• same cause as in A+A?
than for Au+Au
R (fm)
• under investigation

K
p 
STAR preliminary
hep-ph/0108194
m, mT (GeV)
mike lisa - austin texas - 10 sept 2007
mT (GeV)
mT (GeV)
66
Zbigniew Chajecki QM05
3. Resonance effects?
4. Bulk system („hydro”)
in pp?
DELPHI
flow not expected in such
a small system as p+p
R (fm)
e.g. Shuryak: hep-ph/0405066

 Csorgo et al.:
K Buda-Lund
treatment of p+p collision as
d+Au : Rlong doesn’t change
bulk
system
with centrality
p 
(w/ temperature gradients)
hep-ph/0406042
femtoscopy in p+p @ STAR
p+p and A+A measured in same
experiment
• great opportunity to compare physics
• what causes pT-dependence in p+p?
• same causeas in A+A?
1/(2mT)d2n/(dmTdy)
R Z(fm)
1. Heisenberg
uncertainty?
Z0 decay @ LEP
2. String fragmentation? (Lund)
K
p
mT-m (GeV)
RSIDE
RLONG
ROUT
STAR preliminary
hep-ph/0108194
m, mT (GeV)
mike lisa - austin texas - 10 sept 2007
mT (GeV)
mT (GeV)
mT (GeV)
b
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Surprising („puzzling”) scaling
A. Bialasz (ISMD05): Ratio of (AuAu, CuCu, dAu) HBT
I personally feel that its solution mayradii
provide
new
by pp
insight into the hadronization process of QCD
 All pT(mT) dependences of
HBT radii observed by STAR
scale with pp although it’s
expected that different origins
drive these dependences
HBT radii scale with pp
Scary coincidence
or something deeper?
pp, dAu, CuCu - STAR preliminary
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Summary
• Diverse systematic femtoscopic program at RHIC
R(√SNN, b, Npart, A, B, mT, y, , PID1, PID2)
• Naive dramatic expectations disappointed (“puzzle”)
• Sanity check : strong correlation with initial state 
• Explosive dominance extensively mapped in full geometric substructure
• shape - 3D , long-range tail (imaging)
• size-momentum correlations [incl various FSI combos]
• position-momentum correlations [unique information]
• exotic correlations: substructure of space-time dynamics of 
• Physics sensitivity: indications for small latent heat (no “softest point”)
• low-energy QCD connection: H.I.C. as “exotic beam” factory
• Crucial question: apples::apples comparison of geometry hadronic/nuclear collisions
• similarity of p+p & Au+Au (& d+Au) : “deep” or coincidental?
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OPAL @ LEP
CERN-PH-EP/2007-02
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