Transcript Freeze-out and HBT interferometry

Freeze-out and HBT interferometry
Bose-Einstein correlations in heavy-ion collisions
Dan Magestro, The Ohio State University
• Bose-Einstein correlations in heavy ion collisions
• Data, data, data
• Puzzles and surprises
• Some phenomenology on pion freeze-out
• HBT and the case for the quark-gluon plasma
ISMD 2004 Sonoma
HBT, i.e. Bose-Einstein correlations
• Two-particle interferometry: p-space separation  space-time separation
x1

q
p1
qside
p2
Rside
x2
qout
  
q  p2  p1
 1  
k  p 2  p1 
2
qlong
Rout
Ro2 ( K )  ~
xo2  2T ~
xot   T2 t 2

2
~
• B-E correlations: Quantum
between ident. particles
R ( K )interference
 xs
C ( p1 , p2 ) 
P( pR ,( Kp)2 ) ~z 2

2
l1
  event
 t  pairs
real
mixed event pairs
2
P( p1 )P( p2 )
2
2
2
2
2
2
 qout
 
Rout
 qside
Rside
 qlong
Rlong
C (q , k )  1  (k ) e
•
Final-state effects (Coulomb, strong) also can cause
correlations, need to be accounted for
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~
2
Dan Magestro, Ohio State University
C (q)
2
s
2
1
R
1
q (GeV/c)
2
HBT in heavy-ion collisions
• HBT in HI collisions: Explore space-time evolution of system
•
•
Geometry: spatial distribution of emission points
•
Dynamics: hot & dense early stages reflected in freeze-out pattern
•
Lifetime: sensitive to nature of phase transition
Experimental technique: Study as differentially as possible
transverse momentum (kT)
dynamics, collective expansion
beam energy
onset effects, transition phenomena
particle species
differences in emission
collision system
origins of correlations, phase space
azimuthal angle
spatial anisotropies, constrain system evolution
• QGP signature: HBT predicted to elicit long emission times at
RHIC, indicative of a phase transition
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Dan Magestro, Ohio State University
3
HBT in Au+Au at √s = 200 GeV
• PHENIX -HBT: kT , centrality
dependence at 200 GeV
(nucl-ex/0401003)
•
“Partial” Coulomb treatment
causes ~ 10-15% change in
Rout/Rside
x1

q
p1
qside
Rside
x2
p2
qout
qlong
Rout
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 1  
k  p 2  p1 
2
Dan Magestro, Ohio State University
4
HBT: Energy, kT dependence
• Little difference from SPS
to RHIC
•
No anomalous behavior
across large energy range
•
Characteristic kT dependence
observed at all energies
x1

q
p1
qside
Rside
x2
p2
qout
qlong
Rout
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 1  
k  p 2  p1 
2
Dan Magestro, Ohio State University
CERES Coll., NPA714 124 (2003)
5
Agreement among RHIC experiments
Au+Au, 200 GeV
Burt Holzman, QM 2004, nucl-ex/0406027
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Dan Magestro, Ohio State University
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HBT at √s = 62 GeV (fresh)
PRELIMINARY
J. Dunlop, STAR, RHIC/AGS Users Meeting (5/2004)
• STAR -HBT: kT , centrality at 62 GeV (same analysis as 200 GeV)
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Dan Magestro, Ohio State University
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HBT from SPS to RHIC
PRELIMINARY
J. Dunlop, STAR, RHIC/AGS Users Meeting (5/2004)
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Dan Magestro, Ohio State University
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 HBT: Energy dependence
PRELIMINARY
?
(wishful thinking!)
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Dan Magestro, Ohio State University
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kT (mT) dependence in heavy-ion collisions
• x-p correlations arise mostly due
to collective expansion (flow)
•
Radial flow pushes higher-pT
particles more at surface
• Analytical expressions
•
System lifetime (Sinyukov)
T K 2 (mT )
mT K1 (mT )
Rlong  0
expansion duration
•
Transverse flow velocity, system size
Kolb & Heinz, QGP3 (nucl-th/0305084)
Rside 
Rgeom
1
mT 2
f
T
transverse rapidity
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Dan Magestro, Ohio State University
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Q1: Is there more to the kT dependence in
heavy-ion collisions than Hydrodynamics tells us?
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Dan Magestro, Ohio State University
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The HBT Puzzle
• Hydrodynamics at RHIC
Soff, Bass Dumitru
hydro
 Can describe soft pT spectra
and only
v2
consistently, for several particle
species rescatt
hydro+hadronic
• Fast thermalization in partonic phase
(~½ fm/c), lives for ~15 fm/c
 Underpredicts Rside and its kT dependence
 Overpredicts Rout and Rlong by factor ~2
• Hydro doesn’t work. Why is this a
puzzle?
STAR
PHENIX
• Expanding fireball, undergoing
phase
transition, should at least cause Rout > Rside
Hadronic rescattering phase makes it worse
Rside
Rout
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Dan Magestro, Ohio State University
Kolb & Heinz, QGP3 (nucl-th/0305084)
12
The HBT Puzzle
√s = 130 GeV
5. Parton cascade with opacity
Rout (fm)
Alternative approaches to Hydro
STAR
PHENIX
 = 7.73
 = 3.01
 = 0.60
8
Molnar and Gyulassy, nucl-th/0211017
Pion freeze-out distribution sensitive to
transport opacity 
6. Positive xo-t correlation ?!
Rside (fm)
•
4
8
4
Lin, Ko and Pal, PRL 89 (2002) 152301
R (K )  ~
xs2
2
s
Rl2 ( K )  ~
z2

 
2
 t2

Rlong (fm)
Ro2 ( K )  ~
xo2  2T ~
xot   T2 t 2
Lin, Ko and Pal,
PRL 89 (2002) 152301
8
4
0.2
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
0.6
0.4
kT (GeV/c)
0.8
13
The HBT Puzzle
Blast-wave parametrization
Retiere and Lisa, nucl-th/0312024
•
Longitudinal boost invariance
•
Relative particle abundances not fixed
•
Constant parameters at freeze-out
Tf 104  3 MeV
f
•
8.9  0.3 fm/c
Buda-Lund Hydro parameterization
Csorgo et al, ISMD 2003, nucl-th/0311102
•
Not boost invariant (Hubble flow)
•
Freeze-out smeared in temperature
STAR
PHENIX
Retiere, Lisa
8
Csorgo et al
4
Rlong (fm)
•
Rside (fm)
Hinting at the solution
Rout (fm)
√s = 130 GeV
8
4
8
4
To 214  7 MeV
f
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0.2
6.0  0.2 fm/c
Dan Magestro, Ohio State University
0.6
0.4
kT (GeV/c)
0.8
14
Q2: So, what evidence do we have that the
kT (mT) dependence actually does arise
from collective flow?
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
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Exhibit A: Flavor, mT studies at SPS & RHIC
• Kaons, pions, baryons follow mT scaling up to ~1 GeV
•
Consistent lifetimes: f ~ 8-10 fm/c
1
 p0  p1 mT
2
R
NA49, Phys.Lett. B 557 (2003) 157
NA44, nucl-ex/0305014
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Dan Magestro, Ohio State University
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Exhibit B: Non-identical particle correlations
•
Study emission asymmetries with final-state interactions
•
Strong radial flow induces species-dependent x-p correlations
Case 1
Particle emitted closer
to center is slower
•
Case 2
Particle emitted closer
to center is faster
•
Effective interaction time shorter
•
Effective interaction time larger
•
Weaker correlation
•
Stronger correlation
The two cases can be discriminated
•
Two correlation functions: “lighter particle faster”, “lighter particle slower”
•
Compare correlation strength of two CF’s
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Dan Magestro, Ohio State University
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Exhibit B: Non-identical particle correlations
Au+Au, √s = 200 GeV
C(pion faster) / C(pion slower)
pion slower
PRELIMINARY
pion faster
pions
low 
high 
protons
A. Kisiel for STAR
• “pion faster” shows stronger correlation
K
• Blast-wave
pictureto source center
 pions on average
emitted nearer
•

Arises naturally in collective expansion picture
• Similar studies are underway for many particle combinations
•
Exotic correlations like - can yield information about nature of  flow
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
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Universal pion freeze-out
• CERES proposed a simple ansatz to investigate if critical mean free
path for pions f drives freeze-out
•
Mean free path can be estimated
from these two relations:
f 
f


Vf
N
Vf
•
Use HBT radii to estimate freeze-out
volume Vf
N
2
V f  (2 )3 / 2 Rlong Rside
•
Fold - and -N cross sections with
experimentally-measured dN/dy’s
N   N i  i  N N   N  N   
i
CERES, PRL 90 (2003) 022301
• Does this work for lighter systems?
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
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HBT in p+p collisions at RHIC
• RHIC: HBT for 3 very different
systems at same c.m. energy & with
same detector
preliminary
p+p
• kT dependence of HBT radii
presumably arises in different ways
Rlong
p+p
Au+Au
Multistring fragmentation
Collective expansion
Rout
Rside
transverse plane
T. Gutierrez for STAR Coll, poster
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Dan Magestro, Ohio State University
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p+p → d+Au → Au+Au
preliminary
Rout / Rout(pp)
Rside / Rside(pp)
Rout (fm)
Rside (fm)
RlongR/ Rlong
(pp)
(fm)
long
STAR, T. Gutierrez @ QM2004 (nucl-ex/0403012)
•
All three systems exhibit similar kT dependence (?!)
•
Systematic study underway to assess “Gaussian-ness” of correlation
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Dan Magestro, Ohio State University
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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
DM, QM 2004
• f ~ 1 fm seems to hold for light systems as well (!)
• Why are p+p, d+Au and Au+Au so similar?
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Dan Magestro, Ohio State University
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• Q3: Why do p+p, d+Au, and Au+Au exhibit
similar mean free paths at freeze-out in this
phenomenology?
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
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The emerging picture at RHIC
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Dan Magestro, Ohio State University
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The case for the QGP
• 4 theory position papers
http://quark.phy.bnl.gov/~mclerran/qgp/
•
Hadronic Signals of Deconfinement at RHIC, Berndt Müller
•
What RHIC Experiments and Theory tell us about Properties of
Quark-Gluon Plasma? Edward Shuryak
•
New Forms of QCD Matter Discovered at RHIC, Miklos Gyulassy
and Larry McLerran
•
Jet Tomography of Hot and Dense Matter, Xin-Nian Wang
• ~70 pages of interpretation , 4 main observations:
•
Strong collectivity
•
Jet quenching
•
Evidence for coalescence
•
Color Glass Condensate at forward rapidities
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Dan Magestro, Ohio State University
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The proverbial rug...
• 4 theory position papers
•
T
•
p+p, d+Au and Au+Au exhibit similar kT dependence, similar
freeze-out pion mean free path
Only mention of HBT among all four position papers!!
E. Shuryak, RHIC-QGP position paper (p. 12 of 13)
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Dan Magestro, Ohio State University
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So, how does HBT fit into the “emerging picture”?
Q4: Short lifetimes: what’s wrong with Hydro?
•
Initial conditions? Boost-invariant assumptions? Instantaneous
freeze-out (constant T) realistic?
Q5: Do we understand how hadronic system
decouples?
•
Are positive x-t correlations physical? Is a ~1 fm mean free path
physical?
Q6: Can we make QGP claims when models miss HBT?
Q7: Can HBT resolve itself?
•
Is the disagreement an artifact of the analysis, e.g. is Gaussian
correlation model a good-enough approximation?
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
28
Q8: To B-E or not to B-E?
That is the question...
I would prefer
this course of action!
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing, end them?
Hamlet, hep-ph/9408071
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Dan Magestro, Ohio State University
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BACK-UPS
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Dan Magestro, Ohio State University
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HBT of direct photons
• Photon interferometry in heavy ion collisions
•
0 peak
Probes initial state, not final-state interactions
Srivastava and Kapusta; Timmerman et al; Peressounko PRC 67 (2003) 014905
•
A major challenge experimentally!
•
Low relative direct photon yield
•
Many sources of small-Qinv pairs:
photon conversions, 0 HBT,
mis-id ’s, resonance decays, etc.
0.1 < kT < 0.2 GeV/c
Rinv  5.4  0.8 (stat.)  0.9 (sys.) fm
• WA98: First -HBT in R.H.I.C.
0.2 < kT < 0.3 GeV/c
•
Rinv quantitatively similar to
 HBT in same kT region
•
→ Soft photons arise in late WA98 Collaboration, nucl-ex/0310022
stages of collision
Rinv  5.8  0.8 (stat.)  1.2 (sys.) fm
• Direct photon yield can be accessed with 
N Direct N Total  2 WA98 Collaboration, nucl-ex/0310022
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
31
Refined Coulomb treatment
• Final-state interactions (Coulomb, strong) influence correlation signal
• Traditionally, all pairs in CF corrected for Coulomb



A(q )
  K (q ) G (q )
B(q )
1  e
•
 qi2 Ri2
This over-corrects the CF → increases width, decreases radii
• CERES: Apply Coulomb correctionCoulomb-corrected
only to pairs participating in B-E
(Nucl. Phys. A 714 (2003) 124)
uncorrected



A(q )





1


K
(
q
)
G
(
q
)

B(q )
First proposed in:
Bowler PLB 270 (1991) 69
fraction of non-participating pairs
PHENIX Coll, nucl-ex/0401003
• Adopted by in recent papers by STAR, PHENIX
STAR Coll, nucl-ex/0312009; PHENIX Coll, nucl-ex/0401003
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Dan Magestro, Ohio State University
32
HBT() predictions from hydrodynamics
• Hydro: Freeze-out shape sensitive to lifetime, initial conditions
•
kT dependence probes different regions of space-time source
•
Realistic hydro parameters: Source orientation reflected in HBT()
oscillations
Hydro calculations initialized
with fits to RHIC spectra & v2
Heinz & Kolb, PLB 542 (2002) 216
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Dan Magestro, Ohio State University
33
Fourier coefficients of HBT() oscillations
• 0th-order FC: centrality & kT
dependence mirrors -integrated
analyses; quantitatively consistent
means
relative amplitudes
• Relative amplitudes increase from
central to peripheral collisions
• Freeze-out eccentricity can be estimated from
relative amplitudes
• Blast-wave: rel. amplitudes sensitive to spatial
anisotropy, depend weakly on collective flow
Retiere and Lisa, nucl-th/0312024

R 2y  R 2x
R 2y

R 2x
2
R s2, 2
R s2,0
2
2
R os
,2
R s2,0
 2
R o2, 2
R s2,0
no temporal component
STAR Collaboration, nucl-ex/0312009
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Dan Magestro, Ohio State University
34
Azimuthally sensitive  HBT
• HBT(): probe spatial anisotropy at freeze-out
long  266
Wiedemann, PRC 57 q(1998)
qside
qout
•
Freeze-out shape probes nature & timescale of system evolution
•
Rside
How much (if any) initial spatial deformation
survives system expansion?
2
beam into screen
reaction
hydrodynamic expansion
plane
 = 90°
late rescattering
Rside (small)
Rside (large)
x
time
 = 0°

Initial geometry → aniosotropies in pressure gradients

Preferential in-plane expansion → decreases spatial anisotropy

Freeze-out source shape via HBT → measure of pressure, expansion time
(model-dependent)
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
35
HBT(): Centrality & kT dependence
Au+Au, √s = 200 GeV
STAR Coll., PRL 93 (2004) 012301
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Dan Magestro, Ohio State University
36
Fourier coefficients of HBT() oscillations
• Out-of-plane sources at
freeze-out
•
Pressure and/or expansion
time was not sufficient to
quench initial shape
• From v2 we know...
•
Strong in-plane flow →
significant pressure build-up in
system
STAR Collaboration, nucl-ex/0312009
 Short expansion time plays dominant role
in out-of-plane freeze-out source shapes
Ry
Rx
• Evolution of eccentricity → consistent with  ~ 9 fm
from Rlong Sinyukov fit
ISMD 2004 Sonoma
Dan Magestro, Ohio State University
37
HBT() experimental technique
1. Construct correlation functions for
discrete bins w.r.t. reaction plane angle
qlong 
qside
2. Apply HBT formalism to extract Rij2 vs. 
•
qout
reaction
plane
Additional out-side cross-term
3. Oscillations of Rij2 reflect spatial
anisotropies in system
•
Oscillations governed by geometrical symmetries
Out-of-plane
Rside
 = 90°
2
Rside (small)
Rside (large)
In-plane
 = 0°
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Dan Magestro, Ohio State University
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