M. Djordjevic 1

Open questions in heavy flavor physics at RHIC

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:

Heavy meson and single electron suppression results that come from the above mechanisms.

Open questions that can be addressed in the future RHIC experiments.

Radiative energy loss. Collisional energy loss.

M. Djordjevic 5

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-.

From production to decay

D, B

1)

production

2)

medium energy loss

3)

fragmentation

c, b e-

4)

decay

M. Djordjevic 6

D mesons

, ’,

A

B

Initial heavy quark pt distributions

200S GeV

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 7

c

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.

Caused by the multiple interactions of partons in the medium.

M. Djordjevic and M. Gyulassy, Nucl. Phys. A 733, 265 (2004).

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> 0

M. Djordjevic 9

Thickness dependence is closer to linear Bethe-Heitler like form. This is different than the asymptotic energy

quadratic form characteristic for light quarks.

The numerical results for induced radiative energy loss are shown for first order in opacity, for L= 5 fm, =1 fm.

M. Djordjevic 10M. 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 11

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 12

Single electron suppression as a function of pt

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

M. Djordjevic 13

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

1000gdN

dy

M. D. et al., 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 14

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 outdated assumptions (i.e. they used =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 15

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 16

The main 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. Djordjevic 17

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 18

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 19

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 20

Heavy quark suppression with the collisional energy loss

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

CHARM

BOTTOM

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

M. Djordjevic 21

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.

M. Djordjevic 22

The agreement between the theory and the single electron data

may still not be good enough!

However, theoretical predictions depend

on the underlying assumptions.

How good are these assumptions?

What are the open questions?

How can future RHIC experiments improve our

understanding of heavy flavor physics at RHIC?

M. Djordjevic 23

How well do we understand:

Are single electrons good probe of heavy quark energy loss?

Open questions:

1) charm and bottom production at RHIC?

2) charm and bottom contributions to the single electrons?

3) the energy loss at RHIC?

M. Djordjevic 24Need work by both theory and experiment to gain a better understanding!

How well do we understand charm and bottom production at RHIC?

Theoretical computations seem to notably underpredict the data.

Theoretically: Experimentally:

STAR and PHENIX data may be systematically off by factor of 2.

STAR (nucl-ex/0607012) Ralf Averbeck’s talk (QM2004)

M. Djordjevic 25

How well do we understand charm and bottom contributions to the single electrons?

Good agreement with the data if only charm contribution is

taken into account.

Is charm enhanced at RHIC?

Need direct D and B measurements to resolve a puzzle and make stronger conclusions!(S. Wicks, W. Horowitz, M.D. and M. Gyulassy,

nucl-th/0512076)

Current pQCD calculations ce/be Ο(1)

M. Djordjevic 26

How well we understand the energy loss at RHIC?

According to pQCD theory, clear hierarchy in the suppression patterns!

Theoretically:

Gluons are more suppressed than light quarks! Charm is more suppressed than bottom!

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

M. Djordjevic 27

Potential absence of hierarchy would challenge the pQCD energy loss mechanisms!

Data may indicate the same energy loss for charm and bottom!

Data may indicate the same energy loss for gluons and light quarks!

However, experimentally:

Need: direct D and B mesons + high accuracy pbar/p measurements

STAR (nucl-ex/0606003)

M. Djordjevic 28

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

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

Upcoming D and B meson measurements at mid rapidity should resolve this issue

Are single electrons good probe of heavy quark energy loss?

M. Djordjevic 29

How D’s and B’s should be measured in the upcoming

RHIC experiments?

• Measure (just) D mesons directly in mid

rapidity region.

• Subtract D’s from single electrons to get B’s.

• Problem: Instead of mid rapidity B’s, in this

way we would get a mixture of high rapidity

D’s and all rapidity B’s.

NO!

Measure both D and B mesons directly in

central rapidity region.YES!

M. Djordjevic 30

Summary

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.

Future direct D and B measurements will be important to get a better understanding of heavy quark physics at RHIC.

M. Djordjevic 31

Backup slides

M. Djordjevic 32

Most up to date pion and single electron predictions (collisional + radiative)

Inclusion of collisional energy loss leads to good agreement with pions and an improved agreement with single electron data at dNg/dy=1000.

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

M. Djordjevic 33

Path length fluctuations

Important for gluons and consistency of electron and pion predictions.

•Realistic Woods-Saxon nuclear density

•Jets produced ~ TAA

•1+1D Bjorken expantion

Hierarchy of fixed lengths fit the full

geometrical calculations.

No a priori justification for any fixed length.

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

M. Djordjevic 34

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 36

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) Energy loss due to the interaction with the medium

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

c

L

c

1) 2) 3)

M. Djordjevic 37

The uncertainity band obtained by varying the quark mass and scale factors.

Domination of bottom in single electron spectra

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

R. Vogt, talk given at QM2005

M. Djordjevic 38

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 39

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.