Prsentation PowerPoint

1
Tomography of a Quark Gluon Plasma by Heavy
Quarks
P.-B. Gossiaux , V. Guiho J. Aichelin
Subatech/ Nantes/ France
I)Why? II) Approach and ingredients II) Results
for RAA III) Results for v2 IV) Azimuthal
correlations V) Conclusions
2
Schematic view of hidden and open heavy flavor
production in AA collision at RHIC and LHC
Evolution of heavy quarks in QGP (thermalization)
D/B meson 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
3
Heavy quarks in QGP (or in strongly interacting
matter)
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
4
Single trajectories and mean values
Evolution of one c quark inside a m0 -- T400
MeV QGP. Starting from p(0,0,10 GeV/c).
Evolution time 30 fm/c True Brownian motion
pz
py
px
looks very smooth when averaged over many
trajectories .
Relaxation time gtgt collision time
5
When individual heavy quarks follow Brownian
motion we can describe the time evolution of
their distribution by a
Fokker Planck equation
Input reduced to a Drift (A) and a Diffusion
(B) coefficient. Much less complex than a parton
cascade which has to follow the light particles
and their thermalization as well. Can be
calculated using adequate models like hydro for
the dynamics of light quarks
6
The drift and diffusion coefficients
Strategy take the elementary cross sections for
charm/bottom elastic scattering and use a
Vlasov equation to calculate the coefficients (g
thermal distribution of the collision partners)
and the introduce an overall ? factor 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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• 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 Ecgtgtmc and Ecltltmc
• In case of collisions (2 ?2 processes)
  Pioneering work of Cleymans (1985), Svetitsky
  (1987), extended later by Mustafa, Pal
  Srivastava (1997). Teany 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

8
First results on c-quark evolution
E
Relaxation of ltEgt, of and of
for c-quarks produced in 200 GeV
collisions. Evolution in a m0 , T200 MeV QGP.
long relaxation times
60
100
0
Time (fm/c)
f(E)
Approximate scaling for T0.2 ? 0.5
Typical times 60 fm/c Asymptotic energy
distribution not Boltzmann more like a Tsallis
Walton Rafelski (1999) Too much diffusion at
large momentum
(E-m)/T
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The collisional transport
coefficients of charm
A (Gev/fm)
dE/dx (GeV/fm)
T0.5
T0.4
T0.4
T0.3
T0.2
p (GeV/c)
p (GeV/c)
B? (GeV2/fm c)
B// (GeV2/fm c)
p (GeV/c)
p (GeV/c)
10
The transport coefficients used in the
calculation
Two sets parameters

• Coefficients deduced by Mustafa, Pal and
  Srivastava (MPS)
• for A and B
• Calculate A and use of the Einstein relation
  between drift and diffusion coefficient (to get
  asymptotically a thermal distribution)

E
ltEgt
B//
AAth
Bth //
B?
Bth?
pt
Time (fm/c)
11
c-quarks transverse momentum distribution (y0)
Heinz Kolbs hydro Just before the
hadronisation
Plasma will not thermalize the c It carries
information on the QGP
MPS
kcol 5
k40
k10
k20
Conclusion I Kcol(coll only) 10-20 Still far
away from thermalization !!!
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Leptons (? D decay) transverse momentum
distribution (y0)
RAA
Comparison to B0 calculation
Langevin A and B finite ? 20, ?10
0-10
pt
B0 (Just deceleration)
Transition from pure deceleration (high E)
towards thermalization regime (intermediate E)
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"Radiative"coefficients
 radiative  coefficients deduced using the
elementary cross section for cQ ?cQg and its
equivalent for cg ? cg g in t-channel (u
s-channels are suppressed at high energy).
dominant
suppresses by 1/Echarm

if evaluated in the large sqrts limit in the lab
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Evaluated in scalar QCD and in the limit of
Echarm gtgt masses and gtgtqt Factorization of
radiation and elastic scattering
k

In the limit of vanishing masses Gunion
Bertsch PRD 25, 746 But Masses change the
radiation substantially
q
xlong. mom. fraction
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 QED  part of M2 Large at large x and small kt
Abelien all masses 0.001
GeV qt 0.3 GeV
200
 QED 
0
(abelien)
x
0
kt
0.4
2000
0.8
0
0.4
 QCD 
0
 QCD  part of M2 Large at small x and finite
kt transverse momentum change
x
kt
0.8
0.4
16
Influence of finite masses on the radiation
0
Masses Mgluon Mquark 0.01 GeV
x
0
0.8
0
x
kt
1
1
Thermal masses Mgluon Mquark 0.3 GeV
0.8
0
kt
1
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The larger the quark mass the more the gluons
have small kt and x
0
0
x
x
0.5
0.5
bottom
charm
0
0
kt
kt
1
1
18
Dead cone effect Dokshitzer and Kharzeev PLB
519, 199 Masses suppress the gluon emission at
small kt
If one uses the full matrix element the formula
is more complicated but Flt1 for realistic
masses and finite qt2 ? dead cone
19
Input quantities for the calculation

• 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 too 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) ? Bjorken (boost invariant with
  no transverse flow) for tests realistic
  hydrodynamical evolution (Heinz Kolb) for
  comparison

20
Input quantities for the calculation (II)

• Langevin force on c-quarks inside QGP and no
  force on charmed  mesons  during and after
  hadronisation.
• D B meson produced via coalescence mechanism.
  (at the transition temperature we pick a u/d
  quark with the a thermal distribution) but other
  scenarios possible.
• No beauty up to now will be included.

21
As for the collisional energy loss we calculate
with these rates
Ak ltltPk Pkfgtgt
Bkl lt lt(
Pk-Pkf )(Pl-Plf)gtgt
Radiative energy loss gt
collisional energy loss
30
Still preliminary
T360
T260
T160 MeV
0
8
0
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Leptons (? D decay) transverse momentum
distribution (y0)
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
23
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 details
v2 (all d/u)
const quark tagged by c
v2 (d/u met by c)
pt
pt
Reason the (fast) u/d quarks which carry large
v2 values never meet the (slow) c quarks. Hence
in collisions at hadronisation and at coalescence
little v2 transfer.
Bigger enhancement ? helps a little but RAA
becomes worse.
pt
25
Azimutal Correlations for Open Charm
Transverse plane
What can we learn about "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
-
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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. Increasing ? values
wash out the correlation
jc - jcbar
coalescence
Azimutal correlations might help identifying
better the thermalization process and thus the
medium
jD - jDbar
-
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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
Small correlations at small pt,, mostly washed
away by coalescence process.
D
jD - jDbar
-
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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 for the
  v2. Possible explanations for discrepencies are
• Role of the spatial distribution of initial
  c-quarks
• Part of the flow is due to the hadronic phase
  subsequent to QGP
• Caveat of Langevin approach
• Azimutal correlations could be of great help in
  order to identify the nature of thermalizing
  mechanism.

29
Back up
30
Total emission from quark lines
(MproMpost)2
31
Results for open charm rapidity distribution at
RHIC
Heinz Kolbs hydro (boost invariant)
Set II
Tiny diffusion effect (no E loss, no drag)
(Set I)
32
Why so tiny ?
Y
Strong correlation of y vs. Y (spatial rapidity)
y
33
J/ys
34
Other ingredients of the model specific for J/y
production (I)

• J/y are destroyed via gluon dissociation J/y
  g ? c cbar and can be formed through the
  reverse mechanism, following the ideas of Thews.
  Uncorrelated quarks recombination ? quadratic
  dependence in Nc

Question How much is a ???
35
Other ingredients of the model specific for J/y
production (II)

• As sel(J/y) is small, we assume free streaming
  of J/y through QGP (no thermalization of J/y)...
  But possible gluo dissociation
• Clear cut melting mechanism J/y cannot exist /
  be formed if T gt Tdissoc (considered as a free
  parameter, taken between Tc and 300 MeV
  conservative choice according to lattice
  calculations Tdissoc1.5?Tc).
• Up to now No prompt J/y (supposed to be all
  melted)

36
Results for J/y production at mid-rapidity,
central
Component stemming out the recombination
mechanism

• Nc and Tdissoc key parameters as far as the
  total numbers are considered
• Thermalization increases production rates, but
  only mildly.
• Radial expansion of QGP has some influence for a
  very specific set of parameters (cf.
  )
• Firm conclusions can only be drawn when the
  initial number of c-cbar pairs is known more
  precisely.

37
Results for J/y production vs. rapidity

• Scaling like (dNc/dy)2
• A way to test the uncorrelated c-cbar
  recombination hypothesis.
• Grain of salt boost invariant dynamics for the
  QGP assumed.

Rapidity distribution is somewhat narrower for
J/y stemming out the fusion of uncorrelated c and
cbar than for direct J/y.
38
J/y transverse momentum distribution at mid
rapidity
Tdissoc180 MeV
Tdissoc180 MeV
(no transv. flow)
(Heinz Kolb)
Direct J/y (NN scaling)

• Clear evidence of the recombination mechanism
• pt anti-broadening in Au-Au
• effective temperatures gt Tc

Direct J/y (NN scaling)
39
Other conclusions Perspectives

• Heavy quark physics could be of great help in
  the metrology of QGP transport coefficients,
  especially at low momentum Go for the
  differential !
• Recombination mechanism should be there if one
  believes the large value of Tdissoc found on the
  lattice.
• The Fokker Planck equation a useful unifying
  phenomenological transport equation that makes
  the gap between fundamental theory experimental
  observables. Permits to generate input
  configuration for mixed-phase and hadronic-phase
  evolution.
• Mandatory To be done soon Cronin effect /
  relax the N(J/y direct)0 assumption / include
  beauty /find a name.

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So what should we do ???

• No time for thermalization anyhow. Then take
  these FP coefficients as they are, period (at
  least, it comes from some microscopic model).
• Add some more KM coefficients in your game (we
  are not that far from Boltzmann after all). Some
  more ? In fact ? 6 th order
• Do Boltzmann (or whatever microscopic).
• Change your point of view Assume physics of
  c-quark is closer to Fokker Planck (long
  relaxation time) then to Boltzmann collision term
  (QGP, diluted ?), PCM, fixed collision centers,
  Construct some phenomenological A and B (until
  lattice can calculate them) and see if you can
  fit (a lot of) experimental data. (In other field
  of physics, one measures the A and B)

41
So What ???
A)  since the drag and the diffusion
coefficients are not evaluated exactly but in
some valid approximation, typically applying a
perturbative expansion,  (Walton
Rafelski) And later (last sentence of the
paper) B)   only a major change in the
transport coefficients from the results of the
microscopic calculations will lead to a Boltzmann
/ Jüttner equilibrium distribution. 

• My personnal comments
• Wrt A) Boltzmann collision-integral can (at
  least formally) be rewritten as a power series
  implying derivatives of f of higher and higher
  degree (Kramers Moyal expansion). FP
  coefficients ARE the 2 first two coefficients and
  are perfectly defined.
• Wrt A) B) If the approximation (truncation of
  KM series) is valid, why should it be necessary
  to perform a major change on the coeff ?

42
Gunion Bertsch 82
43
Qq Qqg
44
Qq Qqg
45
Heavy quarks in QGP (or in strongly interacting
matter)

• Starting point For heavy quarks, relaxation
  time gtgt collision time at large momentum (as
  for all quarks) but also at low momentum (thanks
  to inertia)

• Heavy quarks behave according to Brownian motion
  / Langevin forces ? c quarks distribution evolves
  according to Fokker Planck equation

N.B. What is the best model (if any) ? FP or
Boltzmann equation ?
46
Non-Photonic electron elliptic-flow at RHIC and
the bites (ouch)
strong coupling
c
D
t1fm/c
t
1
2
3
4
5
No coupling
t4fm/c
r?
Spatial transverse-distribution might play some
role as c-quarks are not from the beginning "on"
the freeze out surface.
SQM06
47
Masses . 33GeV qt2 0.3
48
The transport coefficients (III)
How precisely do we know these transport
coefficients (in the case of heavy quarks) ?

• Start from a more  fundamental  theory
• Two body collisions
  with thermal distribution of the
  collision partner.
• Moments A lt pµf -
  pµi gt
• B lt
  (p?f - p?i )(pµf - pµi ) gt
• In case of collisions (2 ?2 processes)
  Pioneering work of Cleymans (1985), Svetitsky
  (1987), extended later by Mustafa, Pal
  Srivastava (1997).
• For radiation Numerous works on energy loss
  very little seems to have been done on diffusion
  coefficients

49
The transport coefficients (II)
with

• Diffusion (in momentum space) (not to be
  confused with diffusion in "normal" space (D)
  thermalisation
• In isotropic media decomposition of
  into longitudinal and transverse contribution ?
  only 2 independent coefficients.

50
The transport coefficients
with

• drift coefficient is proportional to momentum
  loss per unit of time (Walton and Rafelski)
• At high momenta, one has (assuming f is peaked)

? A(p) and the energy loss per unit of length
are the same quantities

• At low momenta, not true anymore On the
  average, particles can gain/loose energy without
  gaining or loosing momentum (thermalisation)