M. Djordjevic 1

Heavy quark energy loss in a dynamical QCD medium

Magdalena Djordjevic

The Ohio State University

M. Djordjevic and U. Heinz, arXiv:0705.3439 [nucl-th]

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 a 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 in which there are more outgoing than incoming particles:

0th order

1st order

0th order

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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?

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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

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.

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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.

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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]

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Ratio of dynamical and static radiative energy loss at RHIC

75%

M. D. and U. Heinz, arXiv:0705.3439 [nucl-th]

s=0.3, L=5fm, T=225 GeV

CHARM

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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!

M. D. and U. Heinz, arXiv:0705.3439 [nucl-th]

M. Djordjevic 14

What is the origin of such energy loss increase?

2222

22

2

1

3

1

3

11

qqq

q

electric contribution

magnetic contribution

magnetic electricdyn dyn dynE E E

E E E

In dynamical medium both electric and magnetic contributions from the exchanged (virtual) gluons contribute to the energy loss.

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Electric v.s. magnetic contribution to the radiative energy loss in dynamical QCD medium

Both contributions are equally important!

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On the other hand, in static medium only electric contribution from the exchanged gluon contribute to the energy loss:

electric contribution

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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.

M. Djordjevic 18

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 75% larger than in a static medium. Therefore, the constituents of QCD medium

can not be approximated as static scattering centers.

The increase of the energy loss is exclusively due to the magnetic contribution of the exchanged gluon.

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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.

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backup

M. Djordjevic 21

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!

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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

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Radiative energy loss in static QCD medium

Assume thermal QCD medium composed of static sacattering centers.

The static interactions are modeled by Gyulassy-Wang color screened Yukawa potentials:

where is the location of nth (heavy) target parton, and

2

+ +

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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).

Computational assumptions

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Comparison of qz and qt

qt~qz≈q0«

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;

For exchanged gluon, cut 1-HTL gluon propagator cannot be simplified, since both transverse (magnetic) and longitudinal (electric) contributions will prove

to be important.

1-HTL gluon propagator:

Cut 1-HTL gluon propagator:

Radiated gluon Exchanged gluon

For radiated gluon, cut 1-HTL gluon propagator can be simplified to (M.D. and M. Gyulassy, PRC 68, 034914 (2003).

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Radiative energy loss in dynamical QCD medium

M. D. and U. Heinz, arXiv:0705.3439 [nucl-th]

M. Djordjevic 28

Radiative energy loss in static QCD medium

Assume thermal QCD medium composed of static sacattering centers.

2

+ +

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Dynamical vs. static radiative energy loss at the RHIC

Dynamical effects increase the energy loss by almost approximately 75%.