1. 1 -- 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 How can we look into the interior of a QGP?

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

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

4. 4 at 62 AGeV and even et SPS

5. 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. 6 This model explains STRANGENESS ENHANCEMENT especially that the enhancement at SPS is larger than at RHIC Strangeness enhancement in HI is in reality Strangeness suppression in pp string Strangeness suppr in pp PRD 65, 057501 (2002)

7. 7 - Central M i /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 (N core =25). The formation of a possible new state is not size dependent Particle yield is determined at freeze out by phase space (with γ S = 1 (a lower γ S models corona contributions)

8. 8 Rescattering later -> neither yield nor spectra sensitive to state of matter before freeze out Light hadrons insensitive to phase of matter prior to freeze out (v 2 or other collective variables?) Production: hard process described by perturbative QCD  initial dσ/dp T 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 Why are heavy quarks (mesons) better?

9. 9 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) Interaction of heavy quarks with the QGP

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

11. 11     p +p(pQCD) c and b carry direct information on the QGP QGP expansion: Heinz & Kolb’s hydrodynamics K=1 drift coeff from pQCD This may allow for studying plasma properties using pt distribution, v 2 transfer, back to back correlations etc Interaction of c and b with the QGP K< 40: plasma does not thermalize the c or b:

12. 12 R AA or energy loss is determined by the elementary elastic scattering cross sections. q channel: Neither α(t) =g 2 /4  nor κm D 2 = are well determined α(t) =is taken as constant [0.2 < α < 0.6] or α(2πT) m Dself 2 (T) = (1+n f /6) 4πa s ( m Dself 2 ) xT 2 (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 ? Weak points of the existing approaches

13. 13 Loops are formed If t is small (<<T) : Born has to be replaced by a hard thermal loop (HTL) approach like 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. of the artificial scale t * which separates the 2 regimes. B) Debye mass m D regulates the long range behaviour of the interaction PRC78 014904, 0901.0946

14. 14 This concept we extend to QCD HTL in QCD cross sections is too complicated for simulations Idea: - Use HTL (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 ( add to Born a constant  ’ Constant coupling constant -> Analytical formula -> arXiv: 0802.2525 Running -> numerically

15. 15 Effective  s (Q 2 ) (Dokshitzer 95, Brodsky 02) Observable = T-L effective coupling * Process dependent fct “Universality constrain” (Dokshitzer 02) helps reducing uncertainties: IR safe. The detailed form very close to Q 2 =0 is not important does not contribute to the energy loss Large values for intermediate momentum- transfer Additional inputs (from lattice) could be helpful 15 Describes e + e - data A) Running coupling constant

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

17. 17 The expaning plasma

18. 18. 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. Au + Au @ 200 AGeV

19. 19 minimum bias New K=1,5-2 Central and minimum bias events described 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) p T > 2 bottom dominated!! more difficult to stop, compatible with experiment Difference between b and c becomes smaller in minimum bias events RAA b

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

21. 21 6-8 fm 4-6 fm 2-4 fm 0-2 fm The stopping depends strongly on the position where the Q’s are created The spectra at large p T 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 centrality dependence of R AA for c quarks

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

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

24. 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 R AA and v 2. 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. 25 Horowitz et Gyulassy 0804.4330 Gubser PRD76, 126003 Wicks et al. NPA783 493 nucl-th/0701088 Fixed coupling coll+radiative pQCD dσ/dt: only mass dependent in the subdominant u-channel AdS/CFT versus pQCD AdS/CFT: final dp T /dt = -c T 2 /M Q p T AdS/CFT:Anti de Sitter/conformal field theory RHIC central R CB = R AA charm/R AA bottom

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

27. 27 LHC will sort out theories as soon as R CB is measured pQCD: R CB =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 LHC central

28. 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 R AA and v 2. 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. 29 THEN: Optimal choice of  in our OBE model:   (T)  0.15 m D 2 (T) with m D 2 = 4  s (2  T)(1+3/6)xT 2  s ( 2  ) Model C: optimal  2 … factor 2 increase w.r.t. mod B (not enough to explain R AA ) T(MeV) \p(GeV/c)1020 2000.36 (0.18) 0.49 (0.27) 4000.70 (0.35) 0.98 (0.54) Convergence with “pQCD” at high T 13

30. 30 Surprisingly we expect for LHC about the same v 2 as at RHIC despite of the fact that in detail the scenario is rather different

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

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

33. 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. 34 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 prob P t initial [GeV] P t final [GeV] Q with small p t initial gain momentum (thermalization) with large p t inital loose momentum Distribution very broad Tomography of the plasma

35. 35 Where are we?

36. 36 Teaney & Moore 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 (Hallman ) p T > 2 bottom dominated!! more difficult to stop, compatible with experiment central events

37. 37 Where can we improve?

38. 38 Moore and Teaney: Hydro with EOS which gives the largest v 2 possible does not agree with data. Drift Coefficient needed for R AA corresp. to K=12 Van Hees & Rapp Charmed resonances exists in the plasma Dynamics = expanding fireball: K  12 R AA =(dσ/dp T ) AA /(( dσ/dp T ) pp N binary ) v 2 =.. R AA and v 2 need different values of K: Only exotic hadronization mechanisms may explain the large v 2

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

40. 40 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: v 2 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 But if one looks into the details ….