M. Djordjevic 1

Heavy Quark Energy Loss in Nucleus-Nucleus Collisions

Magdalena Djordjevic

The Ohio State University

M. Djordjevic 2

Jet Quenching of light partons strongly suggest that QGP is discovered.

Further tests of jet tomography using heavy quarks could be decisive as a complementary test of the theory.

However, single electron measurements are available.

Is the QGP already discovered at RHIC?

Heavy ion physics has a goal to form and observe a QGP.

Heavy mesons not yet measured at RHIC.

M. Djordjevic 3

1997 Shuryak argued that heavy quarks will have large energy loss in QGP => large suppression of heavy mesons.

2001 Dokshitzer and Kharzeev proposed “dead cone” effect => heavy quark small energy loss

What value of heavy quark suppression we can expect at RHIC?

M. Djordjevic 4

Significant reduction at high pT suggest sizable energy loss!

Single electron suppression measurements at RHIC

V. Greene, S. Butsyk, QM2005 talks J. Dunlop, J. Bielcik; QM2005 talks

Can this be explained by the energy loss in QGP?

M. Djordjevic 5

Outline

1) Radiative energy loss mechanisms.

2) Heavy meson (D and B) and single electron suppression.

3) B mesons can not be neglected in the computation of single electron spectra.

4) Radiative energy loss alone can not explain the experimental data.

5) Inclusion of elastic energy loss as a solution?

M. Djordjevic 6

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-.

D, B

1)

production

2)

medium energy loss

3)

fragmentation

c, b

Single electron suppression

e-

4)

decay

M. Djordjevic 7

To compute the initial charm and beauty pt distributions we applied the MNR

code (Mangano et al. Nucl.Phys.B373,295(1992)).

Parameters values from R.Vogt, Int.J.Mod.Phys.E 12,211(2003).

Initial heavy quark pt distributions

200S GeV

M. Djordjevic 8

Radiative heavy quark energy loss

Three important medium effects control the radiative energy loss:

1) Ter-Mikayelian effect (M. D. and M. Gyulassy, Phys. Rev. C 68, 034914 (2003)) 2) Transition radiation (M. D., to be published). 3) Energy loss due to the interaction with the medium

(M. D. and M. Gyulassy, Phys. Lett. B 560, 37 (2003); Nucl. Phys. A 733, 265 (2004))

c

L

c

1) 2) 3)

M. Djordjevic 9

Ter-Mikayelian effectThis is the non-abelian analog of the well known dielectric

plasmon effect (kpl~ 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

L

vacuum

M. Djordjevic 10

In order to compute the main order radiative energy loss we calculated |Mrad|2, where Mrad is given by Feynman diagram:

We used the optical theorem, i.e.:

Where M is the amplitude of the following diagram:

DielectricEffect

M. Djordjevic 11

The Ter-Mikayelian effect thus tends to enhance the yield of high pT charm quarks relative to the vacuum case.

Comparison between medium and vacuum 0th order in opacity fractional energy loss

Longitudinal contribution is negligible.

The Ter-Mikayelian effect on transverse contribution is important, since for charm it leads to ~30% suppression of the vacuum radiation.

CHARM

M. Djordjevic 12

An additional dielectric effect at 0th order in opacity.

It must be taken into account if the QGP has finite size.

Transition radiation occurs at the boundary between medium and the vacuum.

Transition radiation

c

L

M. Djordjevic 13

medium vacuum

L

medium vacuum

L

c

mgmed

This computation was performed assuming a static medium.

To compute the effect we start from work by B.G. Zakharov, JETP Lett.76:201-205,2002.

M. Djordjevic 14

Transition & Ter-Mikayelian for charm

Two effects approximately cancel each other for

heavy quarks.

Transition radiation lowers Ter-Mikayelian

effect from 30% to 15%.

M. Djordjevic 15

Transition radiation provides natural regularization of m=0 light quark energy loss.

What about light quarks? Problem:

Transition radiation as a solution:

Infinite discontinuity

M. Djordjevic 16

c

c

L

Energy loss due to the interaction with 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.

Caused by the multiple interactions of partons in the medium.

M. Djordjevic 17

This leads to the computation of the fallowing types of diagrams:

++

nz

,n nq a

,n nq a

nz

,n nq a

,n nq a

nznz

,n nq a

,n nq a

To compute energy loss to all orders in opacity we use algebraic recursive method described in (GLV,Nucl.Phys.B594(01)).

M. Djordjevic 18

Final Result to Arbitrary Order in Opacity (L/)n

MQ and mg > 0

Hard, Gunion-Bertsch, and Cascade ampl. in GLV generalized to finite M

Generalizes GLV MQ = mg =0 (Nucl. Phys. B 594, 2001)

M. Djordjevic 19

The numerical results for induced radiative energy loss are shown for first order in opacity.

For 10 GeV heavy quark (c, b) jet, thickness dependence is closer to linear Bethe-Heitler like form L1. This is different than the asymptotic energy quadratic form characteristic for light quarks.

M. Djordjevic 20

light

Quantitative “dead cone effect” for the heavy quark energy loss

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For 5 GeV heavy quark (c, b) jet, thickness dependence is

closer to linear Bethe-Heitler like form, while light quarks

are closer to quadratic form.

As the jet energy increases charm and light quark energy

loss become more similar, while bottom quark remains

significantly different.

As the jet energy increases, the dead cone effect becomes less important.

M. Djordjevic 22

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!

(See Fig. E.3)

Results later confirmed by two independent groups: B. W. Zhang, E. Wang and X. N. Wang, Phys.Rev.Lett.93:072301,2004; N. Armesto, C. A. Salgado, U. A. Wiedemann, Phys.Rev.D69:114003,2004.

M. Djordjevic 23

Pt distributions of charm and bottom before and after quenching at RHIC

Before quenching After quenching

To compute the jet quenching we generalized the GLV method (PLB538:282,2002).

M. Djordjevic 24

Heavy quark suppression as a function of pt

(M. D., M. Gyulassy and S. Wicks, Phys. Rev. Lett. 94, 112301 (2005); Euro Phys. J C 43, 135 (2005). )

Moderate D meson suppression ~ 0.50.1 at RHIC.

M. Djordjevic 25

Panels show single e- from FONLL (done by R. Vogt). (M. D., M. Gyulassy, R. Vogt and S. Wicks, nucl-th/0507019, to appear Phys.

Lett. B (2005))

Single electrons pt distributions before and after quenching at RHIC

Bef

ore

qu

ench

ing

Aft

er q

uen

chin

g

Bottom dominate the single e- spectrum after 4.5 GeV!

M. Djordjevic 26

The ratio of charm to bottom decays to electrons obtained by varying the quark mass and scale factors.

Domination of bottom in single electron spectra

Done by Simon Wicks.

M. Djordjevic 27

Single electron suppression as a function of pt

red curves: be; blue curves: ce; black curves: b+ce;

At pt~5GeV, RAA(e-) 0.70.1 at RHIC.

M. Djordjevic 28

Comparison with single electron data

Disagreement with PHENIX preliminary data!

1000gdN

dy

dNg/dy=1000

M. Djordjevic 29

How can we solve the problem?

Reasonable agreement, but the dNg/dy=3500 is not physical!

3500gdN

dy

dNg/dy=3500N. Armesto et al.,

Phys. Rev. D 71, 054027 (2005)

M. Djordjevic 30

Is elastic energy loss important?

Elastic and radiative energy losses are comparable!

M. G. Mustafa, Phys.Rev.C72:014905,2005)

E. Braaten and M. H. Thoma, Phys. Rev. D 44, 2625 (1991).

M. H. Thoma and M. Gyulassy, Nucl. Phys. B 351, 491 (1991).

Elastic energy loss is negligible!

Conclusion was based on wrong assumptions (i.e. they used =0.2).

Early work:Recent work:

Used correct =0.3

First results indicate that the elastic energy loss may be important (see talk by Simon Wicks)

Available elastic energy loss calculations can give only rough

estimates to jet quenching.

More work is needed!

M. Djordjevic 31

Conclusions

We applied the theory of heavy quark energy loss to compute heavy meson and single electron suppression.

We show that bottom quark contribution can not be neglected in the computation of single electron spectra.

The recent single electron data show significant discrepancies with theoretical predictions based only on

radiative energy loss.

However, the elastic energy loss may have an important contribution to jet quenching.

M. Djordjevic 32

Backup slides:

M. Djordjevic 33

Elastic v.s. radiative energy loss:

Are there other energy loss mechanisms?

Elastic and radiative energy losses are comparable!

(see M. G. Mustafa, Phys.Rev.C72:014905,2005)

BT: E. Braaten and M. H. Thoma, Phys. Rev. D 44, 2625 (1991). TG: M. H. Thoma and M. Gyulassy, Nucl. Phys. B 351, 491 (1991).

M. Djordjevic 34

Heavy quark suppression with the elastic energy loss

The elastic energy loss significantly changes the charm and bottom suppression!

CHARM

BOTTOM

Done by Simon Wicks.

M. Djordjevic 35

Single electron suppression with the elastic energy loss

Reasonable agreement with single electron data,

even for dNg/dy=1000.

(S. Wicks, W. Horowitz, M.D. and M. Gyulassy, in preparation.)

However, overprediction of pion suppression results happens. Possible solution: Include the geometrical fluctuations (W. Horrowitz).

Include elastic energy loss

Done by Simon Wicks.

M. Djordjevic 36

Backup slides

M. Djordjevic 37

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.

g

0

b

b+ce-

However,

1) 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.

M. Djordjevic 38RAA(e-) / RAA(0) > 2

M. Djordjevic 39

M. Djordjevic 40

Collinear factorization

M. Djordjevic 41

Collinear factorization

c

d

A

Ba b

h

M. Djordjevic 42

Ter-Mikayelian backup:

M. Djordjevic 43

Computation was done in the soft gluon limit, i.e. it was assumed that gluon momentum is much smaller than quark momentum.

Additionally we assumed:

Source packet J(p) varies slowly over the range of momentum, i.e. .

Spin in the problem is neglected.

Quark momentum is large, such that we can assume .

M. Djordjevic 44

The momentum distribution of 0th order radiative energy loss

Longitudinal contribution to the energy loss was found to be significant only in the low k < kD region.

(See Eq. 3.23)

M. Djordjevic 45

Fig.2 shows the one loop transverse plasmon mass mg(k)√(2-k2).

We see that mg starts with the value pl=µ/√3 at low k, and that as k grows, mg asymptotically approaches the value of m =µ/√2, in agreement with Rebhan A, Lect. Notes Phys. 583, 161 (2002).

We can conclude that we can approximate the Ter-Mikayelian effect by simply taking mg m .

M. Djordjevic 46

Contrary to the charm, for bottom quark the Ter-Mikayelian effect is negligible.

BOTTOM

M. Djordjevic 47

Transition radiation backup:

M. Djordjevic 48

medium vacuum

L

medium vacuum

L

c

mgmed

This computation was performed assuming a static medium.

M. Djordjevic 49

For massive quarks and medium thickness greater than 3 fm transition radiation becomes independent on the thickness of the medium.

M. Djordjevic 50

Transition radiation lowers Ter-Mikayelian effect from 30% to 15%.

Can this energy loss be smaller in the medium than in the vacuum?

M. Djordjevic 51

medium

vacuum

M. Djordjevic 52

We also have to include the effect of confinement in the vacuum.

There are two approaches to do that:

1) Assume that gluon mass in the vacuum is not exactly zero, but it has some small value on the order of ΛQCD.

2) Assume that vacuum gluon mass is large, i.e. approximately 0.7 GeV.

M. Djordjevic 53

Transition radiation provides natural regularization of m=0 light quark energy loss.

What about confinement in the vacuum? One phenomenological way to simulate confinement in the

vacuum is to assume that gluon has a nonzero mass.

M. Djordjevic 54

Medium induced energy loss backup:

M. Djordjevic 55

In addition to the assumptions used to compute the Ter -Mikayelian effect, we used:

Interaction in a deconfined QGP can be modeled by static color screened Yukawa potentials. The Fourier and color structure of the potential is assumed to be

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

All are distributed with the same density where

The distance between the source and scattering centers is large comparing to the interaction range, i.e. .

M. Djordjevic 56

Difference between net medium and vacuum energy loss

(0) (0) (1)tot TM transE E E E

M. Djordjevic 57

~ gdN

dy

1

3~ ( )gdN

dy

~ gdN

dy

Energy loss dependence on dNg/dy

M. Djordjevic 58

B

D

0.3

Suppression for different coupling parameters

M. Djordjevic 59

“Dead cone” effect for the 0th and 1st order energy loss

M. Djordjevic 60

Single electrons:

M. Djordjevic 61

light

Comparison with pion suppression

M. Djordjevic 62

Charm and Beauty pt distributions in p+p

Charm and Beauty pt distributions in Au+Au

Initial Charm and Beauty pt distributions

M. Djordjevic 63

Panels show single e- from MNR (done by R.Vogt).

Red curves show total single e-; Blue (green) curves show contribution from Charm

(Beauty).

Single electrons at RHIC

Beauty dominate the single e- spectrum after 4.5 GeV!

M. Djordjevic 64

RAA for single electrons at RHICRed solid curve: Raa for non-photonic single e-.

Blue (Green) dashed curves: Raa for single e- from Charm (Beauty) quarks.

We predict small single e- suppression of ~ 0.7

MNR

M. Djordjevic 65

Comparison with experiment

Our predictions do not agree with PHENIX preliminary data.

M. Djordjevic 66

How to explain this puzzle?

From the current model this would be hard to explain because of:

1) Bottom contribution to single electrons

2) Gluon contribution to pions

PHENIX preliminary data suggest single electron suppression similar to pion suppression!

Therefore, to explain the data, we need a model which would eliminate bottom contribution from single electrons + eliminate

gluon contribution from pions!

M. Djordjevic 67

Problems with single electrons I

No centrality dependence

M. Djordjevic 68

Consistency between electron data sets

• STAR systematically (slightly) above PHENIX

• beware: error bars are meant to be taken seriously!

(Slide adapted from Xin Dong, 21st Winter Workshop on

Nuclear Dynamics)

Single electron results can be different by an order of magnitude

Maybe single electrons are not good probe of Heavy quark energy loss?

M. Djordjevic 69

Charm and beauty content in the single electrons is very sensitive to their

fragmentation functions

Problems with single electrons II

Simon Wicks (Columbia U.)

MNR

Single electrons suppression is strongly dependent on

(unknown) charm and beauty fragmentation functions

M. Djordjevic 70

For example for RHIC we should include heavy quarks up to |ymax|=2.5.

For LHC |ymax| could be significantly larger than 3!

Single electron distributions are VERY sensitive to the rapidity window (Ramona Vogt)

At high rapidity, nonperturbative effects may become important!

+

Single electron suppression could be influenced by nonpertutbative effects

We need D mesons!

M. Djordjevic 71pT [GeV/c]

RA

A

M. Djordjevic et al., hep-ph/0410372

N. Armesto et al. hep-ph/0501225

1000gdN

dy

3500gdN

dy

Single electrons from Charm only reproduce Armesto et al. plots

Comparison with results by Armesto et al.

M. Djordjevic 72

Elliptic flow:

M. Djordjevic 73

x

yz

x

py

px

y

y

x

py

px

coordinate-space-anisotropy momentum-space-anisotropy

2cos2 v

What is elliptic flow?

x

ypT

M. Djordjevic 74

Single e 10% Central Au-Au data can be explained by two different approaches:

•Hydro

•PYTHIA pQCD

The answer to this question can give us the measurement of v2 for charm at RHIC.

Observation of the elliptic flow which is much larger than the one predicted by jet quenching, would mean that charm flows at RHIC.

What value of elliptic flow we expect from heavy quark jet quenching?

DOES THE CHARM FLOW AT RHIC?S. Batsouli, S. Kelly, M. Gyulassy , J.L. Nagle

Phys.Lett.B 557 (2003) 26

M. Djordjevic 75

We have estimated v2 for minimum bias case. Here, we have assumed 1+1D Bjorken longitudinal expansion.

According to our estimates, at RHIC we expect charm quark v2 between 0.02 and 0.08.

Shingo Sakai, QM2004

PHENIX preliminary

c

M. Djordjevic 76