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P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS

Heavy quarks diffusion in hydrodynamics or “How confident can we be in the Fokker-Planck coefficients we extract from / constrain with exp. data ?”. Heavy quarks production in heavy-ion collisions, W. Lafayette. P.B. Gossiaux SUBATECH, UMR 6457

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P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS

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  1. Heavy quarks diffusion in hydrodynamicsor“How confident can we be in the Fokker-Planck coefficients we extract from / constrain with exp. data ?” Heavy quarks production in heavy-ion collisions, W. Lafayette P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS With J. Aichelin, M. Bluhm, Th. Gousset, H. van Hees, R. Rapp and S. Vogel, I. Understanding (partly) the present RHIC data on HQ E-loss; the Nantes viewpoint II. Influence of the medium on our understanding Heavy quarks production in heavy ions collisions

  2. Heavy quarks thermalization in ultra relativistic heavy ion collisions: Elastic versus Radiative, P.B. Gossiaux}, V. Guiho & J. Aichelin, Journal of Physics G 32 (2006) S359 • Towards an understanding of the single electron data measured at the BNL Relativistic Heavy Ion Collider (RHIC), P.B. Gossiaux & J. Aichelin, Phys. Rev. C 78, 014904 (2008); [arXiv:0802.2525 ] • Tomography of quark gluon plasma at energies available at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC), P.B. Gossiaux, R. Bierkandt & J. Aichelin, Physical Review C 79 (2009) 044906; [arXiv:0901.0946] • Tomography of the Quark Gluon Plasma by Heavy Quarks, P.-B. Gossiaux & J. Aichelin, J. Phys. G 36 (2009) 064028; [arXiv:0901.2462] • Energy Loss of Heavy Quarks in a QGP with a Running Coupling Constant Approach, P.B. Gossiaux & J. Aichelin, Nucl. Phys. A 830 (2009), 203; [arXiv:0907.4329] • Competition of Heavy Quark Radiative and Collisional Energy Loss in Deconfined Matter, P.B. Gossiaux, J. Aichelin, T. Gousset & V. Guiho, J. Phys. G: Nucl. Part. Phys. 37 (2010) 094019; [arXiv:1001.4166] • Gluon Radiation at small kT and Radiative Energy Loss of Heavy Quarks; I. The Bethe-Heitler Regime, J. Aichelin, P.B. Gossiaux & Th Gousset (In preparation) Based on Heavy quarks production in heavy ions collisions

  3. I. “Understanding” the RHIC HQ-data What is the dominant E loss mechanism @ RHIC ? What can we extract from experimental data ? 01 Heavy quarks production in heavy ions collisions

  4. Collisional E loss : The Peshier – Gossiaux – Aichelin approach (2008) Motivation: Even a fast parton with the largest momentum P will undergo collisions with moderate q exchange and large as(Q2). The running aspect of the coupling constant has been “forgotten/neglected” in most of approaches Effective as(Q2) (Dokshitzer 95, Brodsky 02) aeff(Q2,T=0) “Universality constrain” (Dokshitzer 02) helps reducing uncertainties: Large values for intermediate momentum-transfer => larger cross section IR safe. The detailed form very close to Q2 =0 is not important does not contribute to the energy loss A model; not a renormalizable theory 02 Heavy quarks production in heavy ions collisions

  5. Running as : some Energy-Loss values for purely collisional processes  10 % of HQ energy Drag coefficient Transp. Coef … (reso) … of expected magnitude to reproduce the data (we “explain” the transport coeff. in a rather parameter free approach). E: optimal m, running aeff C: optimal m, as(2pT) 03 Heavy quarks production in heavy ions collisions

  6. Schematic view of the global framework MC@sHQ Bulk Evolution: non-viscous hydro (Heinz & Kolb)  T(M) & v(M) Y suppression MP HG QGP Evolution of HQ in bulk : Fokker-Planck orreaction rate + Boltzmann (no hadronic phase) D/B formation at the boundary of QGP (or MP) through coalescence of c/b and light quark (low pT)or fragmentation (high pT) Quarkonia formation in QGP through c+cY+g fusion process (hard) production of heavy quarks in initial NN collisions + kT broad. (0.2 GeV2/coll 04 Heavy quarks production in heavy ions collisions

  7. Observables (Au-Au) vs (rescaled) Model Best observable so far: RAA for single non-photonic electrons K=2 K=2 K=2 K=2 K=2 One reproduces RAAon all pT rangewith cranking K-factor 2 which permits to accommodate the “unknowns” 05 Heavy quarks production in heavy ions collisions

  8. From P. Braun-Munzinger (INPC 2010) 06 Heavy quarks production in heavy ions collisions

  9. Radiation a deflection of current (semi-classical picture) Basic (massive) Gunion-Bertsch Eikonal limit (large E, moderate q) k’ Dominates as small x as one “just” has to scatter off the virtual gluon k’ with Quark mass Gluon thermal mass ~2T (phenomenological; not in BDMPS) Both cures the colinear divergences and influence the radiation spectra 07 Heavy quarks production in heavy ions collisions

  10. … to convolute with your favorite elastic cross section Radiation spectra For coulomb scattering: Strong dead cone effect for x>mg/MQ (mass hierarchy) Light quark (II) c-quark b-quark (I) Little mass dependence (especially from qc) If typical qT : Strong mass effect in the average Eloss (mostly dominated by region II), similar to AdS/CFT Interesting per se, but not much connected to the quenching or RAA. 08 Heavy quarks production in heavy ions collisions

  11. e  D All non-photonic electrons as[0.2,0.3] • Coherence: Some moderate increase of RAA for D at large pT. • No effect seen for B Results with (Coherent) Radiation Included Conclusions can vary a bit depending on the value of the transport coefficient as[0.2,0.3] Indication that RAA at RHIC is mostly the physics of rather numerous but small E losses, not very sensitive to coherence . e B. as[0.2,0.3] 09 Heavy quarks production in heavy ions collisions

  12. Rescaling: K=0.6 Collisional vs {Radiative + Coll} The present data cannot decipher between the 2 local microscopic E-loss scenarios 10 Heavy quarks production in heavy ions collisions

  13. The heavy-quark physics at play for RHIC measured up to now (RAA and v2) is the one of small (relative) E-loss (and thus of the Fokker-Planck equation)… even at the largest pT Interpretation Explains why purely collisional models “work” so well What we need • D and B separately (in any case) • tagged HQ jets and IAA (and other correlations) RAA and v2 physics Bad control on the theory In our view, it is nevertheless more plausible to describe the physics in terms of a rather strong collisionnal energy loss supplied with an even stronger radiative energy loss (at least for g “>>” 1). 11 Heavy quarks production in heavy ions collisions

  14. h/s  DT/6  2pT D “robust”pQCD 3 x 4p Minimal at Tc Gossiaux & Aichelin, 2008 h/s  DT/2  2pT D 4p • h/s  1.5 at Tc 4p As we reproduce experimental data with rescaled model: Moore-Teaney: QGP properties: low momentum • h/s  0.5 at Tc 4p Strong coupling; AdS/CFT: But diffusion constant of heavy quark is already an interesting quantity in itself and could be evaluated on the lattice !!! 12 Heavy quarks production in heavy ions collisions

  15. Gathering all rescaled models (coll. and radiative): QGP properties: stopping power Challenge Exp. cannot resolve between those various trends quite consistent as the drag coefficient reflects the average momentum loss (per unit time) => large weight on x  1 Seems “under control” 13 Heavy quarks production in heavy ions collisions

  16. D & B meson: RHIC II (radiat + collisional) Collis., rate x 2 Collis. + Rad (LPM), rate x 0.6 as(rad)=0.3 … some small deviations for D spectra at large pT Z. Xu (sqm08) PRC 78 (fig 9) pT=5GeV/c pT=10GeV/c 14 Heavy quarks production in heavy ions collisions

  17. D & B meson: LHC (radiat + collisional) D spectra in Pb-Pb (5.5 TeV): Some window to decipher between the various Energy-loss models, for pT > 20 GeV/c B spectra in Pb-Pb (5.5 TeV): Pretty independent of E-loss model (properly calibrated w.r.t. RHIC data) 15 Heavy quarks production in heavy ions collisions

  18. 1 Quenching 0.9 Nch/ Nchmax 1 QGV in pp at LHC ? arXiv:1012.0764 Motivation: initial energy density e0 in pp (LHC) ~ e0 in CuCu (RHIC)  possible quenching of (heavy flavours) jets Combining MC@sHQ with EPOS Centrality  number n of initial individual parton-parton collisions In EPOS: Nchan c-quarks Less «central» First study, showing the possibility of an effect to be measured Most «central» Experimentally: no base-line for pp  ? 16 Heavy quarks production in heavy ions collisions

  19. II. Influence of the medium on heavy quarks phenomenology • Motivations : • We want to use experimental data to constrain the transport coefficient as much as possible • 2 groups (Texas AM & Nantes) have proposed models compatible with the non-photonic single-electron data, although the drag coefficients differ by a significant amount… How can this be possible ? Role of the other ingredients ? Models microscopic model of HQ-QGP interactions (transport coefficients) + medium + initial distributions + hadronization + kinetic equation + … Methodology: exchanging some ingredients of the models into a single framework (the Nantes MC@sHQ) Need for a collaboration: big thanks to Ralf and Hendrik Caution: The aim of this study is not to reproduce the data at all price 17 Heavy quarks production in heavy ions collisions

  20. Running as Fixed as + resonances Basic ingredients Drag coefficient: Diffusion coefficient B tuned to satisfy Einstein relation: asymptotic thermal distribution 18 Heavy quarks production in heavy ions collisions

  21. Basic ingredients Transport: both solve FP equation through a Langevin Monte Carlo realization… Back to the continuous stochastic process: Multiplicative noise Gaussian auto-correlated • Spurious drift: • Ambiguity: for a small dt, at which value of x should we consider g ? Ito vs Stratonovich But: a) we do not have a continuous process (smallest time scale: the collision) b) we can evaluate the average momentum loss directly from the elastic cross section (fundamental blocks are not g and g but Ap=–g+g g’ and B=2g2 ): No ambigity However: Several realizations are possible Ito pre point (Nantes) Ito post point (Texas AM) In principle equivalent if one chooses: 19 Heavy quarks production in heavy ions collisions

  22. Volume: Basic ingredients The medium: Nantes: Kolb-Heinz 2D+1 ideal hydrodynamics with Bjorken invariance (azhydro V2.0) Texas AM: Fireball of the Landau-Type: T(t), s(t)=S/V(t), e(t) Transverse plane: y y 2a 2a x x 2b 2b 20 Heavy quarks production in heavy ions collisions

  23. Basic ingredients The medium: Texas AM: Everything uniform but the velocity field y t=1.33fm/c Calibration x Kolb-Sollfrank-Heinz (2000) 21 Heavy quarks production in heavy ions collisions

  24. Basic ingredients The medium: Texas AM: Everything uniform but the velocity field Calibration Rather good agreement for the velocity Good agreement for the bulk flow 22 Heavy quarks production in heavy ions collisions

  25. Basic ingredients The medium: Temperature evolution along time: Conclusion: Good confidence that the “bulk” fireball is calibrated at the best T=180 MeV, e=2.25 GeV/fm3 T=165 MeV, e=1.64 GeV/fm3 e=0.82 GeV/fm3 e=0.46 GeV/fm3 Pure QGP Mixed phase EOS of the same type (QGP described within the MIT bag model, 1st order transition), with rather similar parameters. 23 Heavy quarks production in heavy ions collisions

  26. Heavy quark evolution All heavy quarks observables evaluated with the pre-point prescription Nuclear Modification factor Crossed ingredients original models (almost) RAA compatible How can we conclude ? : More coupling with the Nantes microscopic model (as seen from the drag coefficient) 24 Heavy quarks production in heavy ions collisions

  27. Heavy quark evolution All heavy quarks observables evaluated with the pre-point prescription Nuclear Modification factor Crossed ingredients original models (almost) RAA compatible How can we conclude ? : More quenching with the fireball then with the (original) KH hydro 25 Heavy quarks production in heavy ions collisions

  28. Heavy quark evolution Differential Elliptic flow original models (almost) : More coupling with the Nantes microscopic model : Higher elliptic flow from the fireball 26 Heavy quarks production in heavy ions collisions

  29. Heavy quark evolution Inclusive elliptic flow +73% Large deviations at early times Various gedanken decoupling energy densities for the c quarks 27 Heavy quarks production in heavy ions collisions

  30. Summary of HQ Is there something special with Heavy Quarks (due to their inertia) as compared to light ones ? 28 Heavy quarks production in heavy ions collisions

  31. Back on the bulk v2 and on calibration Probes of the bulk v2: I. So called momentum anisotropy with Directly evaluated from the energy-stress momentum; known to be closely related to the elliptic flow (Kolb, Sollfrank & Heinz 2000) The fireball systematically overshoots the hydro, starting from early times !!! HQ just inherits this larger anisotropy 29 Heavy quarks production in heavy ions collisions

  32. Back on the bulk v2 and on calibration II. Elliptic flow of light quarks and ensuing pions Particle spectra: Fireball: freeze out at constant lab time t KH with Cooper-Frye freeze out Asymptotic distribution in the VHR post-point Langevin fireball with Cooper-Frye freeze out fireball with Milekhin-like freeze out 30 Heavy quarks production in heavy ions collisions

  33. Back on the bulk v2 and on calibration several levels of subtle and somehow paradoxal conclusions: KH with Cooper-Frye freeze out fireball with Cooper-Frye freeze out Confirms the excess of intrinsic v2 in the fireball on the absolute level KH with Cooper-Frye freeze out fireball with Milekhin-like freeze out Confirms the proper calibration of the fireball (5.5% v2 for pions) Comparing with 2 different freeze out prescriptions: ? 31 Heavy quarks production in heavy ions collisions

  34. HQ lq HQ lq Calibration at a relative level  ? Bona fide argument: “One should calibrate the fireball using the asymptotic distributions (of light quarks) that results from Langevin transport one uses for the heavy quarks” Hendrik Van Hees Remember: Several realizations are possible Ito pre point (Nantes) Ito post point (Texas AM) • The medium calibration is intricately linked with the transport model one uses (exchanging the ingredient “medium” alone has no meaning) • It is not legitimate to perform the HQ simulations in the fireball with the pre-point prescription. 32 Heavy quarks production in heavy ions collisions

  35. Heavy quarks with pre-point vs post-point All heavy quarks observables evaluated with the Nantes FP coefficients The post-point vs pre-point prescription has little influence on the heavy quark observables (consequences of u.p/p0 are not mass independent). In particular, the post-point prescription does not bring the “fireball results” in the range of the “pre-point KH hydro” 33 Heavy quarks production in heavy ions collisions

  36. Summary and conclusions (1) With respect to the Kolb Heinz hydro + Cooper-Frye reference: fireball Compensation due to the u.p/p0 factor in equil. distribution Larger intrinsic v2 Nearly negligible effect of u.p/p0 factor; pre-point  post-point Overall increase of v2(HQ) hydro Similar v2(p) 0 collectivity Light quark sector heavy quark sector This all together explain why one is able to describe the heavy flavor data with smaller FP coefficients within the fireball than in the KH hydro, although they both reproduce the pions elliptic flow “Bona fide” is sometimes too optimistic 34 Heavy quarks production in heavy ions collisions

  37. Summary and conclusions (2) Third global level of interpretation: After all, the KH hydro with a kinetic freeze out a given rather all energy density is a model among others… Good candidate for medium with a genuine Milekhin freeze out fireball Larger intrinsic v2 HQ rather insensitive to the freeze out assumptions 2 rather different v2(HQ) for a given set of FP coefficient hydro Similar v2(p) 0 collectivity Light quark sector heavy quark sector Large influence of the medium on the extraction of FP coefficient from the experimental data First study, not exhaustive and to be pursued 35 Heavy quarks production in heavy ions collisions

  38. Back Up HQ Heavy quarks production in heavy ions collisions

  39. More on different freeze out prescriptions Toy model: Uniform thermalized fluid at finite velocity vz=0.5c (End of Mixed phase) Assuming locally equilibrated distributions for all flavours Heavy quarks production in heavy ions collisions

  40. Properties of QGP we would like to understand / quantify RAA(p,pT) v2(p,pT) In principle: Mass hierarchy of E loss; in practice: single electron puzzle (SEP) v2(HQ,pT) RAA(HQ,pT) Barometer, h/s but also diffusion coefficient D and drag Challenge n°2 Densitometer, dynamometer Probing the (strong) QGP by hard probe tomography… what does it means exactly ? Basic hard probe – medium interaction scaled by the density Strong (ordered) QGP will act coherently on large distances Shocking quasi-particles with increasing masses when pT decreases ? But we need a consistent description… 01 Heavy quarks production in heavy ions collisions

  41. Optimal parameters : 5-15 GeV2/fm (strong debate TECHQM) dNg/dy: 1400 for both GLV and WHDG (compensation between the additional coll E loss and the path length fluctuations) More pT-dependence in the models than in the data Challenge n°1 Nevertheless, one has to get the “right” parameter (for instance the transport coefficient) from QCD before claiming one “understands” A nice interpolation is not an explanation 03 Heavy quarks production in heavy ions collisions

  42. K. J. Eskola, H. Honkanen, C. A. Salgado and U. A. Wiedemann, Nucl. Phys. A 747(2005) 511 ASW (just radiative energy loss; extended BDMPS) Applying those approaches to HQ Fixed geometry N. Armesto, A. Dainese, C. A. Salgado and U. A. Wiedemann, Phys. Rev D (hep-ph/0501225) &Phys.Lett. B637 (2006) 362-366hep-ph/0511257 Conclude to rough agreement, subjected to b/c ratio in p-p V2 from spatial asymmetry of the path length 04 Heavy quarks production in heavy ions collisions

  43. So-called “Failure of pQCD approach” Applying those approaches to HQ Fixed L Beauty stays the problem… but beauty is there WHDG • coll Eloss (BT and TG) !!! • “…E loss and their fluctuations…” • path length fluctuations in a fixed geometry • Lb > Lc = Lu > Lg (self quenching) helps in the direction of reducing single electron puzzle • no genuine QGP evolution (mocking of Bjorken scenario) • coll E loss distribution assumed gaussian • fixed as 05 Heavy quarks production in heavy ions collisions

  44. HTL for x not << 1 ? Beyond the static scatterer limit: M. Djordjevic, Preprint arXiv:0903.4591 [nucl-th] (2009) and previous work with U. Heinz “Standard” pQCD (WHDG, ASW,…) The weak to strong axis Distorsion of heavy meson fragmentation functions due to the existence of bound mesons in QGP, R. Sharma, I. Vitev & B-W Zhang 0904.0032v1 [hep-ph] Non-perturbative, lattice potential scattering models (see R. Rapp and H Van Hees 0903.1096 [hep-ph] for a review) Non perturbative equivalent for g+Q ? No radiative ! Valuable works, but some questions remains… and how to reconcile them all stays a challenge ADS/CFT 06 from Rapp & Van Hees 0903.1096 Heavy quarks production in heavy ions collisions

  45. Various results from our holographic friends (trailing string): ADS/CFT Drag coefficient (Pretty strong dependence on the mass) Applied for the first time to URHIC by Horowitz and Gyulassy(Phys. Lett. B666 320,2008.) pQCD: DE a If such a strong mass hierarchy in AdS/CFT, how will it solve the single electron puzzle ? Maximal velocity for the validity of present AdS/CFT 07 Heavy quarks production in heavy ions collisions

  46. Applied recently in a more realistic hydro evolution by Akamatsu et al.(0809.1499v3 [hep-ph] & 0907.2981v2 [hep-ph]) ADS/CFT In fact, Fokker Planck with tunable drag coeffi : (cf. Gossiaux & Guiho (SQM04), Van Hees & Rapp (05), Moore & Teaney (05)) So-called Success of ADF/CFT If such a strong mass hierarchy in AdS/CFT, how will it solve the single electron puzzle ? Challenge n°3 08 Heavy quarks production in heavy ions collisions

  47. a possible hierarchy (very prospective) Asymptotic freedom pQCD radiative for the large E parton, but AdS/CFT for the radiated gluon AdS/CFT for the incoming parton pQCD for most of the partons in the jet (C. Marquet & T. Renk: 0908.0880 [hep-ph]) (Akamatsu) pT Novel path length dependences (DE a L3) for light parton 09 Heavy quarks production in heavy ions collisions

  48. m-local-model: medium effects at finite T in t-channel aeff(Q2,T=0) Large |t| Semi-hard hard Max. insensitivity |t*| BT OGE with effective polarisation m2(T)=0.2 mDself2(T) HTL: collective modes mDself2 (T) = (1+nf/6) 4paeff(mDself2) T2 Low |t| Bona Fide running HTL: as-> as(t) in PL and PT 08 Heavy quarks production in heavy ions collisions

  49. m-local-model:Eff. Running as vs lQCD T=0 O. Kaczmarek & F. Zantow (KZ) (nf=2 QCD), P.R.D71 (2005) 114510 Genuine non-pert (string) optimal m, running aeff V:w=0 sector; dE/dx: finite w Finite T T1.1 Tc T1.5 Tc V=F KZ P.R. D71 (2005) Some overshooting at large distance V=U KZ, PoS LAT2005 (2005) 192 aeff aeff Merging at 2 Tc 10 Heavy quarks production in heavy ions collisions

  50. m-local-model:Eff. Running vs fixedas BT Dark bands: Peshier & Peigné (2008) E: optimal m, running aeff Light bands: theoretical uncertainty related to the prescription for the HTL-hard transition Conclusions: • Good agreement with PP for large T and large P • Running as is more than a cranking of BT (different shapes and T-dependences) 11 Heavy quarks production in heavy ions collisions

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