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

M. Djordjevic 21

HTL gluon propagator