Tomography of a Quark Gluon Plasma by Heavy Quarks :

Zimanyi Memorial Workshop July 2007

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Tomography of a Quark Gluon Plasma

by Heavy Quarks :P.-B. Gossiaux , V. Guiho, A. Peshier & J. Aichelin

Subatech/ Nantes/ France

Zimanyi 75 Memorial Workshop


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Present situation:a) Multiplicity of stable hadrons made of (u,d,s) is described by thermal modelsb) Multiplicity of unstable hadrons can be understood in terms of hadronic final state interactionsc) Slopes difficult to interpret due to the many hadronic interactions (however the successful coalescence models hints towards a v2 production in the plasma)d) Electromagnetic probes from plasma and hadrons rather similar

If one wants to have direct information of the plasma one has to find other probes:

Good candidate: hadrons with a c or b quarkHere we concentrate on open charm mesons for which indirect experimental data are available (single electrons)


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Why Heavy Quarks probe the QGP

Idea: Heavy quarks are produced in hard processes with a knowninitial momentum distribution (from pp).

If the heavy quarks pass through a QGP they collide and radiate and therefore change their momentum.

If the relaxation time is larger than the time they spent in the plasma their final momentum distribution carries information on the plasma

This may allow for studying plasma properties usingpt distribution, v2 transfer, back to back correlations


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(hard) production of heavy quarks in initial NN collisions

Evolution of heavy quarks in QGP (thermalization)

Quarkonia formation in QGP through c+c+g fusion process

D/B formation at the boundary of QGP through coalescence of c/b and light quark

Schematic view of our model for hidden and open heavy flavors production in AA collision at RHIC and LHC


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Individual heavy quarks follow Brownian motion: we can describe the time evolution of their distribution by a

Fokker – Planck equation:

fBfAtf

pp

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Input reduced to Drift (A) and Diffusion (B) coefficient.

Much less complex than a parton cascade which has to follow the light particles and their thermalization as well.

Can be combined with adequate models like hydro for the dynamics of light quarks


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From Fokker-Planck coefficients Langevin forces

Evolution of one c quark inside a =0 -- T=400 MeV QGP.

Starting from p=(0,0,10 GeV/c).

Evolution time = 30 fm/c

… looks a little less « erratic » when considered on the average:

Relaxation time >> collision time : self consistent t (fm/c)

pz f

pz

px

py


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The drift and diffusion coefficients

Strategy: take the elementary cross sections for charm and calculate the coefficients (g = thermal distribution of the collision partners)

and then introduce an overall κ factor to studythe physics

Similar for the diffusion coefficient Bνμ ~ << (pν

- pνf )(pμ

- pμf )> >

A describes the deceleration of the c-quark B describes the thermalisation


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c-quarks transverse momentum distribution (y=0)

col

Distribution just before hadronisation

p-p distribution

Plasma will notthermalize the c:It carries informationon the QGP

Heinz & Kolb’s hydro


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Energy loss and A,B are related (Walton and Rafelski)

pi Ai + p dE/dx = - << (pμ – pμf)2

>>

which gives easy relations for pc>>mc and pc<<mc

dE/dx and A are of the same order of magnitude

p (GeV/c)

A (Gev/fm)

T=0.3

T=0.4

T=0.5

T=0.2

dE/dx (GeV/fm)

p (GeV/c)


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In case of collisions (2 2 processes): Pioneering work of Cleymans (1985), Svetitsky (1987), extended later by Mustafa, Pal & Srivastava (1997).

Later Teaney and Moore, Rapp and Hees similar approach but plasma treatment is different

• For radiation: Numerous works on energy loss; very little has been done on drift and diffusion coefficients


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Input quantities for our calculations Au – Au collision at 200 AGeV

. c-quark transverse-space distribution according to Glauber

• c-quark transverse momentum distribution as in d-Au (STAR)… seems very similar to p-p No Cronin effect included; to be improved.

• c-quark rapidity distribution according to R.Vogt (Int.J.Mod.Phys. E12 (2003) 211-270).

• Medium evolution: 4D / Need local quantities such as T(x,t) taken from hydrodynamical evolution (Heinz & Kolb)

•D meson produced via coalescence mechanism. (at the transition temperature we pick a u/d quark with the a thermal distribution) but other scenarios possible.


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Leptons ( D decay) transverse momentum distribution (y=0)

RAA

1 2 3 4 5

0.2

0.4

0.6

0.8

1

κ = 20, κ=100-10%

pt

Comparison to B=0 calculation

2 2 only

Conclusion I:

Energy loss alone is not sufficient

Kcol(coll only) =10-20: Still far away from thermalization !

Langevin A and B finite

B=0 (Just deceleration)


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2 4 6 8PTGeVc0.2

0.4

0.6

0.8

1

1.2

1.4

RAA lept

K10

K20

AuAu; 010% central

Latest Published Phenix Data nucl-ex/0611018

Star and Phenix agree(Antinori SQM 07)

There is a more recent data set


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« radiative » coefficients deduced using the elementary cross section for cQ cQ+g and for cg cg +g in t-channel (u & s-channels are suppressed at high energy).

"Radiative« coefficients

dominant suppresses by Eq/Echarm

ℳqcqg ≡

c

Q+ ++ +

:if evaluated in the large pi

c+ limit in the lab (Bertsch-Gunion)


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q

k

x=long. mom. Fraction of g

In the limit of vanishing masses:Gunion + Bertsch PRD 25, 746

But:

Masses change the radiationsubstantially

Evaluated in scalar QCD and in the limit of Echarm >> masses and >>qt

Factorization of radiation and elastic scattering


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2 4 6 8

0.2

0.4

0.6

0.8

1

1.2

1.4

2 4 6 8

0.2

0.4

0.6

0.8

1

1.2

1.4

RAA

2 4 6 8

0.2

0.4

0.6

0.8

1

1.2

1.4

Leptons ( D decay) transverse momentum distribution (y=0)

0-10% 20-40%

Min bias

Col. (col=10 & 20)

Col.+(0.5x) Rad

Conclusion II:

One can reproduce the RAA either :

• With a high enhancement factor for collisional processes

• With « reasonnable » enhancement

factor (rad not far away from unity)

including radiative processes.

pt

pt

pt

(large sqrts limit)


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Non-Photonic Electron elliptic-flow at RHIC: comparison with experimental results

0.5 1 1.5 2 2.5 3 3.5 4

0.05

0.05

0.1

0.5 1 1.5 2 2.5 3 3.5 4

0.05

0.05

0.1

Collisional

(col= 20)

Collisional + Radiative

c-quarks D

decay eTagged const q

D

cq

Conclusion III:

One cannot reproduce the v2

consistently with the RAA!!! Contribution of light quarks to the elliptic flow of D mesons is small

Freezed out according to thermal distribution at "punch" points of c quarks through freeze out surface:

v2

v2

pt

pt


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Non-Photonic Electron elliptic-flow at RHIC: Looking into the bits…

0.5 1 1.5 2 2.5 3 3.5 4

0.05

0.05

0.1

0.5 1 1.5 2 2.5 3

0.025

0.05

0.075

0.10.125

0.15const quark tagged by c

Bigger coupling helps… a little but

at the cost of RAA

C-quark does not see the « average » const quark… Why ?

v2 (tagged )

v2 (all )

SQM06


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This is a generic problem ! Van Hees and Rapp:Charmed resonances andExpanding fireball (doesnot reproduce non charmedhadrons) Communicate more efficientlyv2 to the c- quarks

Moore and Teaney:Even choice of the EOS which dives the largest v2 possibledoes not predict non charmedhadron data assuming D mesons

Only ‘exotic hadronization mechanisms’ may explain the

large v2

EXPERIMENT ?


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RAA is about 0.25 for large pt

for Star and Phenix

Confirms that large diffusion coefficients are excludedActual problems-- D / c ratio (Gadat SQM07)-- B contribution

D0, D0

D+, D-

Ds+

Ds-

c+

c-

BR (Xe) in %

17.2 1.9

6.71

0.29

8 +6-5

4.5 1.7

X. Lin SQM07

Problems on exp. side

Large discrepancy between Starand Phenix


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Azimutal Correlations for Open Charm

What can we learn about the "thermalization" process from the

correlations remaining at the end of QGP ?c

D

c-bar

Dbar

Transverse plane

Initial correlation (at RHIC); supposed back to back here

How does the coalescence - fragmentation mechanism affects

the "signature" ?

SQM06


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1 2 3 4 5 6

1

2

3

4

5

6

7

8

1 2 3 4 5 6

1

2

3

4

5

6

7

8


c-quarks

Correlations are small at small pt,, mostly

washed away by coalescence process. D

Coll (col= 10)

Coll (col= 20)

Coll (col= 1)

Coll + rad (col= rad = 1)

No interactionSmall pt (pt < 1GeV/c )

coalescence c - cbar

D - Dbar

0-10%

SQM06


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1 2 3 4 5 6

1

2

3

4

5

6

7

8

c-quarks

Conclusion IV: Broadening of the correlation due to medium, but still visible. Results for genuine coll + rad and for cranked up coll differ significantly

1 2 3 4 5 6

1

2

3

4

5

6

7

8

D

Coll (col= 10)

Coll (col= 20)

Coll (col= 1)


No interactionAverage pt (1 GeV/c < pt < 4 GeV/c )

coalescence

Azimutal correlations might help identifying better the thermalization

process and thus the medium

c - cbar

D - Dbar

0-10%

SQM06


241 2 3 4 5 6

0.1

0.2

0.3

0.4

0.5

1 2 3 4 5 6

0.1

0.2

0.3

0.4

0.5


c-quarks

Large reduction but small broadening for increasing coupling with the medium;

compatible with corona effectD

Coll (col= 10)

Coll (col= 20)

Coll (col= 1)


No interactionLarge pt (4 GeV/c < pt )

coalescence c - cbar

D - Dbar

0-10%

SQM06


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Conclusions

• Experimental data point towards a significant (although not complete) thermalization of c quarks in QGP.

• The model seems able to reproduce experimental RAA, at the price of a large rescaling K-factor (especially at large pt), of the order of k=10 or by including radiative processes.

• Still a lot to do in order to understand the v2. Possible explanations for discrepancies are:

1) spatial distribution of initial c-quarks

2) Part of the flow is due to the hadronic phase subsequent to QGP

3) Reaction scenario different

4) Miclos Nessi (v2, ,azimuthal correlations???)

Azimutal correlations could be of great help in order to identify the nature of thermalizing mechanism.


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V2 -- Au+Au -- 200 -- Min. Bias

0.5 1 1.5 2 2.5 3 3.5 4PTGeVc0.02

0.04

0.06

0.08

0.1

0.12v2 lept

K10 K20

min. bias


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Tomography of a Quark Gluon Plasma by Heavy Quarks :