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
Zimanyi Memorial Workshop July
2007
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Present situation:
a) Multiplicity of stable hadrons made of (u,d,s) is
described by thermal models
b) Multiplicity of unstable hadrons can be understood in
terms of hadronic final state interactions
c) Slopes difficult to interpret due to the many hadronic
interactions (however the successful coalescence
models hints towards a v2 production in the plasma)
d) 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)
Zimanyi Memorial Workshop July
2007
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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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2007
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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
(hard) production of heavy
quarks in initial NN collisions
Quarkonia formation in
QGP through c+cY+g
fusion process
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2007
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Individual heavy quarks follow Brownian motion: we can
describe the time evolution of their distribution by a
Fokker – Planck equation:

 
 
f  

A f  B f
p
t  p
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
py
Evolution of one c quark inside a
m=0 -- T=400 MeV QGP.
Starting from p=(0,0,10 GeV/c).
px
Evolution time = 30 fm/c
 p z f
… looks a little less
« erratic » when considered
on the average:
Relaxation time >> collision
time : self consistent
Zimanyi Memorial Workshop July
2007
t (fm/c)
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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 κ factor to study
the physics
Similar for the diffusion coefficient
Bνμ ~ << (pν - pνf )(pμ - pμf )> >
A describes the deceleration of the c-quark
B describes Zimanyi
the thermalisation
Memorial Workshop July
2007
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c-quarks transverse momentum distribution (y=0)
Heinz & Kolb’s hydro
Distribution just before hadronisation
p-p
distribution
kcol 5
k40
k20
k10
Zimanyi Memorial Workshop July
2007
Plasma will not
thermalize the c:
It carries
information
on the QGP
8
Energy loss and A,B are related (Walton and Rafelski)
pi Ai + p dE/dx = - << (pμ – pμf)2 >>
which gives easy relations for pc>>mc and pc<<mc
dE/dx and A are of the same order of magnitude
A (Gev/fm)
T=0.5
dE/dx (GeV/fm)
T=0.4
T=0.3
T=0.2
p (GeV/c)
Zimanyi Memorial Workshop July
2007
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
Zimanyi Memorial Workshop July
2007
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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 temperatureZimanyi
we pick
aWorkshop
u/d quark
with the a
Memorial
July
thermal distribution) but other2007scenarios possible.
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Leptons ( D decay) transverse momentum distribution (y=0)
RAA
Comparison to B=0 calculation
2 2 only
1
Langevin A and B finite
0.8
κ = 20, κ=10
0.6
0-10%
0.4
0.2
1
2
3
B=0 (Just deceleration)
4
5
pt
Conclusion I:
Energy loss alone is not sufficient
Kcol(coll only) =10-20:Zimanyi
Still
far away from thermalization
!
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2007
There is a more recent data set
Star and Phenix agree
(Antinori SQM 07)
RAA lept
1.4
1.2
Au Au; 0 10% central
1
0.8
0.6
K 10
0.4
0.2
K 20
2
4
6
8
PT GeV c
Latest Published Phenix Data nucl-ex/0611018
Zimanyi Memorial Workshop July
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"Radiative« coefficients
« radiative » coefficients deduced using the elementary
cross section for cQ cQ+g and for cg  cg +g in t-channel
(u & s-channels are suppressed at high energy).
ℳq
cqg ≡
c
Q
+
dominant
+
+
+
suppresses by Eq/Echarm
if evaluated in the large pic+ limit in the lab
:
(Bertsch-Gunion)
Zimanyi Memorial Workshop July
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x=long. mom. Fraction of g
Evaluated in scalar QCD and in the limit of Echarm >> masses and >>qt
Factorization of radiation and elastic scattering
k
In the limit of vanishing masses:
Gunion + Bertsch PRD 25, 746
But:
q
Masses change the radiation
substantially
Zimanyi Memorial Workshop July
2007
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Leptons ( D decay) transverse momentum distribution (y=0)
(large sqrts limit)
RAA
0-10%
1.4
20-40%
1.4
1.2
1.2
Col.+(0.5x) Rad
1
1
0.8
0.8
0.6
Col. (kcol=10 & 20) 0.6
0.4
0.4
0.2
0.2
2
4
6
8
2
4
6
8
pt
Conclusion II:
1.4
Min bias
1.2
1
One can reproduce the RAA either :
• With a high enhancement factor for
collisional processes
0.8
0.6
0.4
0.2
2
4
• With « reasonnable » enhancement
factor (krad not far away from unity)
6
8
Zimanyi
Memorial
Workshop
July radiative processes.
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including
2007
pt
pt
Non-Photonic Electron elliptic-flow at RHIC:
comparison with experimental results
v2
0.1
c-quarks
Collisional
(kcol= 20)
decay e
0.05
0.5
1
1.5
2
2.5
3
3.5
4
Collisional + Radiative
v2
Freezed out according to thermal
distribution at "punch" points of c
quarks through freeze out surface:
pt
0.05
D
Tagged
const q
D
q
c
0.1
Conclusion III:
0.05
0.5
0.05
1
1.5
2
One cannot reproduce the v2
consistently with the RAA!!!
2.5
3
3.5
4
Contribution of light quarks to the
Zimanyi Memorial Workshop
July flow of D mesons is small
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elliptic
pt
2007
Non-Photonic Electron elliptic-flow at RHIC: Looking
into the bits…
const quark
tagged by c
0.1
0.05
0.15
0.125
0.1
0.075
0.05
0.025
v2 (all p)
v2 (tagged p)
0.5
0.5
1
1.5
2
2.5
3
3.5
1
1.5
2
2.5
3
4
0.05
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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This is a generic problem !
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
Only ‘exotic hadronization
mechanisms’ may explain the
large v2
Zimanyi Memorial Workshop July
2007
EXPERIMENT 19
?
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
D0,
D0
Large discrepancy between Star
and Phenix
BR 17.2
(X  1.9
e) in
%
Zimanyi Memorial Workshop July
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D+,
D-
Ds+
Ds-
c+
c-
6.71 8 +6- 4.5 
5
1.7

0.29
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Azimutal Correlations for Open Charm
D
Transverse plane
c
What can we learn about the
"thermalization" process from the
correlations remaining at the end of
QGP ?
Initial correlation (at RHIC);
supposed back to back here
c-bar
Dbar
SQM06
How does the coalescence fragmentation mechanism affects
the "signature" ?
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2007
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Azimutal Correlations for Open Charm
Small pt (pt < 1GeV/c )
No interaction
Coll (kcol= 1)
Coll + rad (kcol= krad = 1)
Coll (kcol= 10)
Coll (kcol= 20)
8
7
6
0-10%
c-quarks
5
4
3
2
1
1
8
2
3
4
coalescence
5
6
jc - jcbar
7
6
Correlations are small at small pt,, mostly
washed away by coalescence process.
D
5
4
3
2
1
1
SQM06
2
3
4
5
6
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Azimutal Correlations for Open Charm
Average pt (1 GeV/c < pt < 4 GeV/c )
No interaction
Coll (kcol= 1)
Coll + rad (kcol= krad = 1)
Coll (kcol= 10)
Coll (kcol= 20)
8
7
6
c-quarks
0-10%
5
4
3
2
1
1
2
3
4
coalescence
5
6
jc - jcbar
8
7
D
6
Conclusion IV: Broadening of the
correlation due to medium, but still
visible. Results for genuine coll + rad and
for cranked up coll differ significantly
5
4
3
2
1
1
SQM06
2
3
4
5
6
Azimutal correlations might help
identifying better the thermalization
process and thus the medium
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jDZimanyi
- jDbar
2007
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Azimutal Correlations for Open Charm
Large pt (4 GeV/c < pt )
No interaction
Coll (kcol= 1)
Coll + rad (kcol= krad = 1)
Coll (kcol= 10)
Coll (kcol= 20)
0.5
0.4
c-quarks
0-10%
0.3
0.2
0.1
1
0.5
2
3
coalescence
0.4
4
jc - jcbar
5
6
Large reduction but small broadening for
increasing coupling with the medium;
compatible with corona effect
D
0.3
0.2
0.1
1
SQM06
2
3
4
6 Memorial Workshop July
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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 k=10 or by including radiative
processes.
•
Still a lot to do in order to understand the v2. Possible
explanations for discrepancies are:
1) spatial distribution of initial c-quarks
2) Part of the flow is due to the hadronic phase subsequent to QGP
3) Reaction scenario different
4) Miclos Nessi (v2, ,azimuthal correlations???)
Azimutal correlations could be of great help in order to
Memorial Workshop July
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identify the nature Zimanyi
of thermalizing
mechanism.
2007
V2 -- Au+Au -- 200 -- Min. Bias
v2 lept
0.12
min. bias
0.1
0.08
0.06
0.04
0.02
K 10
0.5
1
1.5
2
K 20
2.5
3
3.5
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PT GeV c
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