Post on 02-Feb-2016
description
transcript
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 1
Femtoscopy in heavy ion collisions:
Wherefore, Whence, & Whither?
Mike Lisa
Ohio State University
MAL, Pratt, Soltz, WiedemannAnn Rev Nucl Part Sci 55 (2005)
• Wherefore (=“why?”)• motivation & (basic) formalism
• Whence (=“from where?”) • systematics over 2 decades
• Whither (=“to where?”) • or “wither”...?
http://www-rnc.lbl.gov/TBS
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 2
Spacetime - The characteristic of H.I.C.
• Non-trivial space-time - the hallmark of R.H.I.C.• Initial state: dominates further dynamics• Intermediate state: impt element in exciting signals•Final state:
• Geometric structural scale is THE defining feature of QGP
STAR, PRC66 (2002) 034904 STAR, PRL93 (2004) 252301
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Ann.Rev.Nucl.Part.Sci. 46 (1996) 71
• Temporal scale sensitive to deconfinement transition (?)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 3
Extraction of length scales
€
C r P
ab(r q ) = d3 ′
r r ⋅Sr
P
ab( ′ r r )∫ ⋅ φ(
r ′ q ,r ′ r )
2
Gaussian parameterization of a-b separation
€
Sr P
ab( ′ r r ) ~ exp −
′ r i − X i[ ] ⋅ ′ r j − X j[ ]
4γ iγ jR i, j2
i, j= o,s,l
∑ ⎧ ⎨ ⎪
⎩ ⎪
⎫ ⎬ ⎪
⎭ ⎪
X i ≡ ′ x a,i − ′ x b,i ; i, j = out,side,long( )
usually used(even for non-id)
maximum-likelihood fit to
€
Cr q ( ) = λ ⋅F Q inv( ) ⋅ 1+ exp − qiq jR ij
2
ij
∑ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥+ 1− λ( ) for identical pions
• F(Qinv) = integrated squared Coulomb wavefunction
• “contamination” included via • NB: Gaussian source: not Gaussian CF
xa
xb
xa
xb
pa
pbxa
xb
pa
pb
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 4
qout
qside
qlong
Reminder
Rsi
de
R long
Rout
x1
x2
12 ppqrrr −=
p1
p2
qr
( )12 pp2
1k
rrr+=
• Two-particle interferometry: p-space separation space-time separation
RRsideside
RRoutout
Pratt-Bertsch (“out-side-long”) decomposition designed to help disentangle space & time
source sp(x) = homogeneity region [Sinyukov(95)]
connections with “whole source” always model-dependent
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 5
Disintegration timescale - INITIAL expectation
3D 1-fluid HydrodynamicsRischke & Gyulassy, NPA 608, 479 (1996)
withtransition
“” “”
Long-standing favorite signature of QGP:
• increase in , ROUT/RSIDE due to deconfinement confinement transition
• hoped-for “turn on” as QGP threshold is reached
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 6
A.D. Chacon et al, Phys. Rev. C43 2670 (1991)G. Alexander, Rep. Prog. Phys. 66 481 (2003)
R = 1.2 (fm)•A1/3
Two decades of systematics
•Pion HBT @ Bevalac: “largely confirming nuclear dimensions”•Since 90’s: increasingly detailed understanding and study w/ high stats
)s(HBT
‘85 ‘90 ‘95 ‘00 ‘05
5
10
15
20AGS/SPS/RHIC HBT papers (expt)
Bo
al/
Je
nn
ing
s/G
elb
ke
Heinz/JacakWiedemann/Heinz
Csorgo
To
ma
sik
/Wie
de
ma
nn
“R = 5 fm”
Lis
a,
Pra
tt,
So
ltz,
Wie
de
ma
nn
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 7
Two decades of systematics
•Pion HBT @ Bevalac: “largely confirming nuclear dimensions”•Since 90’s: increasingly detailed understanding and study w/ high stats
T 1 2 sysˆHBT( ;p , y, b ,b,ms ,m ,A )
r
y
|b|
pT
‘85 ‘90 ‘95 ‘00 ‘05
5
10
15
20AGS/SPS/RHIC HBT papers (expt)
Bo
al/
Je
nn
ing
s/G
elb
ke
Heinz/JacakWiedemann/Heinz
Csorgo
To
ma
sik
/Wie
de
ma
nn
Lis
a,
Pra
tt,
So
ltz,
Wie
de
ma
nn
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 8
Forget homogeneity regions or fancy stuff.
Do femtoscopic length scales increase when they “should?”
Also• SPS [NA44(‘99),NA49(‘00)]• RHIC [STAR(‘05)]
Repeating most basic sanity check at relativistic energies...
p-p correlations
* big bump small source
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 9
ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s φr
•Generalize A1/3 Npart1/3
•not bad @ RHIC!•connection w/ init. size?
Varying initial “source size”
Fixed A+B : vary b
Fixed b : vary A (& B!)
Likely scaling variable: Npart
b
PHENIX, PRL 2004
Au+Au sNN =200 GeV
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 10
•Generalize A1/3 Npart1/3
•not bad @ RHIC!•connection w/ init. size?
•Heavy and light data from AGS, SPS, RHIC•~s-ordering in “geometrical” Rlong, Rside
•Mult ~ K(s)*Npart
•source of residual s dep?
•...Yes! common scaling•final state drives radii, not init. geometry
•(breaks down s < 5 GeV)
ˆT 1b ys2 sHBT( ;p , y, ,b ,m ,m ,A )s φr
PHOBOS
LPSW nucl-ex/0505014
NB: not constant density
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 11
We are not alone...
H. Caines (STAR) QM05
Tounsi, Mischke, RedlichNPA715 565 (2003)
H. Caines (STAR) QM05
NA57 (open)STAR (filled)
NA57 (open)STAR (filled)
S. Manly (PHOBOS) QM05
Entropy determines “everything” at bulk level (soft sector) ?c.f. Helen’s talk
NB: scaling violated s < 4 GeV(as with femtoscopy)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 12
Refinement: chemical effects
• different behaviour below/above AGS
•violates “universal” scaling
•baryon meson dominance
• neglect time/dynamics: gross F.O.
geometry appears determined by
•chemistry
• “universal” mean free path ~ 1 fm (!?)
fm 1~ ⇒==σσ
ρ
NVff
fm.f.p
2sidelong
2/3)2( RRV f π≡~ FO volume
∑ +=≡i
NNii NNNN πππππ σσσσx-section:
Vf
Nσ
CERES, PRL 90 (2003) 022301
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 13
Messages from systematics• AB, |b|, Npart systematics
•sanity check on overall size dependence • final state multiplicity/chemistry determines rough geometry...
c.f. Chajecki - lighter systems
collective/flow-like expansion? probe anisotropically!
...and that geometry is ~2x initial size
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 14
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 φr
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)
?
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 15
• observe the source from all angles
with respect to RP• expect oscillations in HBT radii
big RS
small RS
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φr
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 16
• observe the source from all angles
with respect to RP• expect oscillations in HBT radii
(including “new” cross-terms)
out
side
R2out-side<0
when pair=135º
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φr
out
side
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 17
STAR, PRL93 012301 (2004)Measured final source* shape
* model-dependent, but see Retiere & MAL PRC70 044907 2004
R2out-side<0
when pair=135º
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φr
ever see that symmetry at ycm ?
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 18
STAR, PRL93 012301 (2004)
centralcollisions
mid-centralcollisions
peripheralcollisions
Measured final source* shape
T ˆ 1 ysb 2 sHBT( ;p , y, b , ,m ,m ,A )s φr
* model-dependent, but see Retiere & MAL PRC70 044907 2004
Expected evolution:
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 19
Evolution of size and shape - “the rule of two”
€
R s;pT ,y,r b ,AB,φˆ b
,m1,m2( )
initi
al= fin
al
STAR PRL93 012301 (2004)
Initial size/shape estimated by Glauber calculationFinal config according to Retiere & MAL PRC70 044907 2004
~ x2 size increase ~ 1/2 shape reduction
c.f. Chajecki - lighter systems
2x
2y
2x
2y
RR
RR
+−
≡
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 20
• non-trivial excitation function• does it make sense? Is it
related to bulk dynamics? YES
sNN (GeV)
(approximately same centrality)
AGS: FO init
RHIC: FO < init
“Anisotropic sanity check”
€
Δ ≈β ⊗ v2 ⊗ τ ???
is relation b/t final and near quantitatively sensible?
(in a toy model yes - fordiscusison if asked)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 21
Messages from systematics• AB, |b|, Npart systematics
•sanity check on overall size dependence • final state multiplicity/chemistry determines rough geometry...
, |b|, s systematics•sanity check on shape evolution •geometric evolution ~ consistent with collective bulk dynamics (flow)
look for dynamic signatures & substructure
• more than T versus mass• more than spectral shapes• more than v2
• ...flow is defined by space-momentum correlations
only femtoscopy can probe substructureof dynamic bulk behaviour
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 22
Geometric substructure?
random (non-)system:
all observers measure the
“whole source”
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 23
Specific predictions ofbulk global collective flow:
• space-momentum (x-p) correlations
• faster (high pT) particles come from
•smaller source
•closer to “the edge”
Flow-generated substructure
random (non-)system:
all observers measure the
“whole source”
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 24
Strong flow confirmed by all expts...
€
R s;pT ,y,r b ,AB,φˆ b
,m1,m2( )
LPSW(05)
what agreement!! (what agreement?)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 25
Spectra
v2
HBT
Flow-dominated“Blast-wave” modelPRC70 044907 (2004)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 26
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps φr
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
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 27
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps φr
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)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 28
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps φr
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)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 29
ˆ 1 2 sysbTHBT( ; , y, b , ,m ,m ,A )ps φr
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
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 30
Spectra
v2
HBT
Flow-dominated“Blast-wave” modelPRC70 044907 (2004)
π
K
R (
fm)
mT (GeV/c)
STAR PRL 91 262301 (2003)
space-momentum substructure mapped in detail
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 31
RHIC femtoscopy with wide variety of particle species
π+ π- K+ K- K0S p p
π+
π-
- K+
K-
- - K0S
p
p
R(√SNN, b, Npart, A, B, mT, y, , PID1, PID2)
= prelim or final result available
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 32
Trends, soft sector, and RHI history
A. Wetzler (2005)
M Gyulassy ‘95
Just oneevent!
Finally, weunderstand it!
Then: p-dependent potentials, surface effects, hard-cores, absoption...
• unlike hard and “intermediate” sectors, soft sector has “decades” of systematics
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 33
model comparisons
• unlike hard and “intermediate” sectors, soft sector has “decades” of systematics
• single-point agreement a bit unsatisfying...
• femtoscopic model comparisons: mostly “HBT radii” in b=0 collisions
• RHIC models only expected to work at highest energies...
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 34
Comparison to “perfect” hydro calculations
LPSW(05)
• model sensitivity (not just R=5) •Rout too big (too long emission time?)
• Rlong too big (too long evolution time?)
• Rside too small (?)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 35
Comparison to Boltzmann/cascade models
better! (better than “perfect”...?)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 36
What’s the difference? freeeze-out........ EoS............viscosity
€
Ro2 = ˜ x 2 − 2βT ˜ x ⋅ ˜ t + βT
2 ˜ t 2
RS2 = ˜ y 2 ; RL
2 = ˜ z 2
“HBT radii” from variancesfit calculated* 3D C(q)to Gaussian functional form:
€
C(r q ) =1+ λ ⋅e−q o
2 R o2 −q s
2R s2 −q l
2R l2
*later: how it is calculated
should be the same IF source is Gaussian
hydro cascade
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 37
Non-Gaussian Effects and Model Comparisons - Hydro/BW
C2
qs (GeV/c)
C2
qs (GeV/c)
RO
RS
RL
C2
qs (GeV/c)
KT (GeV/c) KT (GeV/c)
Frodermann, Heinz, MAL PRC63 (2006)Hydrodynamics - CE EOS
Frodermann, Heinz, MAL PRC63 (2006)
KT (GeV/c) KT (GeV/c)
Hydrodynamics - NCE EOS
Frodermann, Heinz, MAL PRC63 (2006)
KT (GeV/c) KT (GeV/c)
Blast Wave
Depending on model (& parameters, like EoS),non-Gauss effects may be important, (also, Hirano, Ko/Li, Rischke)• BW - no big effect• “perfect” hydro - pushes results into “right” direction. NCE EoS close
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 38
Wherefore & Whence
• size & shape; timescale estimate• space-momentum substructure of a flowing system;
dynamics and evolution of• radial flow (size and shift)•elliptic flow (shape and timescale)•directed flow (shape and tilt) [did not show due to time]
• hadronic particle potentials / phase shifts
• Femtoscopy:•well-calibrated, well-established tool• the one most directly connected to space-time - THE defining feature of R.H.I.C.•huge set of systematics of consistent measurements•sensitive to physics in models
• with care: the femtoscope is a precision tool to apply to new systemsLHC, p+p, etc
R(√SNN, b, Npart, A, B, mT, y, , PID1, PID2)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 39
Whither?
• non-id correlations for b≠0 [Retiere & Lisa PRCPRC70 044907 (2004)]
• invert the problem : low-energy phaseshifts from exotic pairs (e.g. π-)
[talk of H. Gos] & [P. Chaloupta QM05]
• space-time substructure in p+p ?? - “direct comparison] [talk of Z. Chajecki][Chajecki et al, WW05]
• imaging - beyond sizes and shifts [Brown, Danielewicz, Pratt, & others]
• first-order azimuthally-sensitive femtoscopy - spacetime aspects of v1[Lisa et al, PLB489 287; PLB496 1]
• relative jets, spin.... (?)
• continue/expand rich program @ ALICE/LHC
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 40
THEEND
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 41
€
R s;pT ,y,r b ,AB,φˆ b
,m1,m2( )
€
R i mT( ) =′ R i
mTα i
Strong flow confirmed by all expts...
Central (~10%) AuAu (PbPb) collisions at y~0
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 42
A simple estimate – 0 from init and final
0Y,XY,X
t.)O.F()t(
ββ ⋅=→
“radial flow”
P. Kolb, nucl-th/0306081
• BW → βX, βY @ F.O. (βX > βY)
• hydro: flow velocity grows ~ t
• From RL(mT): 0 ~ 9 fm/c
consistent picture• Longer or shorter evolution times
X inconsistent
toy estimate: 0 ~ 0(BW)~ 9 fm/c
• too short to account for expansion??
• Need a real model comparison→ asHBT workable “evolutionary clock” constraint for models MAL ISMD03
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 43
“Gaussian fit”(remember: notGaussian CF)
Motivation Formalism Experiment Trends Models
• Usually, quality of data and fit shown in 1D projections
• Narrow integration best
• limited view of data• see talks of Adam, Scott, Sandra• tomorrow: a better way
1D projections: a limited view
out
side long
STAR PRC71 044906 (2005)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 44
The perennial non-GaussiannessMotivation Formalism Experiment Trends Models
• Source has never been fully Gaussian. c.f. J. Sullivan @ SPS
• periodically re-discovered, with little change; information condensation needed to observe systematic data trends
• non-Gaussianness @ RHIC reported in first and subsequent HBT measurements
• imaging is probably best solution (but even then...)
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 45
The perennial non-Gaussianness
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.RO (
fm)
RS (fm
)
Rl (
fm) R
O /RS
Motivation Formalism Experiment Trends Models
CF is “mostly” GaussianSTAR tried “Edgeworth” functional expansion (Csorgo 2000)
among few quantitative estimatesof non-Gaussian shape
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
STAR PRC71 044906 (2005)
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
• 20% effect in Rlong! systematic error...?
• appears fit captures dominant length scale
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 46
Another implication of strong flow: ~ mT scaling
€
R s;pT ,y,r b ,AB,φˆ b
,m1,m2( )
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 47
1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs φr
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
using four of the six “radii”
€
Sr P
ab( ′ r r ) ~ exp −
′ r i − X i[ ] ⋅ ′ r j − X j[ ]
4γ iγ jR i, j2
i, j= o,s,l
∑ ⎧ ⎨ ⎪
⎩ ⎪
⎫ ⎬ ⎪
⎭ ⎪
X i ≡ ′ x a,i − ′ x b,i ; i, j = out,side,long( )
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 48
Au+Au sNN = 2.3 GeV; b5 fm
E895, PLB496 1 (2000)
using ALL of the six “radii”
€
Sr P
ab( ′ r r ) ~ exp −
′ r i − X i[ ] ⋅ ′ r j − X j[ ]
4γ iγ jR i, j2
i, j= o,s,l
∑ ⎧ ⎨ ⎪
⎩ ⎪
⎫ ⎬ ⎪
⎭ ⎪
X i ≡ ′ x a,i − ′ x b,i ; i, j = out,side,long( )
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 49
1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs φr
(o
)
sNN (GeV)
(Beam)
x
y
z
s
? ?
STAR: soon
• 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
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 50
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
mike lisa - Femtoscopy in relativistic heavy ion collisions - Hot Quarks 17 May 2006, Sardinia, Italy 51
1 2 sˆT b ysHBT( ; , y, , ,m ,m ,A )p bs φr
(o
)
sNN (GeV)
(Beam)
x
y
z
s
? ?
STAR: soon ?
• 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