1. Padova, 09.05.2006 Andrea Dainese 1 Parton energy loss in heavy-ion collisions from RHIC to LHC Andrea Dainese INFN Legnaro

2. Padova, 09.05.2006 Andrea Dainese 2 Layout The discovery of “jet quenching” at RHIC High-p T particle production in nucleus-nucleus collisions, according to perturbative QCD Calculating parton energy loss (BDMPS framework) Light-flavour hadron suppression in the Parton Quenching Model at RHIC and LHC Energy loss for heavy quarks RHIC: electrons R AA vs data LHC: testing E loss with heavy-to-light ratios Conclusions

3. Padova, 09.05.2006 Andrea Dainese 3 Discovery at RHIC: high-p T suppression Nuclear modification factor of p T distributions: PHENIX  0 (0-10%) factor 5 suppression! compilation by D.d’Enterria

4. Padova, 09.05.2006 Andrea Dainese 4 What about jets? Jets via di-hadron correlations: highest-p T track trigger: highest-p T track, (4--6 GeV)  distribution: 2 GeV < p T < p T trigger pp  2 back-to-back jets STAR Coll., PRL 90 (2003) 082302. slide courtesy of P.Jacobs near sideaway side

5. Padova, 09.05.2006 Andrea Dainese 5 Discovery at RHIC: no away-side jet in central Au-Au Quantified via ratio of integrals: ~1 in peripheral AA ~0 in central AA STAR Coll., PRL 90 (2003) 082302.

6. Padova, 09.05.2006 Andrea Dainese 6 Is it final-state energy loss? … or saturation of the parton densities in the initial nuclei? Control experiment, without medium: d-Au no high-p T suppressionthe away-side jet is there Final-state effect PHENIX Coll., PRL 91 (2003) 072303. STAR Coll., PRL 91 (2003) 072304.

7. Padova, 09.05.2006 Andrea Dainese 7 Is it final-state energy loss? … or saturation of the parton densities in the initial nuclei? “Control experiment”, with medium-blind probe:  ’s in Au-Au no suppression, but N coll scaling Final-state effect figure by D. d’Enterria

8. Padova, 09.05.2006 Andrea Dainese 8 High-p T particle prod. in AA collisions A schematic view: Ingredients: pp baseline (pQCD) initial-state effects:  PDF (anti)shadowing  k T broadening (Cronin) final-state effects:  energy loss  in-medium hadronization (coalescence) medium formed in the collision Au q q h h q p p q q h h pp  h+X x f g Pb / f g p LHC RHIC SPS R AA 1 Q 2 = 5 GeV 2 pTpT R AB 1 ~2-4 GeV/c kL  kTkL  kT Cronin enhancement

9. Padova, 09.05.2006 Andrea Dainese 9 Parton Energy Loss Partons travel ~4 fm in the high-density medium Bjorken (`82): energy loss due to elastic scattering … Bjorken, FERMILAB-Pub-82/59-THY (1982).

10. Padova, 09.05.2006 Andrea Dainese 10 Parton QCD Energy Loss Partons travel ~4 fm in the high colour-density medium medium-induced gluon radiation Successive calculations (`92  ): a QCD mechanism dominates, medium-induced gluon radiation Coherent wave-function gluon acummulates k T due to multiple inelastic scatterings in the medium  it decoheres and is radiated hard parton path length L Gyulassy, Pluemer, Wang, Baier, Dokshitzer, Mueller, Peigne’, Schiff, Levai, Vitev, Zhakarov, Salgado, Wiedemann, … kTkT

11. Padova, 09.05.2006 Andrea Dainese 11 Calculating Parton Energy Loss Baier, Dokshitzer, Mueller, Peigne‘, Schiff, NPB 483 (1997) 291. Zakharov, JTEPL 63 (1996) 952. Salgado, Wiedemann, PRD 68(2003) 014008. BDMPS-Z formalism path length L kTkT  Radiated-gluon energy distrib.: transport coefficient sets the scale of the radiated energy related to constraint k T < , controls shape at  <<  c Casimir coupling factor: 4/3 for q, 3 for g STATIC MEDIUM (BDMPS case)

12. Padova, 09.05.2006 Andrea Dainese 12 Calculating Parton Energy Loss Probe the medium gluons volume-density and interaction cross section Finite parton energy (qualitatively)  If E <  c (e.g. small p T parton with large L):  dependence on parton energy  : smaller sensitivity to density 

13. Padova, 09.05.2006 Andrea Dainese 13 Application: Parton Quenching Model Dainese, Loizides, Paic, EPJC 38 (2005) 461. BDMPS + Glauber-based medium geometry and density profile + PYTHIA for parton generation and fragmentation The procedure in short: 1)generate parton (q or g) with PYTHIA (or back-to-back pair) 2)calculate its L and average along the path 3)use quenching weights (from  dI/d  ) to get energy loss 4)quench parton and then hadronize it (independent fragm.) PYTHIA Fragmentation pTpT p T –  pTpT dN/dp T

14. Padova, 09.05.2006 Andrea Dainese 14 Model vs RHIC “light” data Density ( ) “tuned” to match R AA in central Au-Au at 200 GeV matches p T -indepence of suppression at high p T Dainese, Loizides, Paic, EPJC 38 (2005) 461. (Quark Matter 05) Similar results by Eskola, Honkanen, Salgado, Wiedemann

15. Padova, 09.05.2006 Andrea Dainese 15 Model vs RHIC data Centrality dependence of R AA p T > 4.5 GeV Centrality evolution according to Glauber-model collision geometry Dainese, Loizides, Paic, EPJC 38 (2005) 461.

16. Padova, 09.05.2006 Andrea Dainese 16 Testing L-dependence? R AA for 63 Cu- 63 Cu R AA STAR preliminary Charged hadrons

17. Padova, 09.05.2006 Andrea Dainese 17 Testing L-dependence? v 2 at high p T from E loss The azimuthal asymmetry --v 2 or R AA (  )-- of high-p T particle yields in non-central collisions tests the path-length dependence of E loss (almond-shaped medium) PHENIX  0 v 2 v 2 from E loss: Dainese, Loizides, Paic, EPJC 38 (2005) 461

18. Padova, 09.05.2006 Andrea Dainese 18 Extrapolation in c.m.s. energy Intermediate RHIC energy  s = 62 GeV energy extrapolation works reasonably well Extrapolation in  s: assuming  N gluons /volume  (  s) 0.6 (EKRT saturation model) First test: EKRT: Eskola, Kajantie, Ruuskanen, Tuominen, NPB 570 (2000) 379. PHENIX Coll., JPG 31 (2005) S473.

19. Padova, 09.05.2006 Andrea Dainese 19 Model prediction for LHC Extrapolation to LHC according to saturation model gives: Most partons are absorbed Already at RHIC, only those from the surface can escape … surface emission dominates

20. Padova, 09.05.2006 Andrea Dainese 20 Model vs RHIC data Disappearence of the away-side jet near side away side STAR Coll., nucl-ex/0501016.

21. Padova, 09.05.2006 Andrea Dainese 21 Observation of true di-jets in Au-Au STAR

22. Padova, 09.05.2006 Andrea Dainese 22 Di-jets associated yields (I AA )

23. Padova, 09.05.2006 Andrea Dainese 23 Tangential di-jets?

24. Padova, 09.05.2006 Andrea Dainese 24 Putting the pieces together

25. Padova, 09.05.2006 Andrea Dainese 25 Limited sensitivity of R AA Strong suppression requires very large density Surface emission scenario R AA determined by geometry rather than by density itself  Limited sensitivity to  Need more differential observables: massive partons study of jet shapes … Eskola, Honkanen, Salgado, Wiedemann, NPA 747 (2005) 511. ? large  R AA indep. of

26. Padova, 09.05.2006 Andrea Dainese 26

27. Padova, 09.05.2006 Andrea Dainese 27 Lower E loss for heavy quarks ? In vacuum, gluon radiation suppressed at  < m Q /E Q  “dead cone” effect Dead cone implies lower energy loss (Dokshitzer-Kharzeev, 2001) : energy distribution  d  /d  of radiated gluons suppressed by angle- dependent factor suppress high-  tail Q Dokshitzer, Khoze, Troyan, JPG 17 (1991) 1602. Dokshitzer and Kharzeev, PLB 519 (2001) 199. Dokshitzer Gluonsstrahlung probability

28. Padova, 09.05.2006 Andrea Dainese 28 Lower E loss for heavy quarks ? Detailed massive calculation shows that: Armesto, Salgado, Wiedemann, PRD 69 (2004) 114003. Medium-induced gluon radiation fills the dead cone Still, k T -integrated radiation is suppressed, but only for quite large m/E (i.e. large m, low p T )* R = 10 5 *Warning: large uncertainties kTkT m/E = 0.1 massive massless dead cone

29. Padova, 09.05.2006 Andrea Dainese 29 Model for heavy quarks Initially only charm Baseline at RHIC: PYTHIA, with EKS98 shadowing, tuned to match p T - shape of D cross section measured in d-Au by STAR (QM04) Heavy-quark E loss using (m/E)- dependent QW extracted from  0,h  R AA (central) Thermalize charms that lose all energy dN/dm T  m T exp(-m T /T), T = 300 MeV Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) 054027. EKS98: Eskola, Kolhinen, Salgado, EPJC 9 (1999) 61. baseline dN/dp T baseline R AA

30. Padova, 09.05.2006 Andrea Dainese 30 Charm R AA at RHIC effect of the mass thermalized component Small effect of mass for charm (~50% for D, ~30% for e) at low p T [large uncertainties!] Basically no effect in “safe” p T -region Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) 054027. (extracted from light-hadron data) larger uncertainties other contributions become important

31. Padova, 09.05.2006 Andrea Dainese 31 Charm + beauty + DY electrons at RHIC (pQCD baseline revised, and its uncertainties) FONLL calculation: Cacciari, Nason, Vogt, PRL95 (2005) 122001 Drell-Yan from: Gavin et al., hep-ph/9502372 Comparison: Armesto, Cacciari, Dainese, Salgado, Wiedemann, hep-ph/0511257 FONLL: electron spectrum may be ~50% c + ~50% b for 3 < p T < 8 GeV Drell-Yan component investigated as well: < 10% up to 10 GeV Large uncertainty on b/c crossing point in p T : from scales/masses variation it changes from 3 to 9 GeV Note: still, electron cross section in pp at 200 GeV underestimated at high p T PHENIX hep-ex/0508034

32. Padova, 09.05.2006 Andrea Dainese 32 R AA of c and b electrons at RHIC Armesto, Cacciari, Dainese, Salgado, Wiedemann, hep-ph/0511257 Due to larger mass of b quark electron R AA increased to ~0.4 Mass uncertainty (in E loss) and scales uncertainty (in pQCD  b/c crossing) were studied c b c+b Theory predicts e R AA (~0.4) larger than  R AA (~0.2) e spectra in principle sensitive to mass hierarchy Perturbative uncertainty on the pp baseline comparable to model-intrinsic uncertainty in determination of Preliminary STAR data not conclusive for comparison with theory

33. Padova, 09.05.2006 Andrea Dainese 33 Heavy Quark Energy Loss at LHC ~100 cc pairs and ~5 bb pairs per central Pb-Pb collision Experiments will measure with good precision R AA for D and B, and for their decay leptons What can we learn from a comparative quenching study of massive and massless probes at the LHC?

34. Padova, 09.05.2006 Andrea Dainese 34 Heavy Flavour R AA at LHC Baseline: PYTHIA, with EKS98 shadowing, tuned to reproduce c and b p T distributions from NLO pQCD (MNR) (m/E)-dep. E loss with MNR: Mangano, Nason, Ridolfi, NPB 373 (1992) 295. Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) 054027. * EKRT Saturation model: Eskola, Kajantie, Ruuskanen, Tuominen, NPB 570 (2000) 379.

35. Padova, 09.05.2006 Andrea Dainese 35 Colour-charge and mass dep. of E loss with Heavy-to-Light ratios at LHC Heavy-to-light ratios: Compare g  h, c  D and b  B mass effect For 10 < p T < 20 GeV, charm behaves like a m=0 quark, light-flv hadrons come mainly from gluons R D/h enhancement probes colour-charge dep. of E loss R B/h enhancement probes mass dep. of E loss Armesto, Dainese, Salgado, Wiedemann, PRD71 (2005) 054027

36. Padova, 09.05.2006 Andrea Dainese 36 Beauty-to-Charm ratio: R B/D Compare c and b  same colour charge Mass effect  Enhancement of factor ~2, independent of (for ) Challenging from experimental point of view…

37. Padova, 09.05.2006 Andrea Dainese 37 Summary One of the most exciting discoveries at RHIC ! We are dealing with energy loss in an extremely opaque medium, but …  theoretically, we are just starting to learn how to probe the medium; still large uncertainties (see also next talk)  experimentally, going to more differential observables  vs system size / azimuthal angle (path-length dependence)  vs quark mass -- c (b) SUPPRESSED at RHIC, but need to disentangle c and b to clarify picture The LHC will be a `hard / heavy probes machine’ and quenching studies will play a central role Example: Heavy-to-light ratios as probes of E loss…  … colour-charge dependence (R D/h )  … parton-mass dependence (R B/h, R B/D ?)

38. Padova, 09.05.2006 Andrea Dainese 38 EXTRA SLIDES

39. Padova, 09.05.2006 Andrea Dainese 39 Parton energy loss at SPS (  s  17 GeV)? R CP (K) vs E loss calculations E loss (Wang) NA49, QM2005 NA57 PLB623 (2005) 17 Wang calculation: pQCD + Cronin + (anti-)shadowing + energy loss (gluon density scaled by dN ch /dh) Good agreement between data and both Wang and PQM calculations ( )

40. Padova, 09.05.2006 Andrea Dainese 40 Open points (2): the opacity problem Can we really probe the medium? Need to relate extracted to an energy density  QCD estimate for ideal QGP: A recent analysis* of RHIC data, similar to that presented, extracts energy density  5 larger than that estimated from produced transverse energy dE T /dy (Bjorken estimate) Opacity problem: the interaction of the hard parton with the medium is much stronger than expected (Baier) Baier, NPA 715 (2003) 209. * Eskola, Honkanen, Salgado, Wiedemann, NPA 747 (2005) 511.

41. Padova, 09.05.2006 Andrea Dainese 41 Collisional energy loss revisited Earlier estimates: collisional (elastic) energy loss is negligible relative to radiative effects New estimate: Boltzmann transport + 1-D Bjorken expansion Mustafa and Thoma, Acta Phys.Hung. A22, 93 (2005) Q(p  ) = R AA Can we really ignore collisional energy loss? R AA = 0.25-0.4 for reasonable pathlength, similar to radiative E-loss

42. Padova, 09.05.2006 Andrea Dainese 42 Reappearance of di-jets: surface emission of tangential partons? p T (assoc) > 5 GeV/c 1/N trig dN/d  STAR Preliminary 8 < p T (trig) < 15 GeV/c

43. Padova, 09.05.2006 Andrea Dainese 43 Medium Expansion The density of scattering centres is time-dependent: Dynamical scaling law: same spectrum obtained for equivalent static trasport coefficient Calculations for a static medium apply to expanding systems Salgado and Wiedemann, PRL 89 (2002) 092303  = 1.5, 1.0, 0.5, 0

44. Padova, 09.05.2006 Andrea Dainese 44 Static vs Bjorken Expansion

45. Padova, 09.05.2006 Andrea Dainese 45 Static vs Bjorken: numbers

46. Padova, 09.05.2006 Andrea Dainese 46 The azimuthal asymmetry --v 2 or R AA (  )-- of D and B mesons in non-central collisions tests: at low/moderate p T : recombination scenario, v 2 of c/b quarks, hence degree of thermalization of medium at higher p T : path-length dependence of E loss (almond-shaped medium => v 2 ~ 0.05--0.10)  = 0  =  /2 PHENIX  0 v 2 Cole @ Quark Matter 05 v 2 from E loss: Dainese, Loizides, Paic, EPJC 38 (2005) 461 Armesto, Cacciari, Dainese, Salgado, Wiedemann, hep-ph/0511257, PLB to appear STAR results withdrawn; new analysis in progress v 2 at high p T from E loss