The HBT excitation function in relativistic heavy ion collisions

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)