The HBT excitation function
in relativistic heavy ion collisions
Mike Lisa
Ohio State University
Plan
ˆ
HBT
) T , y, b ,b,m
HBT(( s ;p
1 ,m2 ,Asys )
I will discuss a set of zero measure in this rich parameter space
• what do we think we can learn from systematics in X (=y, pT, |b|…)?
• what do we think we have learned from systematics in X (=y, pT, |b|…)?
• how does this change with s ?
y
Also, upon request: comments on technical issues
(event-mixing, Coulomb, non-Gaussianness,
RP resolution correction…)
Brief “summary” (intro to discussion)
|b|
pT
Reminder
• Two-particle interferometry: p-space separation  space-time separation
x1
p1

q
qside
Rside
x2
p2
qout
  
q  p2  p1
 1  
k  p 2  p1 
2
qlong
Rout
• HBT: Quantum interference between identical particles
• Final-state effects (Coulomb, strong) also can cause
correlations, need to be accounted for
C (q)
P( p1 , p2 )
real event pairs
C ( p1 , p2 ) 

P( p1 )P( p2 ) mixed event pairs
2
2
2
2
2
2
 qout
Gaussian
 
Rout
 qside
Rside
 qlong
Rlong
model (3-d): C (q , k )  1  (k ) e
~
2
1
R
1
q (GeV/c)
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
Rside
Rout
Pratt-Bertsch (“out-side-long”)
decomposition designed to
help disentangle space & time
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
AGS: sNN  2-5 GeV
• Expected “geometric” scaling of
transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
E895 NPA661 444c (1999)
E802 PRC66 054906 (2002)
Au+Au
14.6 AGeV Si+Al
14.6 AGeV Si+Au
11.6 AGeV Au+Au
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
NA49 NPA661 448c (1999)
AGS: sNN  2-5 GeV
• Expected “geometric” scaling of
transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
RQMD
SPS: sNN  17-20 GeV
• Expected “geometric” scaling of
transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
• apparent ~2x expansion
200 AGeV S+S
158 AGeV p+p
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
AGS: sNN  2-5 GeV
• Expected “geometric” scaling of
transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
SPS: sNN  17-20 GeV
• Expected “geometric” scaling of
transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
• apparent ~2x expansion
NA44, Eur Phys J C18 317 (2000)
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
AGS: sNN  2-5 GeV
STAR nucl-ex/0312009
accepted
to PRL
STAR
PRL87
082301 (2001)
PHENIX nucl-ex/0401003
• Expected “geometric” scaling of
transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
SPS: sNN  17-20 GeV
• Expected “geometric” scaling of
transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
• apparent ~2x expansion
RHIC: sNN = 130-200 GeV
• Expected “geometric” scaling of
transverse radii with |b|, Npart
• RL trend very similar (expected?)
• apparent ~2x expansion
32-72% 12-32% 0-12%
So far…
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
• can learn: how does FO system size track with initial size?
• did learn: transverse expansion ~2x
• HBT radii appear to follow expected increases with (initial) system size
(comforting to remember in present age of uncertainty)
• Rlong(Npart) with s ?
However, recall: HBT radii do not measure entire source,but “homogeneity regions” *
* [Sinyukov, “Hot Hadronic Matter: Theory and Experiment,” NATO ASI Series B 346:309 (1995)]
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
Kolb & Heinz, QGP3 nucl-th/0305084
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
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
MAL et al, PRC49 2788 (1994)
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)
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
• hot core surrounded by cool shell
• important ingredient of Buda-Lund
hydro picture
e.g. Csörgő & Lörstad
PRC54 1390 (1996)
t
x2-p correlation: yes
x-p correlation: no
x2-p correlation: yes
x-p correlation: no
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
80 AMeV Ar+Sc(pp,X)
E895 PRL84 2798 (2000).
y (fm)
decreasing HBT R(p) present at all energies
• sub-AGS energies (protons, IMFs)
• cooling significant
• AGS (and upward) – flow dominated
• signs of trouble in s dep…
(models work at one energy…)
x (fm)
RQMD: Sorge PRC52 3291 (1995)
MAL et al, PRL70 3709 (1993)
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
decreasing HBT R(p) present at all energies
• sub-AGS energies (protons, IMFs)
• cooling significant
• AGS (and upward) – flow dominated
• signs of trouble in s dep…
(models work at one energy…)
• SPS: smooth, almost (!) featureless
transition AGS RHIC
• can the models do that??!
NB: error in CERES paper
E895 PRL84 2798 (2000)
CERES, NPA714 124 (2003)
STAR, PRL87 082301 (2001)
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
NA44) PRC58, 1656 (1998)
At fixed s, a chance to
understand system
D. Hardtke,
thesis
E895Ph.D.
PRL84
2798(1997)
(2000).
• higher energy AGS: hadronic flow
• @ lower s
• could tune RQMD to give less flow…
• model source too small and (maybe)
emits too slowly?
• SPS energy:
• source too large?
• model could be tuned…
• already pre-RHIC: doubts of a
complete understanding
• but RQMD (nor hydro) did not get
p-space perfectly, so…
Rout
Rside
Rlong
NA44
4.88  0.21
4.45  0.32
6.03  0.35
RQMD
6.96  0.14
6.23  0.20
7.94  0.21
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
Kolb &Heinz, hep-ph/0204061
RHIC: new hope!
• hydro reproduces p-space very well
with no/minimal tuning
• details!
• But alas!
• hydro nor hydro+RQMD
nor AMPT simultaneously gets
p- and x-space
QM01
Heinz & Kolb, hep-ph/0204061
• already pre-RHIC: doubts of a
complete understanding
• but RQMD (nor hydro) did not get
p-space perfectly, so…
PHENIX, PRL91(’03)182301.
Hydro: P.Huovinen et al.(’01)
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
• p-space observables well-understood
within hydrodynamic framework
• x-space observables not well-reproduced
• correct dynamical signatures with
incorrect dynamic evolution?
• Too-large timescales modeled?
• emission/freezeout duration (RO/RS)
• evolution duration (RL)
Heinz & Kolb, hep-ph/0204061
dN/dt
CYM & LGT
PCM & clust. hadronization
NFD
NFD & hadronic TM
string & hadronic TM
PCM & hadronic TM
time
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
• p-space observables well-understood
within hydrodynamic framework
• x-space observables not well-reproduced
• correct dynamical signatures with
incorrect dynamic evolution?
• Too-large timescales modeled?
• emission/freezeout duration (RO/RS)
• evolution duration (RL)
• Poor experimentalist’s exploratory tool: BW
• tunable parameters (T, b, timescales..)
T=106 ± 1 MeV
<bInPlane> = 0.571 ± 0.004 c
<bOutOfPlane> = 0.540 ± 0.004 c
RInPlane = 11.1 ± 0.2 fm
ROutOfPlane = 12.1 ± 0.2 fm
Life time (t) = 8.4 ± 0.2 fm/c
Emission duration = 1.9 ± 0.2 fm/c
c2/dof = 120 / 86
BW: F. Retiere & MAL, nucl-th/0312024
Retiere QM04
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
• Poor experimentalist’s exploratory tool: BW
• tunable parameters (T, b, timescales..)
• Similar results from similar hydro-inspired
models
(e.g. Buda-Lund)
T=106 ± 1 MeV
<bInPlane> = 0.571 ± 0.004 c
<bOutOfPlane> = 0.540 ± 0.004 c
RInPlane = 11.1 ± 0.2 fm
ROutOfPlane = 12.1 ± 0.2 fm
Life time (t) = 8.4 ± 0.2 fm/c
Emission duration = 1.9 ± 0.2 fm/c
c2/dof = 120 / 86
Csanád, Csörgő, Lörstad nucl-th/0311102 and nucl-th/0310040
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!
Csanád, Csörgő, Lörstad nucl-th/0311102 and nucl-th/0310040
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
• hot core surrounded by cool shell
• important ingredient of Buda-Lund
hydro picture
e.g. Csörgő & Lörstad
PRC54 1390 (1996)
t
x2-p correlation: yes
x-p correlation: no
x2-p correlation: yes
x-p correlation: no
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

bT
K
pT
p
[click for more details on non-id correlations]
F. Retiere & MAL,Csanád,
nucl-th/0312024
Csörgő, Lörstad nucl-th/0311102 and nucl-th/0310040
HBT( s ;p T , y, b , bˆ , m1,m2 ,Asys )
bT
x (fm)
x (fm)
bT
• extracted shift in emission point x1-x2
w/ flow-dominated
blastwave
• 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
A. Kisiel (STAR) QM04
HBT( s ; p T , y, b , bˆ ,m1,m 2 , Asys )
• latest “puzzle” in HBT?
Rout / Rout(pp)
• HBT radii from pp fall with pT
(as observed previously, usually
attributed to string kT kick)…
• …but as much (proportionally) as
dAu and AuAu ??
• coincidence…?
• something deeper…?
p+p
string fragmentation
Au+Au
Collective expansion
Rside / Rside(pp)
2
p+p+X
Rlong
Rlong / Rlong(pp)
1
Rout
Rside
0.25
0.5
pT
STAR, QM04
transverse plane
HBT( s ; p T , y, b , bˆ ,m1,m 2 , Asys )
• latest “puzzle” in HBT?
• HBT radii from pp fall with pT
(as observed previously, usually
attributed to string kT kick)…
• …but as much (proportionally) as
dAu and AuAu ??
• coincidence…?
• something deeper…?
• What it does NOT mean:
• AA=N*(strings)
• AA=N*(“little blastwaves”)
local
x-p corr.
• AA: global x-p correlations
NB: p-space observables identical in the two cases
So far…
HBT( s ;p T , y, b , bˆ ,m1,m2 ,Asys )
• HBT radii appear to follow expected increases with (initial) system size
• comforting to remember in present age of uncertainty
• Rlong(Npart)(s) less clear
HBT( s ; p T , y, b , bˆ , m1,m2 ,Asys )
• can learn
• what is nature of dynamic x-p correlations?
• how strong is the flow?
• what are the timescales involved?
• did learn
• emitting source dominated by (global) collective flow
• HBT (and non-id) correlations described consistently with p-space
• short evolution and emission timescales indicated
• HBT “puzzle”
puzzle? Get more information!
Obtaining more detailed information in p-space…
• generically: breaking azimuthal symmetry (b0)  more differential detailed picture
• HBT(): as v2, sensitive to interplay b/t anisotropic geometry & dynamics/evolution
• another handle on dynamical timescales – likely impt in HBT puzzle
P. Kolb, nucl-th/0306081
“elliptic flow”
P. Kolb and U. Heinz, hep-ph/0204061
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
What can we learn?
Strongly-interacting 6Li released from an asymmetric trap
O’Hara, et al, Science 298 2179 (2002)
?
in-planeextended
transverse FO shape
+ collective velocity
 evolution time estimate
check independent of RL(pT)
out-of-plane-extended
Teaney, Lauret, & Shuryak nucl-th/0110037
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
(including “new” cross-terms)
big RS
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
y
~x 2
• At AGS: observed at
2, 4, 6 AGeV Au+Au
• including first-order
oscillations at y=0
• elliptical transverse shapes
• strongly tilted w.r.t. beam
• physics of directed flow
R2 (fm2)
• observe the source from all angles
with respect to RP
• expect oscillations in HBT radii
(including “new” cross-terms)
~ 2 2 AGeV; E895, PLB 496 1 (2000)
Au+Au
y
out
40
side
long
x
b
20
y os
ol
10
0
sl
x
qs
-10
0
180
0
180
Coordinate space!
0
180 z
p (°)
(Beam)
Images of --emitting sources (scaled ~ x1014)
~y 2
 1.35
2
~
x
y
similar to naïve
overlap: b~5 fm
y
x’
x’
2 AGeV
3 fm
z
y
qS=47°
x’
4 AGeV
z
6 AGeV
qS=37°
z
qS=33°
Large, positive
tilt angles
E895 – QM01
x
x
x
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
y
• observe the source from all angles
with respect to RP
• expect oscillations in HBT radii
(including “new” cross-terms)
• At AGS: observed at
2, 4, 6 AGeV Au+Au
• including first-order
oscillations at y=0
• elliptical transverse shapes
• strongly tilted w.r.t. beam
• physics of directed flow
~x 2
~y 2
x
b
y
x
qs
• At RHIC:
• no 1st-order RP  no tilt (yet)
z
(Beam)
Coordinate space!
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)
• At AGS: observed at
2, 4, 6 AGeV Au+Au
• including first-order
oscillations at y=0
• elliptical transverse shapes
• strongly tilted w.r.t. beam
• physics of directed flow
• At RHIC:
• no 1st-order RP  no tilt (yet)
• oscillations versus centrality
• oscillations versus pT
• average values  same as
“traditional” HBT (sizes)
• oscillations: transverse shape
STAR, nucl-ex/0312009, PRL in press
HBT( s ; p T , y, b , bˆ ,m1,m 2 ,Asys )
Estimate of initial vs F.O. source shape

R 2y  R 2x
R 2y  R 2x
• estimate INIT from Glauber
• from asHBT:
 FO  2
R S2, 2
R S2,0
• FO < INIT → dynamic expansion
• FO > 1 → source always OOP-extended
• constraint on evolution time
STAR, nucl-ex/0312009, PRL in press
A simple estimate – t0 from init and final
• BW → bX, bY @ F.O. (bX > bY)
• hydro: flow velocity grows ~ t
 b X ,Y ( t )  b X ,Y (F.O.) 
t
t0
• From RL(mT): t0 ~ 9 fm/c
consistent picture
• Longer or shorter evolution times
X inconsistent
P. Kolb, nucl-th/0306081
toy estimate: t0 ~ t0(BW)~ 9 fm/c
• too short to account for expansion??
• Need a real model comparison
→ asHBT valuable “evolutionary clock”
constraint for models
MAL ISMD03
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)
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?
STAR: this year
?
?
sNN (GeV)
y
x
qs
z
(Beam)
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)
L.P. Csernai, D. Rohrich:
Phys. Lett. B 458 (1999)
454
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.)
STAR: this year
?
?
sNN (GeV)
y
x
qs
z
(Beam)
HBT( s ;p T , y, b , bˆ ,m1,m 2 ,Asys )
• neglecting dynamics (flow), timescale, etc:
is it trivial?
• (though much of the interesting stuff is
dynamics and timescales…)
• gross geometrical features dictated by rule
of critical mfp ~ 1 fm?
Mean free path
f 
 f Vf

 ~ 1 fm
 N
Vf
N
2
rough FO volume V f  (2 )3 / 2 Rlong Rside
use measured: N   N i  i  N N   N  N   
i
CERES, PRL 90 (2003) 022301
Same universal freeze-out in p+p, d+Au ?
• Check CERES’ ansatz using dN/dy’s and HBT radii for p+p and d+Au
•
dN/dy’s taken from power-law fits to STAR pT spectra (nucl-ex/0309012)
Vf
N
90
90
80
d+Au
80
70
70
60
60
50
50
40
40
30
p+p
Vf (fm3)
N (fm2)
√s=200 GeV
30
20
20
10
10
0
CERES, PRL 90 (2003) 022301
• f ~ 1 fm seems to hold for light systems as well (!)
• Why are p+p, d+Au and Au+Au so similar?
Quark Matter 2004
Dan Magestro, Ohio State University
Magestro, QM04
HBT( s ; p T , y, b , bˆ ,m1, m2 ,Asys )
broad strokes… (shorter than usual)
• first order: “R=6 fm” (though this means 2x expansion)
• Well… R=(1.2 fm)*A1/3
• Well… R ~ (Npart)1/3
• HBT radii are, indeed, connected with geometry…
• but these are easy rules: dynamical models cannot follow them?
• pT, m1-m2 dep:
• strong global collective flow dominates
• -dep: freezeout in out-of-plane configuration
• non-trivial aspect of excitation function
• IMHO: Soft-sector dynamical observations (x- and p-space) demand
faster timescales than present understanding allows.
• e.g. maybe essentially no hadronic phase?
• personal most worrisome “puzzle”: pp = “small AA”??
parting words
• s scan of HBT worthless? (not huge changes)
• no! at one energy, we would (mistakenly) believe we understood spacetime structure of collisions
• Experimental HBT dataset is richly structured, with huge systematics
and expertise available
• IMHO, real work needed on theory side, and not dismissal
• (meanwhile, experimentalists will mess around with BW to try to discern
what the data is telling us)
• Puzzles may be annoying speedbumps on the way (to Stockholm?),
but one ignores them at one’s peril.