Prsentation PowerPoint

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Tomography of a Quark Gluon Plasma by Heavy
Quarks
P.-B. Gossiaux , V. Guiho, A. Peshier J.
Aichelin Subatech/ Nantes/
France Zimanyi 75
Memorial Workshop
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• Present situation
• Multiplicity of stable hadrons made of (u,d,s) is
  
• described by thermal models
• Multiplicity of unstable hadrons can be
  understood in
• terms of hadronic final state interactions
• Slopes difficult to interpret due to the many
  hadronic
• interactions (however the successful
  coalescence
• models hints towards a v2 production in the
  plasma)
• Electromagnetic probes from plasma and hadrons
• rather similar
• If one wants to have direct information of the
  plasma one
• has to find other probes
• Good candidate hadrons with a c or b quark
• Here we concentrate on open charm mesons for
  which
• indirect experimental data are available (single
  electrons)

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Why Heavy Quarks probe the QGP
Idea Heavy quarks are produced in hard
processes with a known initial momentum
distribution (from pp). If the heavy quarks
pass through a QGP they collide and radiate and
therefore change their momentum. If the
relaxation time is larger than the time they
spent in the plasma their final momentum
distribution carries information on the plasma
This may allow for studying plasma properties
using pt distribution, v2 transfer, back to
back correlations
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Schematic view of our model for hidden and open
heavy flavors production in AA collision at RHIC
and LHC
Evolution of heavy quarks in QGP (thermalization)
D/B formation at the boundary of QGP through
coalescence of c/b and light quark
Quarkonia formation in QGP through cc?Yg fusion
process
(hard) production of heavy quarks in initial NN
collisions
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Individual heavy quarks follow Brownian motion
we can describe the time evolution of their
distribution by a Fokker
Planck equation
Input reduced to Drift (A) and Diffusion (B)
coefficient. Much less complex than a parton
cascade which has to follow the light particles
and their thermalization as well. Can be
combined with adequate models like hydro for the
dynamics of light quarks
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From Fokker-Planck coefficients ? Langevin forces
pz
Evolution of one c quark inside a m0 -- T400
MeV QGP. Starting from p(0,0,10 GeV/c).
Evolution time 30 fm/c
py
px
looks a little less  erratic  when considered
on the average
Relaxation time gtgt collision time self
consistent
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The drift and diffusion coefficients
Strategy take the elementary cross sections for
charm and calculate the
coefficients (g thermal distribution of
the collision partners)
and then introduce an overall ? factor to
study the physics Similar for the diffusion
coefficient B?µ ltlt (p? - p?f
)(pµ - pµf )gt gt A describes the deceleration
of the c-quark B describes the
thermalisation
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c-quarks transverse momentum distribution (y0)
Heinz Kolbs hydro
Distribution just before hadronisation
Plasma will not thermalize the c It carries
information on the QGP
kcol 5
k40
k10
k20
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• Energy loss and A,B are related (Walton and
  Rafelski)
• pi Ai p dE/dx - ltlt (pµ pµf)2 gtgt
• which gives easy relations for pcgtgtmc and pcltltmc
• dE/dx and A are of the same order of magnitude

A (Gev/fm)
dE/dx (GeV/fm)
T0.5
T0.4
T0.3
T0.2
p (GeV/c)
p (GeV/c)
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• In case of collisions (2 ?2 processes)
  Pioneering work of Cleymans (1985), Svetitsky
  (1987), extended later by Mustafa, Pal
  Srivastava (1997).
• Later Teaney and Moore, Rapp and Hees similar
  approach but plasma treatment is different
• For radiation Numerous works on energy loss
  very little has been done on drift and diffusion
  coefficients

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Input quantities for our calculations
Au Au collision at 200 AGeV

• . c-quark transverse-space distribution according
  to Glauber
• c-quark transverse momentum distribution as in
  d-Au (STAR) seems very similar to p-p ? No
  Cronin effect included to be improved.
• c-quark rapidity distribution according to
  R.Vogt (Int.J.Mod.Phys. E12 (2003) 211-270).
• Medium evolution 4D / Need local quantities
  such as T(x,t) ? taken from hydrodynamical
  evolution (Heinz Kolb)
• D meson produced via coalescence mechanism. (at
  the transition temperature we pick a u/d quark
  with the a thermal distribution) but other
  scenarios possible.

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Leptons (? D decay) transverse momentum
distribution (y0)
RAA
Comparison to B0 calculation
2 ?2 only
Langevin A and B finite
? 20, ?10
0-10
pt
B0 (Just deceleration)
Conclusion I Energy loss alone is not
sufficient Kcol(coll only) 10-20 Still far away
from thermalization !
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There is a more recent data set
Star and Phenix agree (Antinori SQM 07)
Latest Published Phenix Data nucl-ex/0611018
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"Radiative  coefficients
 radiative  coefficients deduced using the
elementary cross section for cQ ?cQg and for cg
? cg g in t-channel (u s-channels are
suppressed at high energy).
dominant
suppresses by Eq/Echarm
if evaluated in the large pic limit in the lab
(Bertsch-Gunion)

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xlong. mom. Fraction of g
Evaluated in scalar QCD and in the limit of
Echarm gtgt masses and gtgtqt Factorization of
radiation and elastic scattering
In the limit of vanishing masses Gunion
Bertsch PRD 25, 746 But Masses change the
radiation substantially
k

q
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Leptons (? D decay) transverse momentum
distribution (y0)
(large sqrts limit)
RAA
0-10
20-40
Col.(0.5x) Rad
Col. (kcol10 20)
pt
pt

• Conclusion II
• One can reproduce the RAA either
• With a high enhancement factor for
  collisional processes
• With  reasonnable  enhancement factor (krad
  not far away from unity) including radiative
  processes.

Min bias
pt
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Non-Photonic Electron elliptic-flow at RHIC
comparison with experimental results
Collisional (kcol 20)
v2
Tagged const q
Freezed out according to thermal distribution at
"punch" points of c quarks through freeze out
surface
pt
Collisional Radiative
v2
Conclusion III One cannot reproduce the v2
consistently with the RAA!!! Contribution of
light quarks to the elliptic flow of D mesons is
small
pt
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Non-Photonic Electron elliptic-flow at RHIC
Looking into the bits
v2 (all p)
const quark tagged by c
v2 (tagged p)
C-quark does not see the  average  const quark
Why ?
Bigger coupling helps a little but at the cost
of RAA
SQM06
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Van Hees and Rapp Charmed resonances
and Expanding fireball (does not reproduce non
charmed hadrons) Communicate more efficiently v2
to the c- quarks Moore and Teaney Even choice
of the EOS which dives the largest v2
possible does not predict non charmed hadron data
assuming D mesons
This is a generic problem !
Only exotic hadronization mechanisms may
explain the large v2
EXPERIMENT ?
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Problems on exp. side
X. Lin SQM07
RAA is about 0.25 for large pt for Star and
Phenix Confirms that large diffusion
coefficients are excluded Actual problems -- D
/ ?c ratio (Gadat SQM07) -- B contribution
Large discrepancy between Star and Phenix
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Azimutal Correlations for Open Charm
Transverse plane
What can we learn about the "thermalization"
process from the correlations remaining at the
end of QGP ?
D
c
c-bar
How does the coalescence - fragmentation
mechanism affects the "signature" ?
Dbar
SQM06
-
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Azimutal Correlations for Open Charm
Small pt (pt lt 1GeV/c )
No interaction
Coll (kcol 1)
0-10
c-quarks
jc - jcbar
coalescence
Correlations are small at small pt,, mostly
washed away by coalescence process.
D
jD - jDbar
SQM06
-
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Azimutal Correlations for Open Charm
Average pt (1 GeV/c lt pt lt 4 GeV/c )
No interaction
Coll (kcol 1)
0-10
Conclusion IV Broadening of the correlation due
to medium, but still visible. Results for genuine
coll rad and for cranked up coll differ
significantly
jc - jcbar
coalescence
Azimutal correlations might help identifying
better the thermalization process and thus the
medium
jD - jDbar
SQM06
-
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Azimutal Correlations for Open Charm
Large pt (4 GeV/c lt pt )
No interaction
Coll (kcol 1)
c-quarks
0-10
jc - jcbar
coalescence
Large reduction but small broadening for
increasing coupling with the medium compatible
with corona effect
D
jD - jDbar
SQM06
-
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Conclusions

• Experimental data point towards a significant
  (although not complete) thermalization of c
  quarks in QGP.
• The model seems able to reproduce experimental
  RAA, at the price of a large rescaling K-factor
  (especially at large pt), of the order of k10 or
  by including radiative processes.
• Still a lot to do in order to understand the v2.
  Possible explanations for discrepancies are
• spatial distribution of initial c-quarks
• Part of the flow is due to the hadronic phase
  subsequent to QGP
• Reaction scenario different
• Miclos Nessi (v2, ,azimuthal correlations???)
• Azimutal correlations could be of great help
  in order to identify the nature of thermalizing
  mechanism.

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V2 -- AuAu -- 200 -- Min. Bias
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