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Tomography of a Quark Gluon Plasma by Heavy Quarks :

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. Present situation: Multiplicity of stable hadrons made of (u,d,s) is described by thermal models

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Tomography of a Quark Gluon Plasma by Heavy Quarks :

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  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 Zimanyi Memorial Workshop July 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) 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 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 Zimanyi Memorial Workshop July 2007

  4. Schematic view of our model for hidden and open heavy flavors production in AA collision at RHIC and LHC Evolution of heavy quarks in QGP (thermalization) D/B formation at the boundary of QGP through coalescence of c/b and light quark Quarkonia formation in QGP through c+cY+g fusion process (hard) production of heavy quarks in initial NN collisions 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 Zimanyi Memorial Workshop July 2007

  6. t (fm/c) From Fokker-Planck coefficients  Langevin forces pz Evolution of one c quark inside a m=0 -- T=400 MeV QGP. Starting from p=(0,0,10 GeV/c). Evolution time = 30 fm/c py px …looks a little less « erratic » when considered on the average: Relaxation time >> collision time : self consistent Zimanyi Memorial Workshop July 2007

  7. 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 Zimanyi Memorial Workshop July 2007

  8. 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 Zimanyi Memorial Workshop July 2007

  9. 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 A (Gev/fm) dE/dx (GeV/fm) T=0.5 T=0.4 T=0.3 T=0.2 p (GeV/c) p (GeV/c) 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 treatmentis different • For radiation: Numerous works on energy loss; very little has been done on drift and diffusion coefficients Zimanyi Memorial Workshop July 2007

  11. 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. Zimanyi Memorial Workshop July 2007

  12. 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: Energy loss alone is not sufficient Kcol(coll only) =10-20: Still far away from thermalization ! Zimanyi Memorial Workshop July 2007

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

  14. 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 (Bertsch-Gunion) : Zimanyi Memorial Workshop July 2007

  15. x=long. mom. Fraction of g 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 Zimanyi Memorial Workshop July 2007

  16. 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 Zimanyi Memorial Workshop July 2007 pt

  17. 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 Zimanyi Memorial Workshop July 2007 pt

  18. Non-Photonic Electron elliptic-flow at RHIC: Looking into the bits… v2 (all p) const quark tagged by c v2 (tagged p) C-quark does not see the « average » const quark… Why ? Bigger coupling helps… a little but at the cost of RAA Zimanyi Memorial Workshop July 2007 SQM06

  19. Van Hees and Rapp: Charmed resonances and Expanding fireball (does not reproduce non charmed hadrons) Communicate more efficiently v2 to the c- quarks Moore and Teaney: Even choice of the EOS which divesthe largest v2 possible does not predict non charmed hadron data assuming D mesons This is a generic problem ! Only ‘exotic hadronization mechanisms’ may explain the large v2 Zimanyi Memorial Workshop July 2007 EXPERIMENT ?

  20. Problems on exp. side X. Lin SQM07 RAA is about 0.25 for large pt for Star and Phenix Confirms that large diffusion coefficients are excluded Actual problems -- D / c ratio (Gadat SQM07) -- B contribution Large discrepancy between Star and Phenix Zimanyi Memorial Workshop July 2007

  21. Initial correlation (at RHIC); supposed back to back here Azimutal Correlations for Open Charm Transverse plane What can we learn about the "thermalization" process from the correlations remaining at the end of QGP ? D c c-bar How does the coalescence - fragmentation mechanism affects the "signature" ? Dbar Zimanyi Memorial Workshop July 2007 SQM06 -

  22. Coll (kcol=10) Coll (kcol=20) Coll + rad (kcol=krad=1) Azimutal Correlations for Open Charm Small pt(pt < 1GeV/c ) No interaction Coll (kcol=1) 0-10% c-quarks jc - jcbar coalescence Correlations are small at small pt,, mostly washed away by coalescence process. D jD - jDbar Zimanyi Memorial Workshop July 2007 SQM06 -

  23. c-quarks Coll (kcol=10) Coll (kcol=20) Coll + rad (kcol=krad=1) D Azimutal Correlations for Open Charm Average pt(1 GeV/c < pt < 4 GeV/c ) No interaction Coll (kcol=1) 0-10% Conclusion IV:Broadening of the correlation due to medium, but still visible. Results for genuine coll + rad and for cranked up coll differ significantly jc - jcbar coalescence Azimutal correlations might help identifying better the thermalization process and thus the medium jD - jDbar Zimanyi Memorial Workshop July 2007 SQM06 -

  24. Coll (kcol=10) Coll (kcol=20) Coll + rad (kcol=krad=1) Azimutal Correlations for Open Charm Large pt(4 GeV/c < pt ) No interaction Coll (kcol=1) c-quarks 0-10% jc - jcbar coalescence Large reduction but small broadening for increasing coupling with the medium; compatible with corona effect D jD - jDbar Zimanyi Memorial Workshop July 2007 SQM06 -

  25. 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 • Reaction scenario different • Miclos Nessi (v2, ,azimuthal correlations???) • Azimutal correlations could be of great help in order to identify the nature of thermalizing mechanism. Zimanyi Memorial Workshop July 2007

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

  27. Zimanyi Memorial Workshop July 2007

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