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Tomography of a Quark Gluon Plasma by Heavy Quarks : P. -B. Gossiaux , 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 1

Present situation: a) Multiplicity of stable hadrons made of (u, d, s) is described 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 v 2 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) Zimanyi Memorial Workshop July 2007 2

Why Heavy Quarks probe the QGP Idea: Heavy quarks are produced in hard processes 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 Zimanyi Memorial Workshop July 2007 3

Schematic view of our model for hidden and open heavy flavors production in AA 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 (hard) production of heavy quarks in initial NN collisions Quarkonia formation in QGP through c+c Y+g fusion process Zimanyi Memorial Workshop July 2007 4

Individual heavy quarks follow Brownian motion: we can describe the time evolution of their 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 5

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

The drift and diffusion coefficients Strategy: take the elementary cross sections for charm and 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 Bνμ ~ << (pν - pνf )(pμ - pμf )> > A describes the deceleration of the c-quark B describes Zimanyi Memorial Workshop July thermalisation 2007 7

c-quarks transverse momentum distribution (y=0) Heinz & Kolb’s hydro Distribution just before hadronisation p-p c-quarks transverse momentum distribution (y=0) Heinz & Kolb’s hydro Distribution just before hadronisation p-p distribution kcol =5 k=40 k=20 k=10 Zimanyi Memorial Workshop July 2007 Plasma will not thermalize the c: It carries information on the QGP 8

Energy loss and A, B are related (Walton and Rafelski) pi Ai + p Energy loss and A, B are related (Walton and Rafelski) pi Ai + p d. E/dx = - << (pμ – pμf)2 >> which gives easy relations for pc>>mc and pc<

In case of collisions (2 2 processes): Pioneering work of Cleymans (1985), Svetitsky (1987), 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 Zimanyi Memorial Workshop July 2007 10

Input quantities for our calculations Au – Au collision at 200 AGe. V. c-quark Input quantities for our calculations Au – Au collision at 200 AGe. V. 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. E 12 (2003) 211 -270). • Medium evolution: 4 D / Need local quantities such as T(x, t) taken from hydrodynamical evolution (Heinz & Kolb) • D meson produced via coalescence mechanism. (at the transition temperature. Zimanyi Memorial Workshop July with the a we pick a u/d quark 2007 thermal distribution) but other scenarios possible. 11

Leptons ( D decay) transverse momentum distribution (y=0) RAA Comparison to B=0 calculation 2 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% B=0 (Just deceleration) pt Conclusion I: Energy loss alone is not sufficient Kcol(coll only) =10 -20: Still far away from thermalization ! Zimanyi Memorial Workshop July 12 2007

There is a more recent data set Star and Phenix agree (Antinori SQM 07) 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 13

 "Radiative « coefficients « radiative » coefficients deduced using the elementary cross section for c. Q+g and for cg +g in t-channel (u & s-channels are suppressed at high energy). ℳq cqg ≡ c Q + dominant + + + suppresses by Eq/Echarm if evaluated in the large pic+ limit in the lab : (Bertsch-Gunion) Zimanyi Memorial Workshop July 2007 14

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

Leptons ( D decay) transverse momentum distribution (y=0) RAA (large sqrts limit) 0 -10% Leptons ( D decay) transverse momentum distribution (y=0) RAA (large sqrts limit) 0 -10% 20 -40% Col. +(0. 5 x) Rad Col. (kcol=10 & 20) pt pt Min bias Conclusion II: One can reproduce the RAA either : • With a high enhancement factor for collisional processes • With « reasonnable » enhancement factor (krad not far away from unity) Zimanyi Memorial Workshop July including radiative processes. 16 2007 pt

Non-Photonic Electron elliptic-flow at RHIC: comparison with experimental results v 2 c-quarks Collisional (kcol= Non-Photonic Electron elliptic-flow at RHIC: comparison with experimental results v 2 c-quarks Collisional (kcol= 20) decay e D Tagged const q Freezed out according to thermal distribution at "punch" points of c quarks through freeze out surface: pt Collisional + Radiative D q c Conclusion III: One cannot reproduce the v 2 consistently with the RAA!!! Contribution of light quarks to the Zimanyi Memorial Workshop July 17 elliptic flow of D mesons is small pt 2007

Non-Photonic Electron elliptic-flow at RHIC: Looking into the bits… v 2 (all p) const Non-Photonic Electron elliptic-flow at RHIC: Looking into the bits… v 2 (all p) const quark tagged by c v 2 (tagged p) C-quark does not see the « average » const quark… Why ? Bigger coupling helps… a little but at the cost of RAA SQM 06 Zimanyi Memorial Workshop July 2007 18

This is a generic problem ! Van Hees and Rapp: Charmed resonances and Expanding 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 Zimanyi Memorial Workshop July 2007 EXPERIMENT 19 ?

Problems on exp. side X. Lin SQM 07 RAA is about 0. 25 for Problems on exp. side X. Lin SQM 07 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 SQM 07) -- B contribution D 0, D+, Ds+ c+ D 0 D - D s - c - Large discrepancy between Star and Phenix BR 17. 2 6. 71 8 +6 - 4. 5 (X 1. 9 5 1. 7 e) in 0. 29 % Zimanyi Memorial Workshop July 2007 20

Azimutal Correlations for Open Charm D Transverse plane c What can we learn about Azimutal Correlations for Open Charm D Transverse plane c What can we learn about the "thermalization" process from the correlations remaining at the end of QGP ? Initial correlation (at RHIC); supposed back to back here c-bar Dbar SQM 06 How does the coalescence - fragmentation mechanism affects the "signature" ? Zimanyi Memorial Workshop July 2007 21

Azimutal Correlations for Open Charm Small pt (pt < 1 Ge. V/c ) c-quarks Azimutal Correlations for Open Charm Small pt (pt < 1 Ge. V/c ) c-quarks No interaction Coll (kcol= 1) Coll + rad (kcol= krad = 1) 0 -10% Coll (kcol= 10) Coll (kcol= 20) coalescence D SQM 06 jc - jcbar Correlations are small at small pt, , mostly washed away by coalescence process. Zimanyi Memorial Workshop July j. D - j. Dbar 2007 22

Azimutal Correlations for Open Charm Average pt (1 Ge. V/c < pt < 4 Azimutal Correlations for Open Charm Average pt (1 Ge. V/c < pt < 4 Ge. V/c ) c-quarks No interaction Coll (kcol= 1) Coll + rad (kcol= krad = 1) 0 -10% Coll (kcol= 10) Coll (kcol= 20) coalescence D jc - jcbar Conclusion IV: Broadening of the correlation due to medium, but still visible. Results for genuine coll + rad and for cranked up coll differ significantly Azimutal correlations might help identifying better thermalization process and thus the medium SQM 06 Zimanyi Memorial Workshop July j. D - j. Dbar 2007 23

Azimutal Correlations for Open Charm Large pt (4 Ge. V/c < pt ) c-quarks Azimutal Correlations for Open Charm Large pt (4 Ge. V/c < pt ) c-quarks No interaction Coll (kcol= 1) Coll + rad (kcol= krad = 1) 0 -10% Coll (kcol= 10) Coll (kcol= 20) coalescence D SQM 06 jc - jcbar Large reduction but small broadening for increasing coupling with the medium; compatible with corona effect Zimanyi Memorial Workshop July j. D - j. Dbar 2007 24

Conclusions • Experimental data point towards a significant (although not complete) thermalization of c 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 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? ? ? ) 1. Azimutal correlations could be of great help in order Zimanyi Memorial Workshop July 25 to identify the nature of thermalizing mechanism. 2007

V 2 -- Au+Au -- 200 -- Min. Bias Zimanyi Memorial Workshop July 2007 V 2 -- Au+Au -- 200 -- Min. Bias Zimanyi Memorial Workshop July 2007 26

Zimanyi Memorial Workshop July 2007 27 Zimanyi Memorial Workshop July 2007 27