Tomography of a Quark Gluon Plasma by Heavy Quarks :

1. Tomography of a Quark Gluon Plasma by Heavy Quarks : P.-B. Gossiaux, V. Guiho, A. Peshier & J. Aichelin Subatech/ Nantes/ France INPC Tokyo June 2007

2. Present situation: • Multiplicity of stable hadrons made of (u,d,s) is • described by thermal models • Multiplicity of unstable hadrons can be understood in • terms of hadronic final state interactions • Slopes difficult to interpret due to the many hadronic • interactions (however the successful coalescence • models hints towards a v2 production in the plasma) • 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) INPC Tokyo June 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 radiateand therefore change their momentum. If the relaxation time is larger than the time they spent in the plasmatheir final momentum distribution carries information on the plasma This may allow for studying plasma properties using pt distribution, v2 transfer, back to back correlations INPC Tokyo June 2007

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 INPC Tokyo June 2007

5. The drift and diffusioncoefficients Strategy:take the elementary cross sections for charmand 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 Bνμ ~ << (pν- pνf )(pμ- pμf )> > A describes the deceleration of the c-quark B describes the thermalisation INPC Tokyo June 2007

6. p-p distribution c-quarks transverse momentum distribution (y=0) Heinz & Kolb’s hydro Distribution just beforehadronisation Plasma will not thermalize the c: It carries information on the QGP kcol=5 k=40 k=10 k=20 INPC Tokyo June 2007

7. 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 • In case of collisions (2 2 processes): Pioneering work of Cleymans (1985), Svetitsky (1987), extended later by Mustafa, Pal & Srivastava (1997). Teany 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 INPC Tokyo June 2007

8. Input quantitiesfor 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. INPC Tokyo June 2007

9. Leptons ( D decay) transverse momentum distribution (y=0) RAA Comparison to B=0 calculation 2 2 only Langevin A and B finite κ = 20, κ=10 0-10% pt B=0 (Just deceleration) Conclusion I: Kcol(coll only) =10-20: Still far away from thermalization ! INPC Tokyo June 2007

10. c ℳqcqg≡ + + Q + + "Radiative« coefficients « 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). dominant suppresses by Eq/Echarm if evaluated in the large pic limit in the lab : INPC Tokyo June 2007

11. Leptons ( D decay) transverse momentum distribution (y=0) (large sqrts limit) RAA 0-10% 20-40% Col.+(0.5x) Rad Col. (kcol=10 & 20) pt pt • Conclusion II: • One can reproduce theRAA either : • With a high enhancement factor for collisional processes • With « reasonnable » enhancement factor (krad not far away from unity) including radiative processes. Min bias INPC Tokyo June 2007 pt

12. c-quarks D decay e D q c Non-Photonic Electron elliptic-flow at RHIC: comparison with experimental results Collisional (kcol=20) v2 Tagged const q Freezed out according to thermal distribution at "punch" points of c quarks through freeze out surface: pt Collisional + Radiative v2 Conclusion III: One cannot reproduce thev2consistently with the RAA!!! Contribution of light quarks to the elliptic flow of D mesons is small INPC Tokyo June 2007 pt

13. 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: • spatial distribution of initial c-quarks • Part of the flow is due to the hadronic phase subsequent to QGP • 3) Reaction scenario different • Azimutal correlations could be of great help in order to identify the nature of thermalizing mechanism. INPC Tokyo June 2007

14. Evaluated in scalar QCD and in the limit of Echarm >> masses and >>qt Factorization of radiation and elastic scattering In the limit of vanishing masses: Gunion + Bertsch PRD 25, 746 But: Masses change the radiation substantially k q INPC Tokyo June 2007 x=long. mom. fraction