RHI Collisions. Dense Matter. Anisotropic Flow
Sergei Voloshin
Wayne State University
Outline:
- Anisotropic flow as a tool for early dynamics study
- Most important results of recent years:
- Constituent quark scaling
- mass splitting of v2(pt)
- Approaching “hydro limit”
- First results on directed flow and higher harmonics
- Conclusions and what to expect from exp. in the next couple years
How much the nature of hadronization affects anisotropic flow ?
Do we have constituent quark plasma?
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Anisotropic flow. Definitions.
Anisotropic flow  correlations
with respect to the reaction plane
Picture: © UrQMD
X
Term “flow” does not mean
necessarily “hydro” flow – used
only to emphasize the collective
behavior  multiparticle
azimuthal correlation.
Z

b
XZ – the reaction plane
Fourier decomposition of single particle inclusive spectra:
d 3N
d 2N 1

( 1  2v1 cos (φ )  2v2 cos ( 2φ)  ...)
dpt dy dφ dpt dy 2
Directed flow
Elliptic flow
S.V., Y.Zhang, 1994
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Elliptic Flow – a probe for early time physics.
XZ-plane - the reaction plane
y 2  x 2 
ε 2
y  x 2 
Transverse Plane
Y
Sensitive to the physics of constituent
interactions (needed to convert space
to momentum anisotropy) at early times
(free-streaming kills the initial space
anisotropy)
Zhang, Gyulassy, Ko, PL B455 (1999) 45
X
px  py
2
px  py
2
2
v2  
2
v2 > 0,
page
   cos( 2φ )
t (fm/c)
E877, PRL 73 (1994) 2532
3
The characteristic time scale of 2-4 fm is
similar in any model: parton cascade, hydro, etc.
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Elliptic flow as function of …
It is measured vs:
- collision energy
- transverse momentum
- centrality
- particle ID
- Integrated values of
v2 noticeably increase
with energy
- The slope of v2(pt)
increase slowly
 Most of the
increase in integrated
v2 comes from the
increase in mean pt.
Popular view:
In mid and more
central collisions
elliptic flow is well
described by hydro
model, and not by
microscopic transport
models
PHOBOS
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
MPC
(D. Molnar and M. Gyulassy)
AMPT+”string melting”
(Zi-Wei Lin, C.M.Ko)
Elastic scattering, Baseline (HIJING)
parameters:
gg= 3 mb, tr= 1 mb;
1 gluon  1 charged particle;
dNglue/dy=210. opacity = tr dN/dy =210 mb
HIJING x 80
HIJING x 35
HIJING x 13
HIJING x 1
hydro , sBC
Constituent quark plasma:
tr up 2 - 3 (?) times,
dN/dy up > 2 times,
 Could be close to the data…
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“String melting”:
a) # of quarks in the system = # of
quarks in the hadrons
b) “quark” formation time
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Constituent quark model + coalescence
coalescence
fragmentation
Low pt quarks
High pt quarks
S.V., QM2002
D. Molnar, S.V., PRL 2003
Only in the intermediate region (rare processes) coalescence can be
described by:
2
 d 3 nq

d 3 nM
 pq  pM / 2

d 3 pM  d 3 pq


v2, M ( pt )  2 v2, q ( pt / 2)
v2, B ( pt )  3 v2, q ( pt / 3)
In the low pt region density is large and most quarks coalesce:
N
hadron
~N
e Bpt
2
quark
(e Bpt
2
/4
)2
In the high pt region fragmentation eventually wins:
pt n
(( pt / 2)  n ) 2
Taking into account that in coalescence pt , quark  pt , meson / 2
and in fragmentation
pt , quark  pt ,meson / z
,
there could be a region in quark pt where only few quarks coalesce, but give hadrons
in the hadron pt region where most hadrons are produced via coalescence.
Side-notes:
a) more particles produced via coalescence vs parton
fragmentation  larger mean pt…
b)
 higher baryon/meson ratio
c)
 lower multiplicity per “participant”
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6
-> D. Molnar, QM2004, in progress
-> Bass, Fries, Mueller. Nonaka; Hwa; Levai, Ko; …
-> Eremin, S.V.
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
dNch/dy vs. number of participants
Open symbols: our calculation of Npart
 qq  6 mb - open symbols
 qq  42 / 9 mb - solid symbols
S. Eremin, S.V., PRC 67, 064905( 2003)
Scaled by number of nucleon participants.
The dependence usually explained by a
combination of ‘soft’ and ‘hard’ physics
The ratio Nch/Nq-part slightly
decreases with centrality !
Scaled by number of quark participants
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Constiuent quark scaling: v2 and RCP
- Constituent quark scaling holds very well.
Deviations are where expected.
- Elliptic flow saturates at pt ~ 1 GeV, just at
constituent quark scale. An accident?
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
v2(pt) dependence on mass. Blast wave model.
v1(pt) - S.V., PRC 55 (1997) 1630
v2(pt) - Houvinen, Kolb, Heinz, Ruuskanen, S.V., PLB 503 (2001) 58
Parameters:
T – temperature
0 - radial expansion rapidity
2 - amplitude of azimuthal
variation in expansion rapidity
v2(pt) - STAR Collaboration,
PRL 87 (2001) 182301

STAR
Elementary source density -
 1 2s 2 cos( 2φs )
T (MeV)
0
a
S2
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9
dashed
135  20
solid
100  24
0.52  0.02
0.54  0.03
0.09  0.02 0.04  0.01
0.0
0.04  0.01
- model fits data well
- shape (s2 parameter) agrees with the
interferometry measurements
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
v2(pt) at 200 GeV. Comparison to hydro.
Data: PHENIX, Nucl. Phys.
A715, 599 (2003)
Hydro: P. Huovinen et al., Phys.
Lett. B503, 58 (2001);
Houvinen, Heinz, Kolb
Mass splitting depends on EoS!
Caveats:
- centrality bins are very wide
- Initial conditions are chosen independently
for spectra and v2 descriptions
Mass dependence is well reproduced by
hydrodynamical model calculations,
but can it also be accounted for in the constituent
quark coalescence picture?
(heavier particle  larger difference in
constituent quark momenta)
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
v2 / 
Hydro limits
SPS 40 GeV/A
SPS
RHIC 160 GeV/A
Hydro: P.F. Kolb, et al
Suppressed scale!
Hydro: v2~ 
Ollitrault, PRD 46 (1992) 229
11
Heinz, Kolb, Sollfrank
Low Density Limit: v2~  dN/dy / S
Heiselberg & Levy, PRC C59 (1999) 2716
Questions to address:
- is it saturating?
- rapidity dependence? (next slide)
- what happens at SPS energies? Any ‘wiggle’?
page
b (fm)
v 2  0.04 0.04*
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
dN
/ 3000
dy
S.A. Voloshin
PHOBOS: rapidity dependence
PRL 91, 052303 (2003)
Steinberg, nucl-ex/0105013 (QM01)
(nucl-ex/0406021)
The detailed study of the rapidity dependence
is still to be made, but it looks like v2()
follows very closely dN/d.
Low Density Limit?
Difficulty: ()
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
v2/ and phase transitions
Original ideas: Sorge, PRL 82 2048 (’99), Heiselberg & Levy, PRC 59 2716 (’99)
S.V. & A. Poskanzer, PLB 474 (2000) 27
Uncertainties:
Hydro limits: slightly depend
on initial conditions
Data: no systematic errors,
shaded area –uncertainty in
centrality determinations.
Curves: “hand made”
“Cold” deconfinement?
E877 NA49
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
“Cold” deconfinement, color percolation?
Percolation point by H. Satz
Could it be constituent quark
deconfinement ?
CERN SPS energies
RHIC:
b ~ 7 fm
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b ~ 4 fm
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Charged particle v2 at high-pt
phenix preliminary
nucl-ex/0305013
Above 6 – 8 GeV we do not have a reliable answer
(yet) for the magnitude of the elliptic flow
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Elliptic flow at intermediate pt (jet quenching ?)
STAR, Au+Au, 200 GeV
Hard shell
Hard sphere
Woods-Saxon
Hard shell
== box density profile (+) extreme quenching
E. Shuryak, nucl-th/0112042
Hard sphere == -”- (+) realistic quenching
Woods-Saxon == WS density profile (+) realistic quenching
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Directed flow at RHIC: (Limiting fragmentation, etc.)
Directed flow is most sensitive
to the initial conditions
v1
Looking for the ‘wiggle’:
rapidity
R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu,
PRL 84 (2000) 2803
x
z
x
STAR Preliminary
Baryon stopping
rapidity

A. Tang, HQ2004
x
Radial flow
px

 <x px>
>
0
px, v1
rapidity
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17
“wiggle”
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
v4, v6 @ 200 GeV
STAR, PRL 92, 062301 (2004)
1.4 v22
P. Kolb, hydro
Detailed comparison of the event shape:
not really described by any model
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
SUMMARY
OBSERVATION:
- Anisotropies are strong at RHIC
- The magnitude of elliptic flow is close to hydro predictions (for rather central collisions)
- The mass splitting in v2(pt) finds natural explanation in hydro model. The magnitude
of the splitting requires QGP EoS.
- In the intermediate pt region the constituent quark number scaling is observed.
- No model describes all the details…
QUESTIONS:
-
How well hydro models describe both, spectra and v2, simultaneously?
How much ‘coalescence enhancement’ is reflected in ‘hydro limits’?
‘Mass splitting’ at low pt – is the hydro explanation unique?
Constituent quark plasma picture – is it supported by theory / lattice QCD?
What is the relation to color percolation? Do we have ’cold deconfinement’?
WHAT TO EXPECT:
- Elliptic flow of open charm. Does c-quark flow?
- Elliptic flow of resonances. Check regeneration in the hadronic phase vs direct production
- Elliptic flow up to 10-12 GeV with good accuracy. Check jet quenching mechanism.
- Directed flow of identified particle. Baryon stopping, tilted source.
- Two particle correlation wrt Reaction Plane. Jets, tilted source
- Anisotropic flow in lighter systems (Cu+Cu?). Low Density Limit?
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
2-particle correlations wrt RP
d 2N
( x1 , x2 ; RP ) x – azimuthal angle, transverse
momentum, rapidity, etc.
dx1dx2
CERES, PRL, 2003
Approach: - “remove” flow contribution
- parameterize the shape of what is left
- study RP orientation dependence of the
parameters
Selection of one (or both) of
particles in- or out- of the reaction
plane “distorts” the RP determination
J. Bielcikova, P. Wurm, K. Filimonov
S. Esumi, S.V., PRC, 2003
flow
dN pairs
da ,b
1  2v2,b v2in,a,out cos( 2a ,b )
“a” == “trigger particle”
v2in 
 v2  2
  4v2
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v2out 
 v2  2
  4v2
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Azimuthal correlations from pp to AuAu
AuAu (flow + non-flow)
pp (non-flow)
In VERY
peripheral
collisions,
azimuthal
correlation
in AuAu are
dominated
by non-flow.
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
At high pt in
central
collisions,
azimuthal
correlation in
AuAu could
be dominated
by nonflow.
S.A. Voloshin
“Wiggle”, Pb+Pb, Elab=40 and 158 GeV
Preliminary
v1
<0
158 GeV/A
The “wiggle” is there!
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22
Note different scale for 40 and 158 GeV!
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Centrality dependence. Hydro + RQMD.
Teaney, Lauret, Shuryak nucl-th/0110037
200
400
600
800
dNch/dy
LH8  latent heat = 0.8 GeV/fm^3
Pt slope parameters are about 20% larger
in hydro compared to data
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- v2 increases with dN/dy
- Centrality dependence – close to data
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Talks:
NA49 – A. Wetzler
2
NA45 – J. Slivova
STAR- K. Filimonov
PHENIX – S. Esumi
PHOBOS – S. Manly
v (pT), low transverse momentum
CERES/NA45
STAR
0-55%
30-80%
10-30%
0-10%
Preliminary
24-30%
0-12.5%
12.5-23.5%
>23.5%
1.
2.
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Lines: horizontal – v2=0.1
vertical - pt=1 GeV/c
For midcentral collisions, v2(pt) is quite similar between SPS and RHIC
For “central” collisions NA49 results are lower than STAR
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
Directed flow “wiggle” in cascade models
R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003
R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu,
PRL 84 (2000) 2803
RQMD v2.4
x
z
x
Baryon stopping
rapidity
x

Radial flow
px
UrQMD: Bleicher, Stocker, PRB 526 (2002) 309
Should be better pronounced at higher energies
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
 <x px>
px, v1
“wiggle”
rapidity
International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin
>
0
v1
Hydro: “antiflow”, “third flow component”
Csernai, Rohrich, PLB 458 (1999) 454.
Magas, Csernai, Strottman, hep-ph/0010307
rapidity
Brachmann, Soff, Dumitru, Stocker, Maruhn, Greiner
Bravina, Rischke , PRC 61 (2000) 024909
Net baryon
density
flow
antiflow
- Strongest at the softest point ?
- The same for pions and protons ?
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International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004
S.A. Voloshin