1. 24th Winter Workshop Nuclear Dynamics 1 Towards an understanding of the single electron spectra or what can we learn from heavy quarks of a plasma? P.-B. Gossiaux, A. Peshier & J. Aichelin Subatech/ Nantes/ France arXiv: 0802.2525

2. 24th Winter Workshop Nuclear Dynamics 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. 24th Winter Workshop Nuclear Dynamics 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. 24th Winter Workshop Nuclear Dynamics 4 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

5. 24th Winter Workshop Nuclear Dynamics 5 The drift and diffusion coefficients Strategy: take the elementary cross sections for charm scattering (Qq and Qg) and calculate the coefficients (g = thermal distribution of the collision partners) and then introduce an overall K factor to study the physics Similar for the diffusion coefficient B νμ ~ > A describes the deceleration of the c-quark B describes the thermalisation

6. 24th Winter Workshop Nuclear Dynamics 6 c-quarks transverse momentum distribution (y=0 )     Distribution just before hadronisation p-p distribution Plasma will not thermalize the c: It carries information on the QGP Heinz & Kolb’s hydro

7. 24th Winter Workshop Nuclear Dynamics 7 There is a generic problem ! Van Hees and Rapp: Charmed resonances and expanding fireball. Communicates more efficiently v 2 to the c- quarks than hydro Moore and Teaney: Even choice of the EOS which gives the largest v 2 possible does not predict non charmed hadron data. Only ‘exotic hadronization mechanisms’ may explain the large v 2 K  15

8. 24th Winter Workshop Nuclear Dynamics 8 Can one improve and, if yes, how? Boltzmann vs Fokker-Planck T=400 MeV a s =0.3 collisions with thermal quarks & gluons 2fm/c 10fm/c Fokker-Planck does not give a good description of the energy loss at intermediate times. Reason: Qg->Qg ptpt ptpt FP Boltzm -> Boltzmann equation

9. 24th Winter Workshop Nuclear Dynamics 9 Problems of the existing approaches: RAA or energy loss is determined by the elementary elastic scattering cross section α (t) =g 2 /4  is taken as constant [0.2 < α < 0.6]  m D  gT But α (t) is running and m D is not well determined Is there a way to get a handle on them ? These large artificial K (multiplication) factors or new physical processes are needed to describe the data if

10. 24th Winter Workshop Nuclear Dynamics 10 Information on the strong coupling constant A ) Brodsky et al. PRD 67 055008 - Nonstrange hadronic  decay (OPAL) - e + e - -> hadrons Provide ‘physical’ coupling constants (determined by fits to the experimental data in the time like sector) : R  = R  0 (1+   (m 2  )/  ) R e =  (e + e - -> h)/  (e + e - ->  +  - ) = R 0 (1+  R (s)/  ) They remain finite down to very low values of s.. The physical coupling constant is a summation of all orders of perturbations which nature has done for us.   V (m  2 ) =  e I=1 (s)  s (s) and  s (t) connected by generalized Crewther relations

11. 24th Winter Workshop Nuclear Dynamics 11 The detailed form very close to Q 2 =0 is not important does not contribute to the energy loss b) Dokshitzer NPB 469 (96) 93: Observable = time like effective coupling * Process dependent fct Effective coupling is infrared save This approach we use for the actual calculation

12. 24th Winter Workshop Nuclear Dynamics 12 presently used: But prefactor not well determined taken between 1 and 1/3 How to improve on the Debye mass ? Regulates the long range behaviour of the interaction

13. 24th Winter Workshop Nuclear Dynamics 13 In reality the situation is more complicated: Loops are formed If t is small (<<T) : Born has to be replaced by a hard thermal loop (HTL) approach (Braaten and Thoma PRD44 (91) 1298,2625) For t>T Born approximation is ok In QED the energy loss does not depend on t * which separates the two regimes and which is artificial)  = E-E’

14. 24th Winter Workshop Nuclear Dynamics 14 This concept has been extended to QCD HTL in QCD cross sections is too complicated Idea: - Use HTL (t t * ) amplitude to calculate dE/dx make sure that result does not depend on t * - determine which  gives the same enegry loss if one uses a cross section of the form In reality a bit more complicated: with Born matching region of t * outside the range of validity of HTL -> add to Born a constant  Constant coupling constant -> Analytical formula -> arXiv: 0802.2525 Running -> numerically

15. 24th Winter Workshop Nuclear Dynamics 15 dE/dx does not depend on t * HTL+semihard needed to have the transition in the range of validity of HTL The resulting  values are smaller than those used up to now.

16. 24th Winter Workshop Nuclear Dynamics 16 The matching gives   0.15 m D for running  S for the Debye mass and   0.22 m D not running! standard new c+q->c+q c+g_>c+g Large enhancement of both cross sections at small t Difference between running coupling and fixed coupling for the Debye mass negligible Little change at large t Qq->Qq Qg_>Qg Standard:  (2  T),  =m D

17. 24th Winter Workshop Nuclear Dynamics 17 Consequences for the energy loss Probability P(w) that a c-quark looses the energy w in a collision with a quark and a gluon, T= 400 MeV c+q -> c+q c+g->c+g wP(w) ~ dE/dxdw  contribution to the energy loss

18. 24th Winter Workshop Nuclear Dynamics 18 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  Cronin effect included. 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.

19. 24th Winter Workshop Nuclear Dynamics 19 Consequences for RAA including Cronin effect b and c separated (Cacciari PRL 95 (05) 122001) Old K=12 New K=1.5-2 b c central The new approach reduces the K- factor K=12 -> K=1,5-2 No radiative energy loss yet p T > 2 bottom dominated!! more difficult to stop compatible with experiment

20. 24th Winter Workshop Nuclear Dynamics 20 minimum bias New K=1,5-2 Old K=12 Central and Minimum bias events described by the same parameter Different between b and c becomes smaller

21. 24th Winter Workshop Nuclear Dynamics 21 Out of plane distribution V 2 New K=1,5-2 Old K=20-40 Even with very large K factors the data are out of range Cronin influences little v 2 heavy mesons depends on where fragmentation/ coalescence takes place end of mixed phase beginning of mixed phase

22. 24th Winter Workshop Nuclear Dynamics 22 Back to back correlations of c and cbar pair are unfortunatelly not able to distinguish between the different cross sections  running  = 0.15  (2  T)

23. 24th Winter Workshop Nuclear Dynamics 23 Conclusions Experimental data point towards a significant (although not complete) thermalization of c quarks in QGP. Using a running coupling constant, determined by experiment, and an infrared regulator which approximates hard thermal loop results we are almost able to reproduce the experimental R AA and v 2. The missing factor of two can be due to radiative processes or due uncertainties: 1)spatial distribution of initial c-quarks 2)Part of the flow is due to the hadronic phase subsequent to QGP 3)Dependence on the fragmentation scale in a thermal environment Azimutal correlations could be of great help in order to identify the nature of thermalizing mechanism but does not distinguish between the  ’s  discussed here Single electron data are compatible with pQCD

24. 24th Winter Workshop Nuclear Dynamics 24 (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

25. 24th Winter Workshop Nuclear Dynamics 25 « 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)