Multi-hadron correlations and the space-time structure
of (heavy ion) collisions
Mike Lisa
Ohio State University
Featuring Work of:
Zbigniew Chajeçki, Mercedes López-Noriega, Dan Magestro, Randy Wells
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Outline
• R.H.I.C. / RHIC - what and wherefore?
• geometry and bulk physics in p-space - brief
• ... & in x-space: pion femtoscopy at RHIC
• Au+Au
• d+Au , p+p
• new puzzles, new techniques, global conservation laws
• Summary
mike lisa - University of Rochester nuclear seminar - 4oct2005
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(√SNN, b, Npart, A, B, mT, y, , PID)
• Vary signal ()
• constrain multi-dimensional models
• requires flexible detectors, broad approach
mass
• Vary colliding system
• does physics change?
• requires dedicated program
|b|
• Vary kinematic variables
• dynamics and different regimes
• requires large acceptance
• Vary particle type
• consistent picture?
• unique probe of dynamical structure
pT
• requires good particle identification & acceptance
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Possibilities in a dedicated program: 5 years @RHIC
PHOBOS
PHENIX
1 km
RHIC
BRAHMS
STAR
v = 0.99995c = 186,000 miles/sec
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
AGS
Also: p+p @ 62.4TANDEMS
& 200 GeV
Gunther Roland, QM05
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Possibilities in a dedicated program: 5 years @RHIC
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Also: p+p @ 62.4 & 200 GeV
Gunther Roland, QM05
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Possibilities in a dedicated program: 5 years @RHIC
PHOBOS
PHENIX
RHIC
BRAHMS
STAR
AGS
TANDEMS
STAR ~600 Collaborators
mike lisa - University of Rochester nuclear seminar - 4oct2005
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The STAR Experiment
STAR: Solenoidal Tracker at RHIC
multipurpose detector system for hadronic measurements
Solenoidal
Tracker
At RHIC
• large coverage
(geometrical
acceptance)
• tracking of charged particles in high multiplicity environment
• measure
correlations
of observables
goal: track
“all” charged
hadrons (bags of quarks)
• study ofemitted
hard processes
physics)
in each(jet
collision
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Operation of a Time Projection Chamber
Electric
field
Charged particle flies
thru TPC gas…
“Avalanche” as electrons
approach anode wire...
..generating a cluster
of liberated electrons
Copper pads ~ 1cm2
SCA/ADC
V
DAQ
ADC
Anode wires with +HV
sitting ~5 mm above pads
t
..capacitively inducing
Amplifying and digitizing electronics connected to each
pad
bucket
#
a signal on nearby pads... ..which is amplified, digitized, and recorded for later analysis
mike lisa - University of Rochester nuclear seminar - 4oct2005
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One collision seen by STAR TPC
Momentum determined by track
curvature in magnetic field…
…and by direction relative to beam
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Generating a “deconfined” (?) state
“Present” understanding of
Quantum Chromodynamics (QCD)
• heating
• compression
 deconfined color matter !
Hadronic
Nuclear
Matter
Matter
Quark
Gluon
Plasma
(confined)!
deconfined
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Expectations from Lattice QCD
/T4 ~ # degrees of freedom
deconfined:
many d.o.f.
confined:
few d.o.f.
mike lisa - University of Rochester nuclear seminar - 4oct2005
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The phase diagram of QCD
Temperature
Early universe
critical point ?
quark-gluon plasma
Tc
colour
superconductor
hadron gas
nucleon gas
nuclei
CFL
r0
vacuum
Neutron stars
baryon density
mike lisa - University of Rochester nuclear seminar - 4oct2005
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The phase diagram of QCD
99.5%
Temperature
Early universe
• understanding a theory or
phenomenon (superconductivity...)
 focus on phase transitions
quark-gluon plasma
critical point ?
Tc
• RHIC studies:
partonic condensed matter physics
colour
superconductor
hadron gas
• the crucial feature
of QCD
nucleon
gas (theory):
long-range behaviour
• confinement, etc:
soft-sector crucial
vacuum
nuclei
CFL
r0
?
Neutron stars
baryon density
Au+Au
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Spacetime - the defining aspect of RHI physics
STAR, PRC66 (2002) 034904
STAR, PRL93 (2004) 252301
• Non-trivial space-time - the hallmark of rhic
• Initial state: dominates further dynamics
• Intermediate state: impt element in exciting signals
• Final state:
• Geometric structural scale is THE defining feature of QGP
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Spacetime - the defining aspect of RHI physics
Ann.Rev.Nucl.Part.Sci. 46 (1996) 71
QuickTime™ and a
TIFF (L ZW) d eco mpres sor
are nee ded to s ee this picture.
• Non-trivial space-time - the hallmark of rhic
• Initial state: dominates further dynamics
• Intermediate state: impt element in exciting signals
• Final state:
• Geometric structural scale is THE defining feature of QGP
• Temporal scale sensitive to deconfinement transition (?)
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Is it bulk? Is it a “system?”
1) Superposition of independent p+p:
momenta pointed at random
relative to reaction plane
b
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Is it bulk? Is it a “system?”
1) Superposition of independent p+p:
high
density / pressure
at center
momenta pointed at random
relative to reaction plane
2) Evolution as a bulk system
Pressure gradients (larger in-plane)
push bulk “out”  “flow”
“zero” pressure
in surrounding vacuum
more, faster particles
seen in-plane
b
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Is it bulk? Is it a “system?”
1) Superposition of independent p+p: N
momenta pointed at random
relative to reaction plane
0
/4
/2
0
/4
/2
3/4

3/4

-RP (rad)
2) Evolution as a bulk system
Pressure gradients (larger in-plane)
push bulk “out”  “flow”
more, faster particles
seen in-plane
N
mike lisa - University of Rochester nuclear seminar - 4oct2005
-RP (rad)
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Azimuthal distributions at RHIC
STAR, PRL90 032301 (2003)
b ≈ 6.5 fm
b ≈ 4 fm
“central” collisions
midcentral
collisions
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Azimuthal distributions at RHIC
STAR, PRL90 032301 (2003)
b ≈ 10 fm
b ≈ 6.5 fm
b ≈ 4 fm
peripheral collisions
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Elliptic flow – collectivity
& sensitivity to early system
“Elliptic flow”
STAR, PRL90 032301 (2003)
• evidence of
collective motion
“v2”
• quantified by v2
• geometrical anisotropy
 momentum anisotropy
• sensitive to early pressure
• evidence for
• early thermalization
• QGP in early stage
Hydrodynamic
calculation of
system evolution
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Perfect... ?
mike lisa - University of Rochester nuclear seminar - 4oct2005
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v2 - huge systematics...
Finally, we
understand it!
Just one
event!
Gyulassy 1995
6 decades of E/A
(2 decades of sNN)
Art’s talk. Compiled by
A. Wetzler (2005)
mike lisa - University of Rochester nuclear seminar - 4oct2005
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It starts... ideal hydro: sharp 1st-order rather than lattice EOS ?
P. Houvinen, nucl-th/0505036
Also: Hirano, Gyulassy...
mike lisa - University of Rochester nuclear seminar - 4oct2005
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More direct connection to geometric substructure
• Two-particle correlation functions
probe femtoscopic scales
• “HBT” etc.
mike lisa - University of Rochester nuclear seminar - 4oct2005
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probing source geometry through interferometry
The Bottom line…
p1
r1
x1
  
  to
  i( r  x )p
if a pion is emitted, itis more
likely
i ( r emit
x )p another
1 {
U(x1, p1)e
U(x 2 , p2 )e
 source
T
2
 source
  
 
1 m momentum
r(x) pion with very similar
 the
 if
issmall
i ( r  x )p
i ( r  x )p
1
 U(x 2 , p1)e
5 fm
p2
r2
2
1
1
2
U(x1, p2 )e

2
2
1
*TT  U1*U1  U*2 U 2  1  eiq( x1  x 2 )
experimentally measuring
this enhanced
Creation probability
r(x,p) =probability:
U*U
quite challenging
P(p1, p 2 )
2
C(p1, p 2 ) 
 1 ~
r (q )
P(p1 )P(p 2 )
C (Qinv)
x2
1
1
2
2
}

Width ~ 1/R
2
1
Measurable!
F.T. of pion source
  
q  p 2  p1
mike lisa - University of Rochester nuclear seminar - 4oct2005
0.05
0.10
Qinv (GeV/c)
26
C2(Qinv)
Correlation functions for different colliding systems
STAR preliminary
p+p
R ~ 1 fm
d+Au
Au+Au
R ~ 6 fm
Qinv (GeV/c)
Different colliding systems studied at RHIC
First opportunity to directly compare AA, pp, (&pA)
mike lisa - University of Rochester nuclear seminar - 4oct2005
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More detailed geometry
Relative momentum between pions is a vector q  p1  p 2
 can extract 3D shape information
Rlong – along beam direction
Rout – along “line of sight”
Rside –  “line of sight”
K  p1  p 2
p1
q
Rside
Rout
p2
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Source shape
small RSIDE
6
released from
asymmetric
• Li
“observe”
thean
source
fromtrap
all angles
O’Hara, et al, Science 298 2179 (2002)
relative to the reaction plane
• expect oscillations in radii for
non-round sources
RSIDE
reaction plane
big RSIDE
0
/4
/2
3/4

-RP (rad)
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Measured final source shape
STAR, PRL93 012301 (2004)
Bulk shape evolution
central
collisions
mid-central
collisions
peripheral
collisions
Expected evolution:
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Disintegration timescale
Relative momentum between pions is a vector q  p1  p 2
 can extract 3D shape information
Rlong – along beam direction
Rout – along “line of sight”  increases with emission timescale
Rside –  “line of sight”
K  p1  p 2
p1
q
Rside
Rout
p2
R OUT

R SIDE
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Disintegration timescale - expectation
3D 1-fluid Hydrodynamics
Rischke & Gyulassy, NPA 608, 479 (1996)
with
transition
with
transition
“”
“”
Long-standing favorite signature of QGP:
• increase in , ROUT/RSIDE due to deconfinement  confinement transition
• expected to “turn on” as QGP energy threshold is reached
mike lisa - University of Rochester nuclear seminar - 4oct2005
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HBT puzzle(s)
Heinz & Kolb, hep-ph/0204061
Hirano ‘02
N()
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Why do the radii fall with increasing momentum ??
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Why do the radii fall with increasing momentum ??
It’s collective flow !!
Direct geometrical/dynamical evidence
for bulk behaviour
Amount of flow consistent with p-space
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Flow-dominated model w/ “hand-tuned” short timescales
• Blast-wave model (latest in
long series) reproduces
p- and x-space
• Also non-id, asHBT...
F. Retiere, QM04
F. Retiere & MAL, PRC 70 (2004)
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Bulk size evolution - collisions at 200 GeV
• Au+Au reaction zone:
two-fold expansion
• Preliminary Cu+Cu, d+Au, p+p:
smooth interpolation
• central Cu+Cu = periph Au+Au
• Little expansion for small system
• shorter timescales
or...
• less bulk collectivity...?
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Zbigniew Chajecki QM05
R Z(fm)
1. Heisenberg
uncertainty?
Z0 decay @ LEP
•2.e.g.
G. fragmentation?
Alexander
String
(Lund)
••3.“plausible”
ineffects?
z-direction
pResonance
maybe (??)
T dependence
•• unlikely
in transvrseprobably no
dependence
• mass
e.g. Wiedemann
& DELPHI
Heinz ‘97
[Andersson,
Moriond 2000]
• maybe,
but presumably
 different effect
significantly
femtoscopy in p+p @ STAR
p+p and A+A measured in same
experiment
• great opportunity to compare physics
• what causes pT-dep in p+p?
• same cause as in A+A?
than for Au+Au
R (fm)
• under investigation

K
p 
STAR preliminary
hep-ph/0108194
m, mT (GeV)
mT (GeV)
mike lisa - University of Rochester nuclear seminar - 4oct2005
mT (GeV)
38
Zbigniew Chajecki QM05
3. Resonance effects?
4. Bulk system („hydro”)
in pp?
DELPHI
flow not expected in such
a small system as p+p
R (fm)
e.g. Shuryak: hep-ph/0405066

 Csorgo et al.:
K Buda-Lund
treatment of p+p collision as
d+Au : Rlong doesn’t change
bulk
system
with centrality
p 
(w/ temperature gradients)
hep-ph/0406042
femtoscopy in p+p @ STAR
p+p and A+A measured in same
experiment
• great opportunity to compare physics
• what causes pT-dependence in p+p?
• same causeas in A+A?
1/(2mT)d2n/(dmTdy)
R Z(fm)
1. Heisenberg
uncertainty?
Z0 decay @ LEP
2. String fragmentation? (Lund)
K
p
mT-m (GeV)
RSIDE
ROUT
RLONG
STAR preliminary
hep-ph/0108194
m, mT (GeV)
mT (GeV)
mike lisa - University of Rochester nuclear seminar - 4oct2005
mT (GeV)
mT (GeV)
39
Surprising („puzzling”) scaling
Ratio of (AuAu, CuCu, dAu) HBT
radii by pp
 first-ever pp/AA comparison
yields a surprise!
 similar underlying physics?
HBT radii scale with pp
Scary coincidence
or something deeper?
pp, dAu, CuCu - STAR preliminary
mike lisa - University of Rochester nuclear seminar - 4oct2005
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What the “coincidence” does NOT mean
• pp appears to be blasting system (?!)
• AA ≠(pp)
• would mean local x-p correlations
(giving identical p-space...)
• More like pp = “little AA” !!
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Don’t forget where the “radii” come from...
long-range correlations for small systems
mike lisa - University of Rochester nuclear seminar - 4oct2005
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1D projections: a limited view
STAR PRC71 044906 (2005)
• Usual 1D out-side-long
“Cartesian projections”
Harmonic Decomposition Analysis
• limited view of data
• exploits full out
symmetry of q-space
• ~set of zero measure of 3D CF
• Fit-violating trends may be
hidden
• Salient geometrical effects nontrivially convoluted
• acceptance-dependent (unlike
3D CF)
“Gaussian fit”
• explicit isolation of femtoscopic
(remember: not
(& non-femtoscopic) effects
Gaussian CF)
• full 3D CF seen clearly in few plots
• acceptance-robust (*)
side
long
• Cartesian HD
Danielewicz & Pratt nucl-th/0501003
• Spherical HD
Chajecki,Gutierrez,MAL,Lopez nucl-ex/0505009
mike lisa - University of Rochester nuclear seminar - 4oct2005
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Spherical harmonic decomposition of CF
• Cartesian-space (out-side-long) naturally encodes
physics, but is “inefficient” representation
2
2
2
Q  QOUT
 QSIDE
 QLONG
cos( ) 
• Harmonic Moments -- 1::1 connection to source
geometry
[Danielewicz,Pratt: nucl-th/0501003]
QLONG
QTOT
  arctan
QSIDE
QOUT
• ~immune to acceptance
• full information content at a glance
[thanks to symmetries]
QLONG

Al ,m (| Q |) 
 cos  
4
all.bins
Q


 Yl ,m ( i ,i )C(| Q |, cos  i ,i )
i
QSIDE
QOUT

mike lisa - University of Rochester
Chajecki.,nuclear
Gutierrez,
seminar
MAL,- 4oct2005
Lopez-Noriega, nucl-ex/0505009
44
“Mental calibration” - a Gaussian CF
Chajecki., Gutierrez, MAL, Lopez-Noriega, nucl-ex/0505009
~acceptance free
RL < RT
RL > RT
Simple, Gaussian
source calculations
RO < RS
RO > RS
• Full 3D structure
• (high-L (fine structure) coefficients drop off)
• Different geometrical aspects separate &
use “all” relevant information in the CF
• AL≠0 vanishes in non-femtoscopic region
mike lisa - University of Rochester nuclear seminar - 4oct2005
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STAR Central Au+Au collisions -- Spherical HD
1D o-s-l projections
SH Moments
C(Qout)
A00
A20
C(Qside)

C(Qlong)
Al ,m (| Q |) 
 cos 
4
all.bins


Yl ,m ( i , i )C (| Q |, cos i , i )
A22
i
Chajecki., Gutierrez, MAL
Lopez-Noriega, nucl-ex/0505009
STAR preliminary
mike lisa - University of Rochester nuclear seminar - 4oct2005
46
Baseline problems with smallest systems
STAR preliminary
d+Au peripheral collisions
Gaussian fit
ad hoc, but try it...
mike lisa - University of Rochester nuclear seminar - 4oct2005
47
Try NA22 empirical form
STAR preliminary
d+Au peripheral collisions
Spherical harmonics
NA22 fit
data
L =1
M=0
L =2
M=0
NA22 fit
L =1
M=1
mike lisa - University of Rochester nuclear seminar - 4oct2005
L =2
M=2
48
“account for” constant offset in L=2 components
STAR preliminary
d+Au peripheral collisions
A 00
A 02
Gaussian fit
b
|Q|
Gaussian
|Q|
z
+ constant A02, A22
A 22
also ad-hoc, but with
correct symmetries, “simple” Q-dep
mike lisa - University of Rochester nuclear seminar - 4oct2005
|Q|
49
With L=2 shifts, message remains
STAR preliminary
Ratio of (AuAu, CuCu, dAu) HBT
radii by pp
• Ad hoc formulation not satisfying...
• Detector-induced? No.
• Potential physical non-femtoscopic effects at low multiplicity
• jet-induced? Studies so far: no
• global conservation laws...?
Fit w/o baseline parameterization
NEW fit w/ baseline parameterization
mike lisa - University of Rochester nuclear seminar - 4oct2005
50
EPOS v1.4 (Nexus++)
K. Werner
Conserves momentum...
... somehow
A00
A20
A22
(Gaussian HBT only)
Long-range correlation
not reproduced
mike lisa - University of Rochester nuclear seminar - 4oct2005
51
HEP’s secret weapon: GENBOD (CERNLIB F. James 1968)
A. Stavinskiy, WPCF Aug ‘05
Phasespace weighting
factor - modified by global
conservation laws
3He(e,
+-)X
Unknown (?) in RHI circles !
mike lisa - University of Rochester nuclear seminar - 4oct2005
52
Phasespace distortion
calculation
GenBod...
Only p-conservation
A00
A20
Very promising !!
A22
(Gaussian HBT only)
mike lisa - University of Rochester nuclear seminar - 4oct2005
53
Summary
• Extracting subtle signals at RHIC
• dedicated, systematic, broad program
• comparison to “elementary” p+p crucial
• understanding source of any differences also crucial (e.g. v2 in pp?)
• Bulk, collective physics
•
•
•
•
crucial for QGP study
well-established at RHIC: p- and x-space
really understood at RHIC? (coffee cup time?)
AA is “bulk” : AA ≠ (pp) .... but... AA = K(pp) ? [ pp = AA/K ?]
• pp collisions at RHIC
• first direct comparison HEP with RHI
• x-p correlations indistinguishable from AA - coincidence or deep?
• long-range correlations important
• useful harmonic analysis of CF developed
• accounting for non-femtoscopic correlations - on the way...
mike lisa - University of Rochester nuclear seminar - 4oct2005
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THE
END
mike lisa - University of Rochester nuclear seminar - 4oct2005
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“v2”
pp (non?-)flow
flow
non-flow (?)
mike lisa - University of Rochester nuclear seminar - 4oct2005
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The phase diagram of water
Analogous graphs
• superfluids
• superconductors
• metal/insulator
•…
mike lisa - University of Rochester nuclear seminar - 4oct2005
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