M. Djordjevic 1
Effect of dynamical QCD medium on radiative heavy quark energy loss
Magdalena Djordjevic
The Ohio State University
M. Djordjevic 2
Heavy flavor (charm and beauty) suppression is widely recognized as the excellent probes of QGP
at RHIC and LHC. N. Brambilla et al., e-Print hep-ph/0412158 (2004).
High pt suppression is the consequence of the energy loss.
Reliable computations of energy loss mechanisms are needed.
M. Djordjevic 3
Radiative energy loss Collisional energy loss
Collisional energy loss comes from the processes which have the same number of incoming and outgoing particles:
Radiative energy loss comes from the processes which there are more outgoing than incoming particles:
0th order
1st order
0th order
M. Djordjevic 4
This motivated an approximation by which a medium is composed of static constituents (modeled by
Yukawa potential). This model was used in all heavy flavor radiative energy loss calculations by now.
Approximation consequence: In such a medium, collisional energy loss has to be exactly
equal to zero!
Until recently, a generally held belief was that the radiation is the dominant energy loss mechanism.
(Based on early computations by Braaten and Thoma 1991; Thoma and Gyulassy 1991, BDMPS 1995.)
Apparently consistent
M. Djordjevic 5
However, recent collisional energy loss computations showed that collisional and radiative energy losses are comparable.
0 5 10 15 20 25 30pGeV0
0.05
0.1
0.15
0.2
EE
CHARM
collisional
radiative
M.G.Mustafa,Phys.Rev.C72:014905,2005 M.Djordjevic,Phys.Rev.C74:064907,2006
Collisional energy loss results are inconsistent with static approximation!
Can static medium approximation be used in radiative energy loss calculations?
M. Djordjevic 6
Our goal
We want to compute the heavy quark radiative energy loss in dynamical medium of thermally
distributed massless quarks and gluons.
Why?
To address the applicability of static approximation in radiative energy loss computations.
To compute collisional and radiative energy losses within a consistent theoretical framework.
M. Djordjevic and U. Heinz, arXiv:0705.3439 [nucl-th]
M. Djordjevic 7
k,c
q,a p
220k k
220q q
2
Radiative energy loss in a dynamical medium
We compute the medium induced radiative energy loss for a heavy quark to first (lowest) order in number of scattering centers.
To compute this process, we consider the radiation of one gluon induced by one collisional interaction with the medium.
To simplify the calculations, we consider the Bethe-Heitler limit. The calculations were performed by using two Hard-Thermal Loop
approach.
pp' p'
q, a
k, cQuasiparticle contribution
Landau damping contribution
Optical theorem
M. Djordjevic 8
1st group of diagrams presents contributions where both ends of the exchanged gluon q are attached to the heavy quark, i.e. no 3-gluon vertex is involved:
Logarithmic divergence is a consequence of the absence of magnetic mass.
M. D. and U. Heinz, arXiv:0705.3439 [nucl-th]
M. Djordjevic 9
2nd group of diagrams presents contributions where only one end of the exchanged gluon q
is attached to the heavy quark:
3rd contribution presents a diagram where both ends of the
exchanged gluon q are attached to the radiated gluon k:
M. Djordjevic 10
+
+
=
The divergence is naturally regulated when all the diagrams are taken into account.
M. Djordjevic 11
Similar expressions, with two important differences:
Dynamical medium Static medium
Increases the energy loss rate in the dynamical medium by ~20%.
Increases the energy loss rate in the dynamical medium by additional ~50%.
Comparison of radiative energy loss formulas in dynamical and static medium
M. D. and U. Heinz, arXiv:0705.3439 [nucl-th]
M. Djordjevic 12
0 0.5 1 1.5ETeV
1
1.5
2
2.5
EdynEstat
0 0.5 1 1.5ETeV
1
1.5
2
2.5
EdynEstat
dynstat /
0 1 2 3 4 5MGeV
1.65
1.7
1.75
1.8
EdynEstat
u,d
c
b
statdyn
There is no jet energy domain where the assumptions of static scattering scatterers
becomes a valid approximation.
Dynamical vs. static radiative energy loss at the LHC
Dynamical effects important for all types of quarks!
80%
M. D. and U. Heinz, arXiv:0705.3439 [nucl-th]
s=0.3, L=5fm, T=400 GeV
M. Djordjevic 13
SummaryWe studied the radiative energy loss for both light and heavy
quarks, in dynamical medium of thermally distributed massless quarks and gluons.
While each individual contribution to the energy loss in a dynamical medium is infrared divergent (due to the absence of magnetic screening), there sum lead to an infrared safe result.
The energy loss in a dynamical medium is almost 80% larger than in a static medium. Therefore, the constituents of QCD medium
can not be approximated as static scattering centers.
M. Djordjevic 14
Conclusion and future directions
The dynamical effects are important, and have to be included in the computation of jet energy loss.
The observed quark energy loss could be significantly larger than previously thought.
The computation of heavy quark energy loss in a finite size dynamical QCD medium is the next important goal to obtain the the reliable quantitative predictions of radiative energy loss and jet suppression in the upcoming RHIC and LHC experiments.
M. Djordjevic 15
backup
M. Djordjevic 16
Comment on BDMPS approach2max
2 2max
0
3~ ( );
2
qdE ET L
dq q v q where qdz
2
2 2 2( )
( )statv qq
2 2max max
2 2 2 2
0 0
( ) ( )q q
stat dyndq q v q dq q v q
Static medium:2
2 2 2( )
( )dynv qq q
Dynamical medium:
2 2 2 2max max max max2
2 2 2 2 2 2 2 22 2 2 2 2 2 2 2
0 0 0 0
1 1( )
( ) ( ) ( )
q q q q
statdq q v q dq q dq dqq q q
2 2 2max max max2 2
2 2 2 2 2 2 22 2 2 2 2 2
0 0 0
( )( ) ( )
q q q
dyndq q dq q dq q v qq q q q
0
• Deep LPM regime
• Huge number of scatterings
BDMPS does not distinguish between dynamical and static
medium!
M. Djordjevic 17
In BDMPS approach, the only difference between dynamical and static medium can come from qmax.
2 2max max
2 2 2 2
0 0
( ) ( )q q
stat dyndq q v q dq q v q
max
3
2stat
stat
ET Lq
Static medium: Dynamical medium:
max
3
2dyn
dyn
ET Lq
22
3~ ln
2stat
stat
dE ET L
dz
22
3~ ln
2dyn
dyn
dE ET L
dz
is not well defined in dynamical medium. There are two possible choices:
dynstatstat dyn
dEdE
dz dz
10 dyn
dyn
dE
dz
M. Djordjevic 18
Dynamical vs. static radiative energy loss at the RHIC
dynamic
static static
static
dynamic dynamic
0 10 20 30 40pGeV0
0.2
0.4
0.6
0.8
Erad1
E
LIGHT
0 10 20 30 40pGeV0
0.1
0.2
0.3
0.4
0.5
Erad1
E
CHARM
0 10 20 30 40pGeV0
0.05
0.1
0.15
0.2
0.25
Erad1
E
BOTTOM
Dynamical effects increase the energy loss by almost factor of 2.
s=0.3, L=5fm, T=225 GeV
M. Djordjevic 19
Ratios at RHIC
Gluon spectrums defined as:
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Transverse momentum depemdence of exchanged and radiated gluon
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HTL gluon propagator