1. Zimanyi Memorial Workshop July 2007 1 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

2. Zimanyi Memorial Workshop July 2007 2 Present situation: a)Multiplicity of stable hadrons made of (u,d,s) is described by thermal models b)Multiplicity of unstable hadrons can be understood in terms of hadronic final state interactions c)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 quark Here we concentrate on open charm mesons for which indirect experimental data are available (single electrons)

3. Zimanyi Memorial Workshop July 2007 3 Why Heavy Quarks probe the QGP Idea: Heavy quarks are produced in hard processes with a known initial 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 using pt distribution, v 2 transfer, back to back correlations

4. Zimanyi Memorial Workshop July 2007 4 (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

5. Zimanyi Memorial Workshop July 2007 5 Individual heavy quarks follow Brownian motion: we can describe the time evolution of their distribution by a Fokker – Planck equation: 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

6. Zimanyi Memorial Workshop July 2007 6 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) pzpz pxpx pypy

7. Zimanyi Memorial Workshop July 2007 7 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 study the physics Similar for the diffusion coefficient B νμ ~ > A describes the deceleration of the c-quark B describes the thermalisation

8. Zimanyi Memorial Workshop July 2007 8 c-quarks transverse momentum distribution (y=0 )    col       Distribution just before hadronisation p-p distribution Plasma will not thermalize the c: It carries information on the QGP Heinz & Kolb’s hydro

9. Zimanyi Memorial Workshop July 2007 9 Energy loss and A,B are related (Walton and Rafelski) p i A i + p dE/dx = - > which gives easy relations for p c >>m c and p c <<m c 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)

10. Zimanyi Memorial Workshop July 2007 10 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

11. Zimanyi Memorial Workshop July 2007 11 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.

12. Zimanyi Memorial Workshop July 2007 12 Leptons (  D decay) transverse momentum distribution (y=0) R AA κ = 20, κ=10 0-10% pt Comparison to B=0 calculation 2  2 only Conclusion I: Energy loss alone is not sufficient K col (coll only) =10-20: Still far away from thermalization ! Langevin A and B finite B=0 (Just deceleration)

13. Zimanyi Memorial Workshop July 2007 13 Latest Published Phenix Data nucl-ex/0611018 Star and Phenix agree (Antinori SQM 07) There is a more recent data set

14. Zimanyi Memorial Workshop July 2007 14 « 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 E q /E charm ℳ q cqg ≡ c Q + + + + : if evaluated in the large p i c+ limit in the lab (Bertsch-Gunion)

15. Zimanyi Memorial Workshop July 2007 15 q k x=long. mom. Fraction of g In the limit of vanishing masses: Gunion + Bertsch PRD 25, 746 But: Masses change the radiation substantially Evaluated in scalar QCD and in the limit of E charm >> masses and >>qt Factorization of radiation and elastic scattering

16. Zimanyi Memorial Workshop July 2007 16 R AA 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 R AA either : With a high enhancement factor for collisional processes With « reasonnable » enhancement factor (  rad not far away from unity) including radiative processes. pt (large sqrts limit)

17. Zimanyi Memorial Workshop July 2007 17 Non-Photonic Electron elliptic-flow at RHIC: comparison with experimental results Collisional (  col = 20 ) Collisional + Radiative c-quarksD decay e Tagged const q D c q Conclusion III: One cannot reproduce the v 2 consistently with the R AA !!! 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: v2v2 v 2 pt

18. Zimanyi Memorial Workshop July 2007 18 Non-Photonic Electron elliptic-flow at RHIC: Looking into the bits… const quark tagged by c Bigger coupling helps… a little but at the cost of R AA C-quark does not see the « average » const quark… Why ? v 2 (tagged  ) v 2 (all  ) SQM06

19. Zimanyi Memorial Workshop July 2007 19 This is a generic problem ! Van Hees and Rapp: Charmed resonances and Expanding fireball (does not reproduce non charmed hadrons) Communicate more efficiently v 2 to the c- quarks Moore and Teaney: Even choice of the EOS which dives the largest v 2 possible does not predict non charmed hadron data assuming D mesons Only ‘exotic hadronization mechanisms’ may explain the large v 2 EXPERIMENT ?

20. Zimanyi Memorial Workshop July 2007 20 R AA is about 0.25 for large p t for Star and Phenix Confirms that large diffusion coefficients are excluded Actual problems -- D /  c ratio (Gadat SQM07) -- B contribution D0,D0D0,D0 D+,D-D+,D- Ds+Ds-Ds+Ds- c+c-c+c- BR (X  e) 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 Star and Phenix

21. Zimanyi Memorial Workshop July 2007 21 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

22. Zimanyi Memorial Workshop July 2007 22 Azimutal Correlations for Open Charm - c-quarks Correlations are small at small p t,, mostly washed away by coalescence process. D Coll (  col = 10 ) Coll (  col = 20 ) Coll (  col = 1 ) Coll + rad (  col =  rad = 1 ) No interaction Small p t (p t < 1GeV/c ) coalescence  c -  cbar  D -  Dbar 0-10% SQM06

23. Zimanyi Memorial Workshop July 2007 23 Azimutal Correlations for Open Charm - 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 D Coll (  col = 10 ) Coll (  col = 20 ) Coll (  col = 1 ) Coll + rad (  col =  rad = 1 ) No interaction Average p t (1 GeV/c < p t < 4 GeV/c ) coalescence Azimutal correlations might help identifying better the thermalization process and thus the medium  c -  cbar  D -  Dbar 0-10% SQM06

24. Zimanyi Memorial Workshop July 2007 24 Azimutal Correlations for Open Charm - c-quarks Large reduction but small broadening for increasing coupling with the medium; compatible with corona effect D Coll (  col = 10 ) Coll (  col = 20 ) Coll (  col = 1 ) Coll + rad (  col =  rad = 1 ) No interaction Large p t (4 GeV/c < p t ) coalescence  c -  cbar  D -  Dbar 0-10% SQM06

25. Zimanyi Memorial Workshop July 2007 25 Conclusions Experimental data point towards a significant (although not complete) thermalization of c quarks in QGP. The model seems able to reproduce experimental R AA, at the price of a large rescaling K-factor (especially at large p t ), of the order of k=10 or by including radiative processes. Still a lot to do in order to understand the v 2. 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 (v 2,,azimuthal correlations???) Azimutal correlations could be of great help in order to identify the nature of thermalizing mechanism.

26. Zimanyi Memorial Workshop July 2007 26 V2 -- Au+Au -- 200 -- Min. Bias

27. Zimanyi Memorial Workshop July 2007 27