-- do hadrons, consisting of u,d,s, allow for this  we will see: no

1. How can we look into the interior of a QGP? -- do hadrons, consisting of u,d,s, allow for this  we will see: no -- what’s about heavy mesons (c,b)  tomography of a plasma possible Collaborators: P.-B. Gossiaux, R. Bierkandt, K. Werner Subatech/ Nantes/ France Nuclear Winter Workshop, Big Sky, Febr 09

2. Centrality Dependence of Hadron Multiplicities can be described by a very simple model (confirmed by EPOS) arXiv: 0810.4465 No (if stat. Model applied) or one free parameter Calculation of the Cu+Cu results without any further input

3. works for non strange and strange hadrons at 200 AGeV strange non-strange Theory = lines Cu+Cu: completely predicted from Au+Au and pp

4. and even et SPS at 62 AGeV

5. ….. and even if one looks into the details: For all measured hadrons the core/corona ratio is strongly correlated with ratio of peripheral to central HI collisions Theory reproduces the experimental results quantitatively Eror bars are not small enough to improve the simple model

6. Strangeness suppr in pp This model explains STRANGENESS ENHANCEMENT especially that the enhancement at SPS is larger than at RHIC PRD 65, 057501 (2002) Strangeness enhancement in HI is in reality Strangeness suppression in pp string

7. Central Mi /N part same in Cu+Cu and Au+Au (pure core) • - very peripheral same in Cu+Cu and Au+Au (pp) •  increase with N part stronger in Cu+Cu • - all particle species follow the same law •  Φ is nothing special (the strangeness content is not • considered in this model) •  Strangeness enhancement is in reality strangeness • suppression in pp (core follows stat model predictions • which differ not very much) • works for very peripheral reactions (Ncore =25). The • formation of a possible new state is not size dependent • Particle yield is determined at freeze out by phase space • (with γS = 1 (a lower γS models corona contributions)

8. Rescattering later -> neither yield nor spectra sensitive to state of matter before freeze outLight hadrons insensitive to phase of matter prior to freeze out (v2 or other collective variables?) Why are heavy quarks (mesons) better? Production: hard process described by perturbative QCD  initial dσ/dpT is known (pp)  comparison of final and initial spectrum: gives direct information on the interaction of heavy Q with the plasma  if heavy quarks are not in thermal equilibrium with the plasma : tomography possible

9. Interaction of heavy quarks with the QGP 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 for the dynamics of light quarks and gluons (here hydrodynamics of Heinz and Kolb)

10. drift and diffusioncoefficient :take the elementary cross sections for charm scattering (Qq and Qg) and calculate the coefficients (g = thermal distribution of the collision partners) Strategy: |M|2 = lowest order QCD with (αs( 2πT) , m_D) and then introduce an to study the physics. Diffusion (BL , BT) coefficient Bνμ ~ << (pν- pνf )(pμ- pμf )> > taken from the Einstein relation A = p/mT BL A (drift) describes the deceleration of the c-quark B (diffusion) describes the thermalisation overall K factor

11. p +p(pQCD) Interaction of c and b with the QGP QGP expansion: Heinz & Kolb’s hydrodynamics K=1 drift coeff from pQCD c and b carry direct information on the QGP K< 40: plasma does not thermalize the c or b: K =5 K=40 K=10 K=20 This may allow for studying plasma properties using pt distribution, v2 transfer, back to back correlations etc

12. RAA or energy loss is determined by the elementary elastic scattering cross sections. q channel: Weak points of the existing approaches Neitherα(t) =g2/4 nor κmD2= are well determined α(t) =is taken as constant [0.2 < α < 0.6] or α(2πT) mDself2 (T) = (1+nf/6) 4πas( mDself2) xT2(Peshier hep-ph/0607275) But which κ is appropriate? κ =1 and α =.3: large K-factors are necessary to describe data Is there a way to get a handle on α and κ ?

13. B) Debye mass PRC78 014904, 0901.0946 mD regulates the long range behaviour of the interaction Loops are formed If t is small (<<T) : Born has to be replaced by a hardthermal loop (HTL) approachlike in QED: (Braaten and Thoma PRD44 (91) 1298,2625) For t>T Born approximation is ok QED: the energy loss ( = E-E’) Energy loss indep. ofthe artificial scale t* which separates the 2 regimes .

14. This concept we extend to QCD HTL in QCD cross sections is too complicated for simulations Idea: - Use HTL (t<t*) and Born (t>t*) amplitude to calculate dE/dx make sure that result does not depend on t* - determine which  gives the same energy loss as 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 (<T) -> add to Born a constant ’ Constant coupling constant -> Analytical formula -> arXiv: 0802.2525 Running -> numerically

15. A) Running coupling constant • Effective as(Q2) (Dokshitzer 95, Brodsky 02) Observable = T-L effective coupling * Process dependent fct “Universality constrain” (Dokshitzer 02) helps reducing uncertainties: Additional inputs (from lattice) could be helpful Describes e+e- data IR safe. The detailed form very close to Q2 =0 is not important does not contribute to the energy loss Large values for intermediate momentum-transfer 15

16. The matching gives   0.2 mD for running S for the Debye mass and   0.15 mD not running! Large enhancement of cross sections at small t Little change at large t Largest energy transfor from u-channel gluons

17. The expaning plasma

18. Au + Au @ 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 (FONLL)  Cronin effect included. • c-quark rapidity distribution according to R.Vogt (Int.J.Mod.Phys. E12 (2003) 211-270). • QGP 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. minimum bias RAA Central and minimum bias eventsdescribed by the same parameters. The new approach reduces the K- factor K=12 -> K=1,5-2 No radiative energy loss yet (complicated: Gauge+LPM) pT > 2 bottom dominated!! more difficult to stop, compatible with experiment Difference between b and c becomes smaller in minimum bias events b New K=1,5-2

20. Centrality dependence of integrated yield minimum bias out of plane distribution v2 v2 of heavy mesons depends on where fragmentation/ coalescence takes place end of mixed phase beginning of mixedphase New K=1,5-2

21. centrality dependence of RAA for c quarks • The stopping depends • strongly on the position • where the Q’s are created • The spectra at large pT • are insensitive to the • Q’s produced in the center • of the plasma • No info about plasma center At high momenta the spectrum is dominated by c and b produced close to the surface Conclusion: Singles tell little about the center of the reactions 6-8 fm 4-6 fm 0-2 fm 2-4 fm

22. c cbar pairs are more sensitive to the center Strong correlation between centrality of the production and the final momentum difference of Q and Qbar A ) Decreasing relative energy loss with increasing pt B) Small ΔpT  same path length  from center Pairs with small ΔpT can be used to test the theory to explore the center of the reaction

23. p(Q)  p(Qbar) pairs Due to geometry: The final momentum difference is smaller for centrally produced pairs Singles: RAA flat at large pt Pairs : RAA increases with pt Less relative energy loss Typical pQCD effect Not present in AdS/CFT

24. Conclusions • Experimental data point towards a significant (although not complete) thermalization of c and b quarks in QGP  tomography of the plasma possible • Using a running coupling constant, determined by experiment, and an infrared regulator which approximates hard thermal loop pQCD calculations come close to the experimental RAA and v2. • Radiative energy loss has to be developed • Ads/CFT prediction differ: Experiment will decide • pQCD calculations make several predictions which can be checked experimentaly • Very interesing physics program with heavy quarks after the upgrate of RHIC and with LHC

25. AdS/CFT versus pQCD AdS/CFT:Anti de Sitter/conformal field theory pQCD dσ/dt: only mass dependent in the subdominant u-channel RCB = RAA charm/RAAbottom RHIC central Wicks et al. NPA783 493 nucl-th/0701088 Fixed coupling coll+radiative Horowitz et Gyulassy 0804.4330 Gubser PRD76, 126003 AdS/CFT: final dpT/dt = -c T2/MQ pT

26. and at LHC? Cacciari et al. hep-ph/0502203 and priv. communication For large pT: distribution of b and c identical

27. LHC will sort out theories as soon as RCB is measured LHC central pQCD: RCB =1 for high pt: neither initial distr nor σ depends on the mass AdS/CFT mass dependence remains But: what is the limit of the model?? For very large pt pQCD should be the right theory

28. Conclusions • Experimental data point towards a significant (although not complete) thermalization of c and b quarks in QGP  tomography of the plasma possible • Using a running coupling constant, determined by experiment, and an infrared regulator which approximates hard thermal loop pQCD calculations come close to the experimental RAA and v2. • Radiative energy loss has to be developed • Ads/CFT prediction differ: Experiment will decide • pQCD calculations make several predictions which can be checked experimentaly • Very interesing physics program with heavy quarks after the upgrate of RHIC and with LHC

29. as(2pT) Model C: optimal m2 THEN: Optimal choice of m in our OBE model: m2(T)  0.15 mD2(T) with mD2 = 4pas(2pT)(1+3/6)xT2 … factor 2 increase w.r.t. mod B (not enough to explain RAA) Convergence with “pQCD” at high T 13

30. Surprisingly we expect for LHC about the same v2 as at RHIC despite of the fact that in detail the scenario is rather different

31. -dmn Braaten-Thoma: HTL: convergent kinetic (matching 2 regions) (Peshier – Peigné) Low |t|: large distances Large |t|: close coll. HTL: collective modes Bare propagator + Indep. of |t*| ! SUM: (provided g2T2<< |t*| << T2 ) 11

32. Transport coefficients Drag coefficient Diff. coefficient Caution: One way of implementing running as Long. fluctuations E: optimal m, running as,eff C: optimal m, as(2pT) Running as and Van Hees &Rapp: roughly same trend mod C – mod E - AdS/CFT Evolution? Not so clear 19

33. HTL+semihard, needed to have the transition in the range of validity of HTL dE/dx does not depend on t* The resulting  values are considerably smaller than those used up to now.

34. Tomography of the plasma Goal: find observables which are sensitive to the interaction of heavy quarks with the plasma -> agreement of predictions provide circumstantial evidence that the plasma is correctly described Q with small pt initial gain momentum (thermalization) with large pt inital loose momentum Distribution very broad prob Pt initial [GeV] Pt final [GeV]

35. Where are we?

36. central events central Teaney & Moore K=12 b The new approach reduces the K- factor K=12 -> K=1,5-2 No radiative energy loss yet (Hallman ) pT > 2 bottom dominated!! more difficult to stop, compatible with experiment c New K=1.5-2

37. Where can we improve?

38. RAA=(dσ/dpT)AA /((dσ/dpT )pp Nbinary) Moore and Teaney: Hydro with EOS which gives the largest v2 possible does not agree with data. Drift Coefficient needed for RAA corresp. to K=12 Van Hees & Rapp Charmed resonances exists in the plasma Dynamics = expanding fireball: K12 RAA and v2 need different values of K: Only exotic hadronization mechanisms may explain the large v2 v2 = <cos2φ> ..

39. momentum loss of c in the plasma Averaged of inital positions and of the expanding plasma pT final (>5GeV) = pT ini – 0.08 pT ini – 5 GeV dominant at large pT Functional form expected from the underlying microscopic energy loss but numerical value depends on the details of the expansion

40. But if one looks into the details …. There is a double challenge: description of the expanding plasma AND description of interaction of the heavy quarks with this plasma Model of van Hees and Rapp: v2 seems to depend on how the expanding plasma is described if we use their drift coefficient in our (Heinz-Kolb) hydro approach (which describes the v_2 of the other mesons) we get 50% less v_2 Preliminary and presently under investigation