The HBT excitation functionin relativistic heavy ion collisions
Mike LisaOhio State University
Plan
)s(HBT T 1 2 sysˆHBT( ;p , y, b ,b,ms ,m ,A )
y
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 ?
Also, upon request: comments on technical issues (event-mixing, Coulomb, non-Gaussianness, RP resolution correction…)
|b|
pT
Brief “summary” (intro to discussion)
qout
qside
qlong
Reminder
Rsi
de
R long
Rout
x1
x2
12 ppq
p1
p2
q
12 pp2
1k
• Two-particle interferometry: p-space separation space-time separation
• HBT: Quantum interference between identical particles
pairsevent mixed
pairsevent real
)(P)(P
),(P),(
21
2121
pp
ppppC
2long
2long
2side
2side
2out
2out)(1),(
RqRqRqekkqC
q (GeV/c)q (GeV/c)
C (
q)C
(q)
11
22R
1~
• Final-state effects (Coulomb, strong) also can cause correlations, need to be accounted for
Gaussian model (3-d):
qout
qside
qlong
Reminder
Rsi
de
R long
Rout
x1
x2
12 ppq
p1
p2
q
12 pp2
1k
• Two-particle interferometry: p-space separation space-time separation
RRsideside
RRoutout
Pratt-Bertsch (“out-side-long”) decomposition designed to help disentangle space & time
ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s
E802 PRC66 054906 (2002)
14.6 AGeV Si+Al 14.6 AGeV Si+Au11.6 AGeV Au+Au
AGS: sNN 2-5 GeV
• Expected “geometric” scaling of transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s
158 AGeV Pb+Pb
200 AGeV S+S
158 AGeV p+p
RQMD
NA49 NPA661 448c (1999)
“initial” Rside
SPS: sNN 17-20 GeV
• Expected “geometric” scaling of transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
• apparent ~2x expansion
AGS: sNN 2-5 GeV
• Expected “geometric” scaling of transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s
SPS: sNN 17-20 GeV
• Expected “geometric” scaling of transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
• apparent ~2x expansion
AGS: sNN 2-5 GeV
• Expected “geometric” scaling of transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
NA44, Eur Phys J C18 317 (2000)
ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s
SPS: sNN 17-20 GeV
• Expected “geometric” scaling of transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
• apparent ~2x expansion
AGS: sNN 2-5 GeV
• Expected “geometric” scaling of transverse radii with |b|, Npart
• RL: trend (and expectation) less clear
RHIC: sNN = 130-200 GeV
• Expected “geometric” scaling of transverse radii with |b|, Npart
• RL trend very similar (expected?)
• apparent ~2x expansion
PHENIX nucl-ex/0401003
STAR nucl-ex/0312009accepted to PRL
32-72% 12-32% 0-12%
STAR PRL87 082301 (2001)
So far…
ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s
• 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)]
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
Kolb & Heinz, QGP3 nucl-th/0305084
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
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
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 correlationsearly times: small, hot source
late times: large, cool source
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
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)
1500 fm/c (!)
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
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 picturee.g. Csörgő & LörstadPRC54 1390 (1996)
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
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 picturee.g. Csörgő & LörstadPRC54 1390 (1996)
t
Each scenario generatesx-p correlations but…
x2-p correlation: yesx-p correlation: yes
x2-p correlation: yesx-p correlation: no
x2-p correlation: yesx-p correlation: no
80 AMeV Ar+Sc(pp,X)
MAL et al, PRL70 3709 (1993)
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
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 OK @ one s but…)
x (fm)
y (f
m)
E895 PRL84 2798 (2000).
RQMD: Sorge PRC52 3291 (1995)
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
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 OK @ one s but…)
• SPS: smooth, almost (!) featureless transition AGS RHIC• can the models do that??!
E895 PRL84 2798 (2000)CERES, NPA714 124 (2003)STAR, PRL87 082301 (2001)
NB: error in CERES paper
E895 PRL84 2798 (2000).At fixed s, a chance to
understand system• 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…
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
NA44 RQMD
Rout 4.88 0.21 6.96 0.14
Rside 4.45 0.32 6.23 0.20
Rlong 6.03 0.35 7.94 0.21
NA44) PRC58, 1656 (1998)D. Hardtke, Ph.D. thesis (1997)
• already pre-RHIC: doubts of a complete understanding•but RQMD (nor hydro) did not get p-space perfectly, so…
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
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
Hydro: P.Huovinen et al.(’01)PHENIX, PRL91(’03)182301.
Kolb &Heinz, hep-ph/0204061
QM01Heinz & Kolb, hep-ph/0204061
time
dN/dt
PCM & clust. hadronization
NFD
NFD & hadronic TM
PCM & hadronic TM
CYM & LGT
string & hadronic TM
• 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)
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
Heinz & Kolb, hep-ph/0204061
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
T=106 ± 1 MeV<InPlane> = 0.571 ± 0.004 c<OutOfPlane> = 0.540 ± 0.004 cRInPlane = 11.1 ± 0.2 fmROutOfPlane = 12.1 ± 0.2 fm
Life time () = 8.4 ± 0.2 fm/cEmission duration = 1.9 ± 0.2 fm/c2/dof = 120 / 86
BW: F. Retiere & MAL, nucl-th/0312024
• Poor experimentalist’s exploratory tool: BW• tunable parameters (T, , timescales..)
• 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)
Retiere QM04
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
T=106 ± 1 MeV<InPlane> = 0.571 ± 0.004 c<OutOfPlane> = 0.540 ± 0.004 cRInPlane = 11.1 ± 0.2 fmROutOfPlane = 12.1 ± 0.2 fm
Life time () = 8.4 ± 0.2 fm/cEmission duration = 1.9 ± 0.2 fm/c2/dof = 120 / 86
• Poor experimentalist’s exploratory tool: BW• tunable parameters (T, , timescales..)
• Similar results from similar hydro-inspired models (e.g. Buda-Lund)
Csanád, Csörgő, Lörstad nucl-th/0311102 and nucl-th/0310040
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
• 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
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
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 picturee.g. Csörgő & LörstadPRC54 1390 (1996)
t
Each scenario generatesx-p correlations but…
x2-p correlation: yesx-p correlation: yes
x2-p correlation: yesx-p correlation: no
x2-p correlation: yesx-p correlation: no
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps
• 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
Csanád, Csörgő, Lörstad nucl-th/0311102 and nucl-th/0310040
[click for more details on non-id correlations]
F. Retiere & MAL, nucl-th/0312024
pT
T
K
p
ˆT 2 sysb 1HBT( ;p , y, b , m ,m, ,A )s
• 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
• extracted shift in emission point x1-x2 consistent w/ flow-dominated blastwave
A. Kisiel (STAR) QM04
x
(fm
)
x (
fm)
T T
T s1b y2 sˆHBT( ; , y, b , ,m ,m , )p As
• 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…?
Rout
Rside
Rlong
p+p+X
pT
0.25 0.5
2
1
STAR, QM04
Rout / Rout(pp) Rside / Rside(pp)
Rlong / Rlong(pp)
Au+AuCollective expansion
p+pstring fragmentation
transverse plane
T s1b y2 sˆHBT( ; , y, b , ,m ,m , )p As
• 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”)
• AA: global x-p correlations
localx-p corr.
NB: p-space observables identical in the two cases
So far…ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s
• HBT radii appear to follow expected increases with (initial) system size• comforting to remember in present age of uncertainty
• Rlong(Npart)(s) less clear
ˆ sT 1 2 ysbHBT( ; , y, b , , ,A )p m ,ms
• 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!
• generically: breaking azimuthal symmetry (b0) 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 and U. Heinz, hep-ph/0204061P. Kolb, nucl-th/0306081
“radial flow”
“elliptic flow”
Obtaining more detailed information in p-space…
Strongly-interacting 6Li released from an asymmetric trapO’Hara, et al, Science 298 2179 (2002)
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s
What can we learn?
in-plane-extended
out-of-plane-extended
Teaney, Lauret, & Shuryak nucl-th/0110037
transverse FO shape+ collective velocity evolution time estimate
check independent of RL(pT)
?
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s
• observe the source from all angles with respect to RP
• expect oscillations in HBT radii (including “new” cross-terms)
big RS
small RS
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s
• observe the source from all angles with respect to RP
• expect oscillations in HBT radii (including “new” cross-terms)
• At AGS: observed at2, 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
p (°) 0 180
0
0 180 0 180
10
-10
20
40
R2 (
fm2 ) out side long
ol os sl
Au+Au 2 AGeV; E895, PLB 496 1 (2000)
(Beam)
Coordinate space!
x
y
z
s
b
2y~
2x~
x
y
Images of --emitting sources (scaled ~ x1014)
Mike Lisa:
1 fm = 1/4”
Mike Lisa:
1 fm = 1/4”
3 fm
x ’
y
2 AGeV
x
zS=47°
x ’
y
4 AGeV
x
zS=37°
x ’
y
6 AGeV
x
zS=33°
Large, positivetilt angles
35.1x~
y~
2
2
similar to naïveoverlap: b~5 fm
E895 – QM01
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s
• observe the source from all angles with respect to RP
• expect oscillations in HBT radii (including “new” cross-terms)
• At AGS: observed at2, 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)
(Beam)
Coordinate space!
x
y
z
s
b
2y~
2x~
x
y
1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs
• observe the source from all angles with respect to RP
• expect oscillations in HBT radii (including “new” cross-terms)
• At AGS: observed at2, 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
Estimate of initial vs F.O. source shape
2x
2y
2x
2y
RR
RR
20,S
22,S
FO R
R2
• estimate INIT from Glauber
• from asHBT:
FO < INIT → dynamic expansion
FO > 1 → source always OOP-extended
• constraint on evolution time
STAR, nucl-ex/0312009, PRL in press
FO =
init
1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs
1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs
2x
2y
2x
2y
RR
RR
sNN (GeV)
(approximately same centrality)
AGS: FO init
RHIC: FO < init
• transverse shape:• non-trivial excitation function• increased flow*time rounder
FO geometry @ RHIC• insufficient [flow]x[time] to
become in-plane
1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs
(o
)
sNN (GeV)
(Beam)
x
y
z
s
? ?
STAR: this year
• 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?
AGS
v1 predictions (QGP invoked)
J. Brachmann et al., Phys. Rev. C. 61 024909 (2000)
L.P. Csernai, D. Rohrich: Phys. Lett. B 458 (1999) 454
x-p transverse-longitudinal coupling may be affected in early (v1) stage
1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs
(o
)
sNN (GeV)
(Beam)
x
y
z
s
? ?
STAR: this year
• 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.)
AGS
ˆT 1 2 sysbHBT( ;p , y, b , ,m ,m ,A )s
• 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?
fm 1~
N
V fffMean free path
2sidelong
2/3)2( RRV f rough FO volume
i
NNii NNNN use measured:
Vf
N
CERES, PRL 90 (2003) 022301
Quark Matter 2004 Dan Magestro, Ohio State University
Same universal freeze-out in p+p, Same universal freeze-out in p+p, d+Au ?d+Au ?
Vf
N
CERES, PRL 90 (2003) 022301
10
20
30
40
50
60
70
80
90
10
20
30
40
50
60
70
80
90
Vf (
fm3 )
d+Au
p+p
√s=200 GeV
0
N
(fm
2 ) ff ~ 1 fm seems to hold for light systems as well (!) ~ 1 fm seems to hold for light systems as well (!)
• Why are p+p, d+Au and Au+Au so similar?Why are p+p, d+Au and Au+Au so similar?
• Check CERES’ ansatz using dN/dy’s and HBT radii for p+p and d+AuCheck 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 pdN/dy’s taken from power-law fits to STAR pTT spectra (nucl-ex/0309012) spectra (nucl-ex/0309012)
Magestro, QM04
• 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”??
ˆT 1 2 sysbp , y, b , ,m ,HBT( m; ,As )
broad strokes… (shorter than usual)