Dynamical QCD medium effects on jet energy loss

1
Dynamical QCD medium effects on jet energy loss
Magdalena Djordjevic Arkansas State University
2
Quark Gluon Plasma
At extremely high energy densities, QCD predicted
formation of new form of matter (QGP), consisting
of interacting (anti)quarks and gluons.
Heavy quarks (charm and beauty, Mgt1 GeV) are
widely recognized as the excellent probes of QGP.
N. Brambilla et al., e-Print hep-ph/0412158
(2004).
3
To use heavy flavor suppression data as a tool to
study the properties of QGP, reliable theoretical
predictions are needed.
High pt suppression is a consequence of the
energy loss.
Reliable computations of energy loss mechanisms
are needed.
4
Radiative energy loss
Collisional energy loss
Radiative energy loss comes from the processes in
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
1st order
5
Single electron puzzle at RHIC
M. D. et al., Phys. Lett. B 632, 81 (2006)
Radiative energy loss predictions with dNg/dy1000
M. D. and M. Gyulassy, PRC 2003, PLB 2003,
NPA 2004 M. D. PRC 2006
Disagreement!
Radiative energy loss is not able to explain the
single electron data as long as realistic
parameter values are taken into account!
6
(No Transcript)
7
Talk overview
Collisional energy loss
The effects of dynamical QCD medium also have to
be considered.
Notably improves the agreement with the data.
Radiative energy loss in infinite size dynamical
QCD medium
Finite size effects
8
Collisional energy loss in a finite size QCD
medium
Consider a medium of size L in thermal
equilibrium at temperature T.
The main order collisional energy loss is
determined from
M. D., Phys.Rev.C74064907,2006
9
Collisional v.s. medium induced radiative energy
loss
M. D., PRC 74, 2006
10
Single electron prediction (collisional
radiative)
(S. Wicks, W. Horowitz, M.D. and M. Gyulassy,
Nucl.Phys.A784426-442,2007)
Inclusion of collisional energy loss leads to
better agreement with single electron data.
11
A fundamental problem opened by non-zero
collisional energy loss
However, as shown in the previous slides,
collisional and radiative energy losses are
comparable.
Collisional energy loss results are inconsistent
with static approximation!
Can static medium approximation be used in
radiative energy loss calculations?
12
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. D. and U. Heinz, Phys.Rev.C77024905,2008
Phys.Rev.Lett.101022302,2008 M.D. in
preparation (2008)
13
Radiative energy loss in an infinite size
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.
14
For radiated gluon, cut 1-HTL gluon propagator
can be simplified to (M.D. and M. Gyulassy, PRC
68, 034914 (2003).
For exchanged gluon, cut 1-HTL gluon propagator
cannot be simplified, since both transverse
(magnetic) and longitudinal (electric)
contributions will prove to be important.
15
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
M. D. and U. Heinz, Phys.Rev.C77024905,2008.
Logarithmic divergence is a consequence of the
absence of magnetic mass.
16
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
17
The divergence is naturally regulated when all
the diagrams are taken into account.
18
Radiative energy loss in dynamical QCD medium
M. D. and U. Heinz, Phys.Rev.C77024905,2008.
19
Radiative energy loss in static QCD medium
Assume thermal QCD medium composed of static
sacattering centers.
20
Comparison of radiative energy loss formulas in
dynamical and static medium
M. D. and U. Heinz, Phys.Rev.C77024905,2008.
Dynamical medium
Static medium
Similar expressions, with two important
differences
21
Dynamical vs. static radiative energy loss at the
RHIC
MeV
22
Ratio of dynamical and static radiative energy
loss at RHIC
?s0.3, L5fm, T225 MeV
CHARM
75
M. D. and U. Heinz, Phys.Rev.C77024905,2008.
23
Dynamical vs. static radiative energy loss at the
LHC
?s0.3, L5fm, T400 MeV
80
There is no jet energy domain where the
assumptions of static scattering scatterers
becomes a valid approximation.
Dynamical effects important for all types of
quarks!
M. D. and U. Heinz, Phys.Rev.C77024905,2008.
24
Finite size effects in dynamical QCD medium
Previous calculations are done under the
assumptions of infinite size QCD medium.
However, in URHIC a medium of finite size is
created.
Are dynamical effects still important once the
finite size effects are taken into account?
25
Calculation of the radiative energy loss in the
finite size QCD medium
We consider a medium of finite size L, and assume
that the collisional interaction has to occur
inside the medium.
L
The calculations were performed by using two
Hard-Thermal Loop approach.
M. D. and U. Heinz, Phys.Rev.Lett.101022302,2008
M.D. in preparation (2008).
26
Finite size QCD medium
Bethe-Heitler limit
Can be off-shell
Three cuts can contribute to the energy loss.
27
We calculated all the relevant diagrams that
contribute to this energy loss
Each individual diagram is infrared divergent,
due to the absence of magnetic screening!
The divergence is naturally regulated when all
the diagrams are taken into account.
So, all 24
diagrams have to be included to obtain sensible
result.
M. D. and U. Heinz, Phys.Rev.Lett.101022302,2008
M.D. in preparation (2008).
28
Comparison of radiative energy loss formulas in
finite size dynamical and static QCD medium
M. D. and U. Heinz, Phys.Rev.Lett.101022302,2008.

M. D. and M. Gyulassy, NPA733265-298,2004.
Dynamical medium
Static medium
Similar expressions, with two important
differences
29
Ratio of dynamical and static radiative energy
loss at RHIC
?s0.3, L5fm, T225 MeV
?s0.3, E20 GeV, T225 MeV
60
There is no jet energy domain at RHIC where the
assumptions of static scattering scatterers
becomes a valid approximation.
Dynamical effects important for all types of
quarks!
M. D. and U. Heinz, Phys.Rev.Lett.101022302,2008,
M.D. in preparation (2008).
30
Dynamical vs. static radiative energy loss at the
LHC
At asymptotic energies static QCD medium becomes
valid approximation. However, at realistic
RHIC and LHC energies, taking into account
dynamical medium is highly important!
M. D. and U. Heinz, Phys.Rev.Lett.101022302,2008
M.D. in preparation (2008).
31
Summary We studied the radiative energy loss for
both light and heavy quarks, in both infinite
size and finite size dynamical QCD 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), their sum leads to an infrared safe
result. The energy loss in a dynamical medium
is significantly larger than in a static medium.
Therefore, the constituents of QCD medium can
not be approximated as static scattering
centers. The dynamical effects are important,
and have to included in order to obtain the
reliable quantitative predictions of radiative
energy loss and jet suppression in the upcoming
RHIC and LHC experiments.
32
Measurement of the heavy flavor suppression at
the upcoming RHIC and LHC experiments is in the
current focus of intensive experimental efforts.
High pt suppression is a consequence of the
energy loss.
Our study enables us to provide the most reliable
calculations of the energy loss in QGP.
Future goal Make precise and reliable
theoretical predictions for the heavy flavor
suppression, which can be directly compared with
the data to study the properties of QGP.
33
backup
34
Computational assumptions

• Computation was done in the soft gluon, soft
  rescattering limit, that is we assume that
• E ? ? ? kt, qt, where ? (E) is the gluon (jet)
  energy, and kt (qt) is the transverse momentum of
  the radiated (exchanged) gluon.
• Additional assumptions
• Spin in the problem is neglected.
• Highly energetic jet, such that we can assume
  ??????1 (M is the mass of the heavy
  quark jet).

35
Comparison of qz and qt
qtqzq0?
36
(No Transcript)
37
(No Transcript)
38
What is the origin of such energy loss increase?
electric contribution
magnetic contribution
In dynamical medium both electric and magnetic
contributions from the exchanged (virtual) gluons
contribute to the energy loss.
39
On the other hand, in static medium only electric
contribution from the exchanged gluon contribute
to the energy loss
electric contribution
static medium
40
Inclusion of dynamical effects leads to a slight
reduction of the electric contribution to the
radiative energy loss.
Additional magnetic contibution is the reason for
a significant increase of the radiative energy
loss in dynamical medium.
41
Jet suppression
Heavy meson suppression is considered to be an
excellent probe of QCD matter.
What is suppression?
41
42
Why are heavy quarks good probes?
Heavy quarks can be produced only during the
early stage of QCD matter.
Early stage
g
c
_
No c and c production
_
g
c
?
1/Mc
42
43
Charm/bottom mass is small enough
Charm/bottom quark mass is large enough
Significantly interacts with surrounding light
quarks and gluons
Mc,b ? ?QCD
Perturbative calculations of heavy quark
production and energy loss are possible
Sensitive to the properties of the medium
43
44
Disadvantages of heavy quarks?
Theoretically Computations are more involved
with heavy quarks than with light quarks.
Experimentally Small number of heavy quarks is
produced, and it is not easy to detect them.
Heavy mesons not yet measured at RHIC, but are
expected soon.
44