M. Djordjevic 1

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Heavy quark energy loss radiative v.s.
collisional Magdalena Djordjevic The Ohio State
University
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Quark Gluon Plasma
Form, observe and understand Quark-Gluon Plasma
(QGP).
High Energy Heavy Ion Physics
Heavy quarks (charm and beauty, M1 GeV) are
widely recognized as the cleanest probes of QGP.
N. Brambilla et al., e-Print hep-ph/0412158
(2004).
Heavy mesons not yet available, but they are
expected soon!
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Indirect probe- single electron suppression is
available
V. Greene, S. Butsyk, QM2005 talks
J. Dunlop, J. Bielcik QM05 talks
Significant reduction at high pT suggests
sizeable heavy quark energy loss!
Can this be explained by the energy loss in QGP?
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Outline

• Discuss the heavy quark energy loss mechanisms
• Radiative energy loss.
• Collisional energy loss.
• Single electron suppression results that come
  from the above mechanisms.

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• Radiative heavy quark energy loss
• Three important medium effects control the
  radiative energy loss
• Ter-Mikayelian effect (M.L.Ter-Mikayelian (1954)
  Kampfer-Pavlenko (2000) Djordjevic-Gyulassy
  (2003))
• Transition radiation (Zakharov (2002) Djordjevic
  (2006)).
• Medium induced radiative energy loss
  (Djordjevic-Gyulassy
  (2003) Zhang-Wang-Wang (2004)
  Armesto-Salgado-Wiedemann (2004))

1)
2)
3)
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Transition Ter-Mikayelian effects on 0th order
radiative energy loss
M.D., Phys.Rev.C73044912,2006
CHARM
BOTTOM
Transition Ter-Mikayelian effects approximately
cancel each other for heavy quarks.
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Medium induced radiative energy loss
Caused by the multiple interactions of partons in
the medium.
To compute medium induced radiative energy loss
for heavy quarks we generalize GLV method, by
introducing both quark M and gluon mass mg.
Neglected in further computations.
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This leads to the computation of the fallowing
types of diagrams
Final Result to Arbitrary Order in Opacity (L/l)
with MQ and mg 0
M. D. and M. Gyulassy, Phys. Lett. B 560, 37
(2003) Nucl. Phys. A 733, 265 (2004)
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Numerical results for 1st order in opacity
induced radiative energy loss
LHC, dNg/dy3000
RHIC, dNg/dy1000
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Can single electron suppression be explained by
the radiative energy loss in QGP?
M. D., M. Gyulassy, R. Vogt and S. Wicks, Phys.
Lett. B 632, 81 (2006)
Radiative energy loss predictions with dNg/dy1000
Disagreement!
Radiative energy loss alone is not able to
explain the single electron data as long as
realistic parameter values are taken into account!
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Is collisional energy loss also important?
Early work
Recent work
E. Braaten and M. H. Thoma, Phys. Rev. D 44,
2625 (1991). M. H. Thoma and M. Gyulassy, Nucl.
Phys. B 351, 491 (1991).
Collisional energy loss is negligible!
Conclusion was based on inaccurate assumptions
(i.e. they used a0.2), and assumed that
dE/dLCollisional and radiative energy losses are
comparable! M.G.Mustafa,Phys.Rev.C72014905,2005 A
. K. Dutt-Mazumder et al.,Phys.Rev.D71094016,2005

Will collisional energy loss still be important
once finite size effects are included?
Above computations are done in an ideal infinite
QCD medium.
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Radiative energy loss
Collisional energy loss
Radiative energy loss comes from the processes
which there are more outgoing than incoming
particles
Collisional energy loss comes from the processes
which have the same number of incoming and
outgoing particles
0th order
0th order
1st order
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Collisional energy loss in a finite size QCD
medium
M.D., nucl-th/0603066
Consider a medium of size L in thermal
equilibrium at temperature T.
The 0th order collisional energy loss is
determined from
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Comparison between computations of collisional
energy loss in finite and infinite QCD medium
M.D., nucl-th/0603066
Finite size effects are not significant, except
for very small path-lengths.
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Comparison between charm and bottom collisional
energy loss
Bottom quark collisional energy loss is
significantly smaller than charm energy loss.
M.D., nucl-th/0603066
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Collisional v.s. medium induced radiative energy
loss
M.D., nucl-th/0603066
Complementary approach by A. Adil et al.,
nucl-th/0606010 consistent results obtained.
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Most up to date single electron prediction
(collisional radiative)
See talk by S. Wicks, parallel session I
Radiative energy loss alone is not able to
explain the single electron data, as long as
realistic gluon rapidity density dNg/dy1000 is
considered.
Inclusion of collisional energy loss leads to
better agreement with single electron data, even
for dNg/dy1000.
(S. Wicks, W. Horowitz, M.D. and M. Gyulassy,
nucl-th/0512076)
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Conclusions Radiative energy loss mechanisms
alone are not able to explain the recent single
electron data. Collisional and radiative energy
losses are comparable, and both contributions are
important in the computations of jet quenching.
Inclusion of the collisional energy loss lead
to better agreement with the experimental
results.
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Acknowledgements
Miklos Gyulassy (Columbia University) Simon
Wicks (Columbia University) Ramona Vogt (LBNL,
Berkeley and University of California,
Davis) William Horowitz (Columbia University)
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Ter-Mikayelian effect
This is the non-abelian analog of the well known
dielectric plasmon effect w(k) wpl gT. In pQCD
vacuum gluons are massless and transversely
polarized. However, in a medium the gluon
propagator has both transverse (T) and
longitudinal (L) polarization parts.
T
vacuum
L
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In order to compute the main order radiative
energy loss we calculated Mrad2, where Mrad is
given by Feynman diagram
We used the optical theorem, i.e.
Where M is the amplitude of the following diagram
Dielectric Effect
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To compute the effect we start from work by B.G.
Zakharov, JETP Lett.76201-205,2002.
This computation was performed assuming a static
medium.
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Single electron suppression

• 1) Initial heavy quark pt distributions
• 2) Heavy quark energy loss
• 3) c and b fragmentation functions into D, B
  mesons
• 4) Decay of heavy mesons to single e-.

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Initial heavy quark pt distributions
M. Cacciari, P. Nason and R.Vogt,
Phys.Rev.Lett.95122001,2005 MNR code (M. L.
Mangano, P.Nason and G. Ridolfi,
Nucl.Phys.B373,295(1992)).
R.Vogt, Int.J.Mod.Phys.E 12,211(2003).
High quark mass, i.e. M?QCD
Perturbative calculations of heavy quark
production possible.
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Pt distributions of charm and bottom before and
after quenching at RHIC
M. Gyulassy, P. Levai and I. Vitev,
Phys.Lett.B538282-288 (2002).
M. D., M. Gyulassy and S. Wicks, Phys. Rev. Lett.
94, 112301 (2005).
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Single electrons pt distributions
Panels show single e- from FONLL M. Cacciari, P.
Nason and R. Vogt, Phys.Rev.Lett.95122001,2005 M.
D., M. Gyulassy, R. Vogt and S. Wicks,
Phys.Lett.B63281-86,2006
Before quenching
After quenching
Bottom dominate the single e- spectrum above 4.5
GeV!
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Single electron suppression as a function of pt
At pt5GeV, RAA(e-) ? 0.70.1 at RHIC.
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Are there other energy loss mechanisms?
Finite size effects significantly lower
collisional energy loss S. Peigne, P.-B.
Gossiaux, T. Gousset, hep-ph/0509185
Collisional and radiative energy losses are
comparable! M.G.Mustafa,Phys.Rev.C72014905,2005
The paper, however, did not make separation
between elastic and part of radiative energy loss
effects.
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The numerical results can be understood from
1st order energy loss can not be characterized
only by a Dead-cone effect!
LPM effects are smaller for heavy than for light
quarks!
Results confirmed by two independent groups

B. W. Zhang, E. Wang and X. N. Wang,
Phys.Rev.Lett.93072301,2004
N. Armesto, C. A. Salgado, U. A. Wiedemann,
Phys.Rev.D69114003,2004.
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Why, according to pQCD, pions have to be at least
two times more suppressed than single electrons?
Suppose that pions come from light quarks only
and single e-from charm only.
Pion and single e- suppression would really be
the same.

• However,
• Gluon contribution to pions increases the pion
  suppression, while

2) Bottom contribution to single e- decreases the
single e- suppression leading to at least factor
of 2 difference between pion and single e- RAA.
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Comparison with other models
Ideal infinite QCD medium case

• Thoma-Gyulassy (1990) (linear response approach).
• Braaten-Thoma (1991) (quantum-mechanical
  approach).
• Romatasche-Strickland (2003) (anisotropic medium).

Finite QCD medium case

• Peigne-Gossiaux-Gousset (hep-ph/0509185, 2005)
  (linear response approach) Finite size effects
  significantly reduce the collisional energy loss.
• Wang (nucl-th/0604040, 2006) (quantum-mechanical
  approach)
  interference effects exist
  at 0th order energy loss level.
• Adil-Gyulassy-Horowitz-Wicks (nucl-th/0606010,
  2006) (linear response approach) obtained
  consistent results.