Ridges%20and%20v2%20without%20hydrodynamics

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Ridges and v2 without hydrodynamics

• Rudolph C. Hwa
• University of Oregon

Intnal Symposium on Multiparticle
Dynamics Berkeley, August 2007
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Prevailing paradigm on azimuthal asymmetry in
heavy-ion collisions at low pT is hydrodynamical
flow.
Calling v2 elliptic flow is a distinctive mark
of that paradigm.
What if hydrodynamics is found invalid at early
times?
Are there any alternatives? Why bother?
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Results on single-particle distributions from
hydro
RHIC 130 GeV
Kolb Heinz, QGP3
?00.6 fm/c (RHIC 130, 200), ?00.8 fm/c (SPS 17)
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Elliptic flow -- v2
Agree with data for pTlt1.5GeV/c possible only if
?00.6 fm/c
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Conventional wisdom
Azimuthal anisotropy can be understood in terms
of hydrodynamical flow for pTlt1.5 GeV/c
It requires fast thermalization. ?00.6 fm/c
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Conventional wisdom BNL-PR
strongly interacting QGP perfect liquid
What is the direct experimental evidence that
either verifies or falsifies the conclusion on
perfect liquid?
Not expected nor understood in QCD.
Instability?
What if ?01-1.5 fm/c? If so, then the
hydro results would disagree with data. How
much of sQGP and perfect liquid can still be
retained?
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Alternative approach

• must be sensitive to the initial configuration
  (hard)
• must be able to describe the bulk behavior
  (soft)

For pTlt1.5 GeV/c (the region that hydro claims
success) we consider semi-hard scattering
Semi-hard parton qT 2-3 GeV/c (??0.1 fm/c) can
have significant effect on thermal partons for
pTlt1.5 GeV/c.
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Ridgeology
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Jet structure
R
J
Putschke, QM06
ridge R Jet J
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In a high pT jet, a hard- scattered parton near
the surface loses energy to the medium.
Power-law behavior is a sign of Jet production
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? puzzle
Blyth (STAR) SQM 06
?? distribution of associated particles shows
what seems like jet structure.
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The ? puzzle is solved by recognizing that the ?
trigger and its associated particles are all
produced by the thermal partons in the ridge.
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Putschke, QM06
Jet
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Summary of ridgeology

• Ridges are the recombination products of
  enhanced thermal partons stimulated by
  semi-hard scattering near the surface.
• At low pT there can be ridges without Jets
  (peaks).

The ridge would not be there without a semi-hard
scattering, but it does not appear as a
usual jet.

It is a Jet-less jet.
Ridges of low pT hadrons are there, with or
without triggers, so long as there are semi-hard
partons near the surface to generate enhanced
thermal partons.
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Azimuthal Asymmetry
Now to
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Relevant physics must be sensitive to the
initial configuration.
Phantom jets are produced at early times, if hard
enough, but should be soft enough so that there
are many of them produced in each collision.
(That is not true at large forward ?.)
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Each scattering sends semi-hard partons in random
directions.
Initial configuration
Recoil partons thermalize the bulk medium.
If the phantom jets are soft enough, there are
many of them, all restricted to ? lt ?.
Thermalization of partons takes time, but the
average direction of each ridge is determined at
initial time.
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Bulk
partons
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v2
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Use ?T45 MeV
T0.29 GeV
Get T2.12 GeV
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Centrality dependence
?(b)cos-1 b/2R
at pT0.5 GeV/c Maxv2pT/?T0.075
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STAR Au-Au at 130 GeV
PRC 66, 034904 (2002)
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Normalized impact parameter
?b/2R
sin2?(b) ? f(?) sin(2cos-1?)
STAR data on v2 for Au-Au at 130GeV, normalized
to 1 at max ?1/v2
f(?) is universal, so it should be the same for
Cu-Cu and at other vs.
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Nouicer (PHOBOS) QM06
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Proton
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pT for pion mT-mp for proton
Transverse kinetic energy EK
A property that is independent of the hadron
species h. T is a property of the partons that
recombine.
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KET Scaling
PHENIX preliminary
Baryons
Mesons
R.Lacey, ETD-HIC 07
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Mid-rapidity region
Forward rapidity

• Semi-hard scattering involve small x partons
• more phantom jets
• many ridges

?gt0

• larger x partons, thus lower multiplicity
• fewer phantom jets
• ridge effect reduced

?0
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Conclusion

• Azimuthal anisotropy is mainly a ridge effect.
  No fast thermalization or hydrodynamical flow are
  needed.
• Hydrodynamics may still be applicable after
  some time, but it is not needed for v2, for which
  the relevant physics at ?lt1 fm/c is crucial ---
  semi-hard scattering at qTlt3.
• For pTlt1.5 GeV/c, the analysis is simple, and
  the result can be expressed in analytic form that
  agrees with data.
• For pTgt1.5 GeV/c, shower partons must be
  considered. Jet dominance (gt3GeV/c) will saturate
  v2.
• No part of the study suggests that the medium
  behaves like a perfect fluid.

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EXTRA SLIDES
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In peripheral collisions there are some
complications. It is harder to produce protons
in the bulk because of lower density of soft
partons. (remember pp collisions) Thermal parton
distributions in Fuud are not factorizable. T in
B(pT) is lower.
Thus phantom jets are relatively more effective
in enhancing the thermal partons for p production
at large b.
So B(pT)/R(pT) for proton is smaller than for pion
Hence, v2(pT,b) continues to increase for ?(b)
smaller than ?/4.
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How universal is ?
Ridge phenomenology is rudimentary, and at low pT
there is no unreliable framework to do
theoretical calculation.
Enhanced thermal partons in the ridge T/T1?
Since the bulk T encapsules the dependences on
energy, system size, thermalization,
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PHOBOS PRL 94, 122303 (2005)
v2 at all ? and various s
? ln x for some ltmTgt
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BRAHMS has pT dependence at ?3.2
nucl-ex/0602018
Recombination of thermal partons in comoving
frame at ?.
Exponential
Ridge due to semi-hard parton at ?gt ? of bulk.
R/B decreases with increasing x as a
function of F(x).
v2 ? R/B decreases with increasing ? as a
function of F(x), thus exhibiting a scaling
behavior.