M. Djordjevic 1

Heavy quark energy loss: radiative v.s. collisional

Magdalena Djordjevic

The Ohio State University

M. Djordjevic 2

Quark Gluon Plasma

Form, observe and understand Quark-Gluon Plasma (QGP).

Heavy quarks (charm and beauty, M>1 GeV) are widely recognized as the cleanest probes of QGP.

High Energy Heavy Ion Physics

Heavy mesons not yet available, but they are expected soon!

N. Brambilla et al., e-Print hep-ph/0412158 (2004).

M. Djordjevic 3

Significant reduction at high pT suggests sizeable heavy quark energy loss!

Indirect probe- single electron suppression – is available

V. Greene, S. Butsyk, QM2005 talks J. Dunlop, J. Bielcik; QM05 talks

Can this be explained by the energy loss in QGP?

M. Djordjevic 4

Outline

Discuss the heavy quark energy loss mechanisms:

Radiative energy loss.

Collisional energy loss.

Single electron suppression results that come from the above mechanisms.

M. Djordjevic 5

Radiative heavy quark energy loss

Three important medium effects control the radiative energy loss:

1) Ter-Mikayelian effect (M.L.Ter-Mikayelian (1954); Kampfer-Pavlenko (2000);

Djordjevic-Gyulassy (2003)) 2) Transition radiation (Zakharov (2002); Djordjevic (2006)). 3) Medium induced radiative energy loss

(Djordjevic-Gyulassy (2003); Zhang-Wang-Wang (2004); Armesto-Salgado-Wiedemann (2004))

c

L

c

1) 2) 3)

M. Djordjevic 6

Transition & Ter-Mikayelian effects on 0th order radiative energy loss

Transition & Ter-Mikayelian effects approximately cancel each other for heavy quarks.

M.D., Phys.Rev.C73:044912,2006

CHARM BOTTOM

M. Djordjevic 7

c

c

L

Medium induced radiative energy loss

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 8

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

Final Result to Arbitrary Order in Opacity (L/) with MQ and mg> 0M. D. and M. Gyulassy, Phys. Lett. B 560, 37 (2003); Nucl. Phys. A 733, 265 (2004)

M. Djordjevic 9

LHC, dNg/dy=3000 RHIC, dNg/dy=1000

Numerical results for 1st order in opacity induced radiative energy loss

M. Djordjevic 10

Radiative energy loss alone is not able to explain the single electron data as long as realistic parameter values are taken into account!

1000gdN

dy

M. D., M. Gyulassy, R. Vogt and S. Wicks, Phys. Lett. B 632, 81 (2006)

Can single electron suppression be explained by the radiative energy loss in QGP?

Radiative energy loss predictions

with dNg/dy=1000

Disagreement!

M. Djordjevic 11

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

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

Collisional energy loss is negligible!

Conclusion was based on inaccurate assumptions (i.e. they used α=0.2), and assumed that

dE/dL<0.5 GeV/fm is negligible.

Early work: Recent work:

Is collisional energy loss also important?

Collisional and radiative energy losses are comparable!

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

A. K. Dutt-Mazumder et al.,Phys.Rev.D71:094016,2005

Will collisional energy loss still be important once finite size

effects are included?

Above computations are done in an ideal infinite QCD medium.

M. Djordjevic 12

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 13

The 0th order collisional energy loss is determined from:

L

Collisional energy loss in a finite size QCD medium

The effective gluon propagator:

Consider a medium of size L in thermal equilibrium at temperature T.

M.D., nucl-th/0603066

M. Djordjevic 14

Comparison between computations of collisional energy loss in finite and infinite QCD medium

Finite size effects are not significant, except for very small path-lengths.

M.D., nucl-th/0603066

M. Djordjevic 15

Bottom quark collisional energy loss is significantly smaller than charm energy loss.

M.D., nucl-th/0603066

Comparison between charm and bottom collisional energy loss

M. Djordjevic 16

Collisional v.s. medium induced radiative energy loss

Collisional and radiative energy losses are comparable!

M.D., nucl-th/0603066

Complementary approach by A. Adil et al., nucl-th/0606010: consistent results obtained.

M. Djordjevic 17

Most up to date single electron prediction (collisional + radiative)

Inclusion of collisional energy loss leads to better agreement with single electron data, even

for dNg/dy=1000.

(S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076)

Radiative energy loss alone is not able to explain the single

electron data, as long as realistic gluon rapidity density

dNg/dy=1000 is considered.

See talk by S. Wicks, parallel session I

M. Djordjevic 18

Conclusions

Radiative energy loss mechanisms alone are not able to explain the recent single electron data.

Collisional and radiative energy losses are comparable, and both contributions are important

in the computations of jet quenching.

Inclusion of the collisional energy loss lead to better agreement with the experimental results.

M. Djordjevic 19

Acknowledgements:

Miklos Gyulassy

(Columbia University)

Simon Wicks

(Columbia University)

Ramona Vogt

(LBNL, Berkeley and University of California, Davis)

William Horowitz

(Columbia University)

M. Djordjevic 20

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 21

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 22

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 23

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-.

Single electron suppression

D, B

1)

production

2)

medium energy loss

3)

fragmentation

c, b e-

4)

decay

M. Djordjevic 24

D mesons

, ’,

A

B

Initial heavy quark pt distributions

200S GeV

High quark mass, i.e. M»ΛQCD

Perturbative calculations of heavy quark production possible.

M. Cacciari, P. Nason and R.Vogt, Phys.Rev.Lett.95:122001,2005;

MNR code (M. L. Mangano, P.Nason and G. Ridolfi,

Nucl.Phys.B373,295(1992)).

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

M. Djordjevic 25M. D., M. Gyulassy and S. Wicks, Phys. Rev. Lett. 94, 112301 (2005).

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

Before quenching After quenching

M. Gyulassy, P. Levai and I. Vitev, Phys.Lett.B538:282-288 (2002).

M. Djordjevic 26

Panels show single e- from FONLL M. Cacciari, P. Nason and R. Vogt, Phys.Rev.Lett.95:122001,2005

M. D., M. Gyulassy, R. Vogt and S. Wicks, Phys.Lett.B632:81-86,2006

Single electrons pt distributionsB

efor

e q

uen

chin

g

Aft

er q

uen

chin

g

Bottom dominate the single e- spectrum above 4.5 GeV!

M. Djordjevic 27

Single electron suppression as a function of pt

At pt~5GeV, RAA(e-) 0.7±0.1 at RHIC.

M. Djordjevic 28

Are there other energy loss mechanisms?

Collisional and radiative energy losses are comparable!

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

Finite size effects significantly lower collisional energy loss

S. Peigne, P.-B. Gossiaux, T. Gousset, hep-ph/0509185

The paper, however, did not make separation between elastic and part of

radiative energy loss effects.

M. Djordjevic 30

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 31

Comparison with other models

Ideal infinite QCD medium case:

Thoma-Gyulassy (1990) (linear response approach).

Braaten-Thoma (1991) (quantum-mechanical approach).

Romatasche-Strickland (2003) (anisotropic medium).

Finite QCD medium case:

Peigne-Gossiaux-Gousset (hep-ph/0509185, 2005) (linear response approach): Finite size effects significantly reduce the collisional energy loss.

Wang (nucl-th/0604040, 2006) (quantum-mechanical approach): interference effects exist at 0 th order energy loss level.

Adil-Gyulassy-Horowitz-Wicks (nucl-th/0606010, 2006) (linear response approach): obtained consistent results.