Femtoscopy at the highest energies:
From p+p to A+A; From AGS/SPS/RHIC to LHC
Mike Lisa
Ohio State University
• Wherefore (=“why?”)
• motivation & basic formalism
• Whence (=“from where?”)
• systematics over 2 decades
• Whither (=“to where?”)
• femtoscopy at (ALICE@)LHC
malisa - AliceClub & HeavyIonForum - CERN April 2007
1
Microexplosions
Femtoexplosions
• fast
 plasma 1 J
s energy deposition
0.1 J
3 = 1036phase
hydro expansion
to original
1017 J/m3  cooling
5 GeV/fm
J/m3
T
106 K
200 MeV = 1012 K
• do
geometric
& infer
rate
1018 “postmortem”
K/sec
1035momentum
K/s
malisa - AliceClub & HeavyIonForum - CERN April 2007
3
Microexplosions
Femtoexplosions
• fast
 plasma 1 J
s energy deposition
0.1 J
3 = 1036phase
hydro expansion
to original
1017 J/m3  cooling
5 GeV/fm
J/m3
T
106 K
200 MeV = 1012 K
• do
geometric
& infer
rate
1018 “postmortem”
K/sec
1035momentum
K/s
malisa - AliceClub & HeavyIonForum - CERN April 2007
4
Spacetime - THE distinguishing feature of H.I. physics
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: probes of dense, dynamic geometry
• Final state:
• Geometric structural scale is THE defining feature of QGP
• Temporal scale sensitive to deconfinement transition (?)
malisa - AliceClub & HeavyIonForum - CERN April 2007
5
Spacetime - THE distinguishing feature of H.I. physics
dN/dt
malisa - AliceClub & HeavyIonForum - CERN April 2007
time
6
Femtoscopic information
xa
pa
pa
pb
pb
xa
xb
C (q) 
ab
P
Sab
( r )
P
xb
 d r S
3
ab
P
( r )   (q, r )
2
= x a - x b  distribution
 (q, r ) = (a,b) relative wavefctn

know/assume relative wavefunction
 extract spatial distributions

OR
know/assume source distrib
 extract interaction (scat. length..)
malisa - AliceClub & HeavyIonForum - CERN April 2007
7
Conditional probability
if a pion* is emitted, it is more* likely to emit another
pion with very similar momentum if the source is small
* varies w/
PID, q
malisa - AliceClub & HeavyIonForum - CERN April 2007
8
3D information
p1
x1
Au+Au: central collisions

q
C(Qout)
qside
Rside
x2
p2
qout
qlong
Rout
 1  
k  p 2  p1 
2
C(Qside)
  
q  p2  p1
C(Qlong)
Rside
Rout
malisa - AliceClub & HeavyIonForum - CERN April 2007
3 “radii” by using
3-D vector q
9
Baseline: 20-year systematic program
ˆ
HBT( s ;p T , y, b ,b,m
1 ,m2 ,Asys )
y
|b|
pT
• Pion HBT @ Bevalac: “largely confirming nuclear dimensions”
• Since 90’s: increasingly detailed understanding and study w/ high stats
malisa - AliceClub & HeavyIonForum - CERN April 2007
11
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
•entropy - natural
hydrodynamic driver
malisa - AliceClub & HeavyIonForum - CERN April 2007
13
Hydro: overly long timescale?
LPSW(05)
BW estimates: 9 fm/c
hydro: ~15 fm/c
malisa - AliceClub & HeavyIonForum - CERN April 2007
14
Time, (isotropic) pressure gradients and (isotropic) flow
old figures
dv flow
dt

dv
radial flow   dt  flow
dt
0
pressure gradient 
femtoscopy  
(model-dep)
hydro models:
 pressure too low & time too long??
• impacts EoS
• need
higher energy to confirm
malisa - AliceClub & HeavyIonForum - CERN
April 2007
15
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)
malisa - AliceClub & HeavyIonForum - CERN April 2007
16
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
small RS
big RS
malisa - AliceClub & HeavyIonForum - CERN April 2007
17
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
central
collisions
mid-central
collisions
peripheral
collisions
malisa - AliceClub & HeavyIonForum - CERN April 2007
18
The rule of 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
400
~ 1/2 shape reduction
Initial size/shape estimated by Glauber calculation
malisa - AliceClub & HeavyIonForum - CERN April 2007
19
Beyond overall geometry - into dynamics
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
why do the radii fall with pT?
LPSW(05)
malisa - AliceClub & HeavyIonForum - CERN April 2007
21
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 – THE signature of collectivity
malisa - AliceClub & HeavyIonForum - CERN April 2007
22
R(√SNN, b, Npart, A, B, mT, y, , PID)
PRC 71 044906 (2005)
Spectra
v2
HBT
slow  region
fast  region
malisa - AliceClub & HeavyIonForum - CERN April 2007
23
R(√SNN, b, Npart, A, B, mT, y, , PID)
• Geom. substructure probed in detail
• BW: consistently with p
• but we can do more...
Spectra
v2
HBT
slow  region
fast  region
malisa - AliceClub & HeavyIonForum - CERN April 2007
24
R(√SNN, b, Npart, A, B, mT, y, , PID)
Spectra
K-
v2
PRL 91 262301 (2003)
HBT
 emission region
K emission region
malisa - AliceClub & HeavyIonForum - CERN April 2007
25
R(√SNN, b, Npart, A, B, mT, y, , PID)
+
K-
-






K+
K-
p
p
STAR, PRL 2004






p




p







K0S
PRL 91 262301 (2003)
K0S
K-


K+


-

+



MAL,Pratt Soltz,Wiedemann nucl-ex/0505014

PRL 93just
012301
‘04
Full program
started
Evolution with energy?
 emission region
K emission region
malisa - AliceClub & HeavyIonForum - CERN April 2007
26
Source imaging - “inverting” Koonin-Pratt equation
C (q) 
ab
P
Sab
( r )
P
 d r S
3
ab
P
( r )   (q, r )
2
= x a - x b  distribution
 (q, r ) = (a,b) relative wavefctn
• not “inverting” so much as
spline-fitting
• Non-Gaussian source in 1D
(long-known)
• high-precision low-q: resolves longrange component
• Suggestive of resonances
[check size scaling]
PHENIX nucl-ex/0605032
malisa - AliceClub & HeavyIonForum - CERN April 2007
27
Whither - expectations and
directions at ALICE/LHC
malisa - AliceClub & HeavyIonForum - CERN April 2007
28
6.4 = RHICx1.6
6
5
1000
5.5 TeV
PHOBOS White Paper: NPA 757, 28
malisa - AliceClub & HeavyIonForum - CERN April 2007
29
NNUS*: Multiplicity sets scale: all else fixed
6.4 = RHICx1.6
6
5
MAL,Pratt Soltz,Wiedemann nucl-ex/0505014
1000
5.5 TeV
PHOBOS White Paper: NPA 757, 28
* NNUS = Nothing New Under the Sun
malisa - AliceClub & HeavyIonForum - CERN April 2007
30
Multiplicity sets scale: all else fixed
6.4 = RHICx1.6
• PHOBOS-based extrapolation:
• RLHC / RRHIC = (1.6)1/3 = 1.17
6
5
1000
5.5 TeV
PHOBOS White Paper: NPA 757, 28
malisa - AliceClub & HeavyIonForum - CERN April 2007
31
Multiplicity sets scale: all else fixed
• PHOBOS-based extrapolation:
• RLHC / RRHIC = (1.6)1/3 = 1.17
• CGC prediction of multiplicity
• RLHC / RRHIC = (11/3.6)1/3 = 31/3 = 1.45
malisa - AliceClub & HeavyIonForum - CERN April
2007 Levin & Nardi NPA747 609 (2005)
Kharzeev,
32
Beyond multiplicity
T. Humanic,
Int.J.Mod.Phys.E15197(2006)
• PHOBOS-based extrapolation:
• RLHC / RRHIC = (1.6)1/3 = 1.17
• RLHC / RRHIC = (11/3.6)1/3 = 31/3 = 1.45
dN/d
• CGC prediction of multiplicity
• Humanic Rescattering Model
• “real” model predicting dN/d and HBT
• (dN/d[LHC] / dN/d[RHIC])1/3 ~ 1.9
malisa - AliceClub & HeavyIonForum - CERN April 2007
33
• PHOBOS-based extrapolation:
• RLHC / RRHIC = (1.6)1/3 = 1.17
T. Humanic,
Int.J.Mod.Phys.E15197(2006)
dN/dt
Beyond multiplicity
• CGC prediction of multiplicity
• RLHC / RRHIC = (11/3.6)1/3 = 31/3 = 1.45
• Humanic Rescattering Model
• (dN/d[LHC] / dN/d[RHIC])1/3 ~ 1.9
• LHC / RHIC = 2 :: (recall Rlong~~ )
Rlong (fm)
• “real” model predicting dN/d and HBT
• dynamic effect
• Rlong[LHC] / Rlong[RHIC] ~ 1.5-2
• all are connected??
malisa - AliceClub & HeavyIonForum - CERN April 2007
34
Beyond multiplicity
T. Humanic,
Int.J.Mod.Phys.E15197(2006)
• PHOBOS-based extrapolation:
• RLHC / RRHIC = (1.6)1/3 = 1.17
• CGC prediction of multiplicity
• RLHC / RRHIC = (11/3.6)1/3 = 31/3 = 1.45
• Humanic Rescattering Model
• “real” model predicting dN/d and HBT
• (dN/d[LHC] / dN/d[RHIC])1/3 ~ 1.9
• LHC / RHIC = 2 :: (recall Rlong~~ )
• dynamic effect
• Rlong[LHC] / Rlong[RHIC] ~ 2
• all are connected?
• RS, RO larger, but not a simple factor
malisa - AliceClub & HeavyIonForum - CERN April 2007
35
Beyond multiplicity
T. Humanic,
Int.J.Mod.Phys.E15197(2006)
• PHOBOS-based extrapolation:
• RLHC / RRHIC = (1.6)1/3 = 1.17
• CGC prediction of multiplicity
• RLHC / RRHIC = (11/3.6)1/3 = 31/3 = 1.45
• Humanic Rescattering Model
• “real” model predicting dN/d and HBT
• (dN/d[LHC] / dN/d[RHIC])1/3 ~ 1.9
• LHC / RHIC = 2 :: (recall Rlong~~ )
• dynamic effect
• Rlong[LHC] / Rlong[RHIC] ~ 2
• all are connected?
• RS, RO larger, but not a simple factor
• steeper pT-dep due to more flow?
• dynamic effect
malisa - AliceClub & HeavyIonForum - CERN April 2007
36
Cascade / Hydro models versus RHIC data
cascade
• AMPT does ~Ok
- needs string melting
& 6-10 mb parton
hydro
• does not do as well as
cascades, but nevertheless
we’ll look next for guidance...
malisa - AliceClub & HeavyIonForum - CERN April 2007
37
AMPT @ LHC
• All radii increase
• ~10% for transverse
• ~30% for long
• RO/RS [LHC] < RO/RS [RHIC]
• But... RHIC radii too large in this
configuration of model ???
C.M. Ko; WPCF Sept. 2006
malisa - AliceClub & HeavyIonForum - CERN April 2007
38
Eskola et al PRC72044904 (2005)
Hydro predictions I: Scales
• Neglecting flow, to cool to C[QGP] :
C = 0(C /0)3/4
• Cno flow[RHIC] = 6 fm/c
initial conditions from
pQCD+saturation
• Cno flow[LHC] = 20 fm/c
malisa - AliceClub & HeavyIonForum - CERN April 2007
39
Eskola et al PRC72044904 (2005)
Hydro predictions I: Scales
• Neglecting flow, to cool to C[QGP] :
C = 0(C /0)3/4
• Cno flow[RHIC] = 6 fm/c
• Cno flow[LHC] = 20 fm/c
• Much larger flow @LHC
• signif. reduction of timescale @ LHC
[similar to RHIC]
• larger transverse size @ FO
malisa - AliceClub & HeavyIonForum - CERN April 2007
40
Eskola et al PRC72044904 (2005)
Hydro predictions I: Scales
• Neglecting flow, to cool to C[QGP] :
C = 0(C /0)3/4
• Cno flow[RHIC] = 6 fm/c
• Cno flow[LHC] = 20 fm/c
• Much larger flow @LHC
• signif. reduction of timescale @ LHC
[similar to RHIC]
• larger transverse size @ FO
• No HBT prediction per se, but...
• RL[LHC] / RL[RHIC] ~ 1.1 ÷ 1.2
• RS[LHC] / RS[RHIC] ~ 1.5 ÷ 2
• (different than HRM)
• steeper pT-dependence
malisa - AliceClub & HeavyIonForum - CERN April 2007
41
Eskola et al PRC72044904 (2005)
Hydro predictions I: Scales
• Neglecting flow, to cool to C[QGP] :
C = 0(C /0)3/4
• Cno flow[RHIC] = 6 fm/c
• Cno flow[LHC] = 20 fm/c
• Much larger flow @LHC
• signif. reduction of timescale @ LHC
[similar to RHIC]
• larger transverse size @ FO
• No HBT prediction per se, but...
Heinz&Kolb, PLB542 216 (2002)
• RL[LHC] / RL[RHIC] ~ 1.1 ÷ 1.2
• RS[LHC] / RS[RHIC] ~ 1.5 ÷ 2
• (different than HRM)
• steeper pT-dependence
• Consistent w/ independent hydro
for non-central collisions
malisa - AliceClub & HeavyIonForum - CERN April 2007
42
Hydro predictions II: Shapes
• easy prediction: importance of -dep
measurements will continue @ LHC
• asHBT
O’Hara, et al, Science 298 2179 (2002)
• probes timescale & dynamics
• non-trivial (& incomplete!) excitation fctn
E895 2 GeV
PLB496 1 (2000)
malisa - AliceClub & HeavyIonForum - CERN April 2007
STAR 200 GeV
PRL93 012301 (‘04)
43
Hydro predictions II: Shapes
• easy prediction: importance of -dep
measurements will continue @ LHC
• asHBT
• probes timescale & dynamics
• non-trivial (& incomplete!) excitation fctn
• hydro @ RHIC
• misses scale (well-known)
• impressive agreement on -dep
“RHIC”
malisa - AliceClub
& HeavyIonForum
- CERN AprilSTAR
2007
Heinz&Kolb,
PLB542 216 (2002)
PRL93 012301 (2004)
44
Hydro predictions II: Shapes
• easy prediction: importance of -dep
measurements will continue @ LHC
• asHBT
• probes timescale & dynamics
• non-trivial (& incomplete!) excitation fctn
• hydro @ RHIC
• misses scale (well-known)
• impressive agreement on -dep
• prediction @ LHC
• sign change in shape & oscillations
“RHIC”
Heinz&Kolb, PLB542 216 (2002)
malisa
- AliceClub & HeavyIonForum - CERN April 2007
“IPES” (LHC)
Heinz&Kolb, PLB542 216 (2002)
45
E895 2 GeV
Tilt from -dependence
PLB496 1 (2000)
• Correlating with first-order RP:
tilt of emission region rel. beam
• Spatial analog of v1
• ~40º at AGS
y
x
QS
z
(Beam)
Reaction plane
malisa - AliceClub & HeavyIonForum - CERN April 2007
46
x (fm)
Geometry of “3rd flow component” - sensitive to early EoS
z (fm)
J. Brachmann et al., PRC61 024909 (2000)
Magda, Csernai, Strottman hep-ph/0101125
requires:
• 1st-order RP; 3D transport/hydro
• related to “v1 wiggle”
malisa - AliceClub & HeavyIonForum - CERN April 2007
47
Will we see predicted 3rd component?
70
60
Tilt (deg)
50
40
30
20
10
Data
?
RQMD [cs]
RQMD [mf]
0
0.1
1
10
100
sqrt(s[NN])-2*m[N] (GeV)
1000
10000
• Early softening
• Early thermalization
malisa - AliceClub & HeavyIonForum - CERN April 2007
48
p+p: a short diversion and “practice,” or a crucial question?
• “minimalist” physics
• Momenta & parentage from PYTHIA
• space by hand: x= “1 fm” + p/E
• pT-dep from x-p correlations
• resonances
• formation time 
• some from rescatt
• mult dep from rescatt only
i-th particle
Initial “disk”
of radius r
T. Humanic, presentation
to ALICE PW2 (March 2006)
malisa - AliceClub & HeavyIonForum - CERN April 2007
49
p+p: a short diversion and “practice,” or a crucial question?
• “minimalist” physics
• Momenta & parentage from PYTHIA
• space by hand: x= “1 fm” + p/E
• pT-dep from x-p correlations
• resonances
• formation time 
• some from rescatt
• mult dep from rescatt only
jet
p
p
jet
• R(dN/d)  space-time properties of jet
fragmentation/hadronization? [fundamental]
• prediction of pT-dependence needed to test
whether hard processes are really dominant here
Paic and Skowronski
J. Phys. G31 1045 (2005)
see also Csorgo & Zajc
hep-ph/0412243 (ISMD04)
malisa - AliceClub & HeavyIonForum - CERN April 2007
50
p+p: a short diversion and “practice,” or a crucial question?
• “minimalist” physics
• Momenta & parentage from PYTHIA
• space by hand: x= “1 fm” + p/E
• pT-dep from x-p correlations
• resonances
• formation time 
• some from rescatt
• mult dep from rescatt only
• R(dN/d)  space-time properties of jet
fragmentation/hadronization? [fundamental]
• prediction of pT-dependence needed to test
whether hard processes are really dominant here
Humanic, Koch, Stocker hep-ph/0607097
• may be copiously produced (depending on mass)
• look for long lifetimes (if d large) in high mult events
???
• even more fundamental, but expectations unclear
[prelim from T. Humanic: small effect on HBT...]
malisa - AliceClub & HeavyIonForum - CERN April 2007
Hossenfelder, Hofmann, Bleicher, Stocker
Phys.Rev. D66 (2002) 101502
• Black Holes / extra dimensions at LHC p+p ?
51
Caution: femtoscopy in p+p @ STAR
Z. Chajecki WPCF05
• 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?
STAR preliminary
mT (GeV)
malisa - AliceClub & HeavyIonForum - CERN April 2007
mT (GeV)
52
Surprising („puzzling”) scaling
!! But !! significant issues with nontrivial
interplay non-femtoscopic correlations
• 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?
Ratio of (AuAu, CuCu, dAu) HBT
radii by pp
A. Białasz (ISMD):
I personally feel that its solution may provide new
HBT radii scale with
insightpp
into the hadronization process of QCD
Scary coincidence
or something deeper?
pp, dAu, CuCu - STAR preliminary
malisa - AliceClub & HeavyIonForum - CERN April 2007
53
le menu des espérances au LHC
boissons
entrées
hydro
p+p
• signif pT dep
• R increase w/ mult
jet
p
jet
p
• R increase w/ mult
• other details??
• very large RO in high mult??
RL small increase (~30%)
[huge flow  rapid cooling  short ]
RO,S : huge flow 
• larger increase (~60%)
• steeper pT dep
shape inversion; oscillation sign flip
large tilt for central region?
plats principaux
NNUS: naive extrapolation
5
as before (same pT dep etc)
but scale by ~17%
as before (same pT dep etc)
but scale by ~45%
HRM and AMPT
RL (50-100% 30%increase)
[dynamics / chemistry / both ??]
RO,S
• smaller increase (~30% 10%)
• higher flow  steeper pT dep
malisa - AliceClub & HeavyIonForum - CERN April 2007
54
What’s under the next mountain?
scans
3D [] s [EoS] m1,m2 [x-p,] p+p [?]
 [, shape]
pT,y [x-p]
stats [fine struc] 55
malisa - AliceClub & HeavyIonForum - CERN April 2007
A [size]
What’s under the next mountain?
• “simple” 
• entropy dominance?
• increased collectivity?
• shape
• inversion of transverse shape?
• tilt at midrapidity
• imaging - long range tail
• non-identical particle correlations - full grid
• richer detail of substructure
• inversion of K-P formula  extraction of hadronic phase shifts
• pp
• jets [space-time structure of hadronization]
• non-id - is it collectivity?
• very low multiplicity collisions - does it vanish?
malisa - AliceClub & HeavyIonForum - CERN April 2007
56
THE END
malisa - AliceClub & HeavyIonForum - CERN April 2007
57
“Inverting the femtoscopic paradigm”
• 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 !!
• important new physics direction
• “invert the femtoscopic paradigm”
• c.f. K0-K0 / p-p
• possible effect of residual
correlations - could not reliably
calculate (for now...)
• significant technical effort (and
more information) required
STAR, accepted to Phys Rev
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Hanna Gos (Warsaw)
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