1. High Momentum probes Nuclear Suppression Correlations Identified particle measurements (for theory see lecture 5)

2. hadrons leading particle Jet: A localized collection of hadrons which come from a fragmenting parton Parton Distribution Functions Hard-scattering cross-section Fragmentation Function a b c d Parton Distribution Functions Hard-scattering cross-section Fragmentation Function High p T (> 2.0 GeV/c) hadron production in pp collisions: ~ Hadronization in QCD (the factorization theorem) “Collinear factorization”

3. High-energy parton loses energy by rescattering in dense, hot medium. q q “Jet quenching” = parton energy loss Described in QCD as medium effect on parton fragmentation: Medium modifies perturbative fragmentation before final hadronization in vacuo. Roughly equivalent to an effective shift in z: Important for controlled theoretical treatment in pQCD: Medium effect on fragmentation process must be in perturbative q 2 domain.

4. Induced Gluon Radiation  ~collinear gluons in cone  “Softened” fragmentation Modification according to Gyulassy et al. (nucl-th/0302077) attributable to radiative rather than collisional energy loss

5. Modification of fragmentation functions (hep-ph/0005044)

6. STAR, nucl-ex/0305015 energy loss pQCD + Shadowing + Cronin pQCD + Shadowing + Cronin + Energy Loss R AA and high-pT suppression Deduced initial gluon density at   = 0.2 fm/c dN glue /dy ≈ 800-1200  ≈ 15 GeV/fm 3, eloss = 15*cold nuclear matter (compared to HERMES eA) (e.g. X.N. Wang nucl-th/0307036)

7. Jet quenching I: hadrons are suppressed, photons are not

8. 8   nucl-ex/0504001 Energy dependence of R AA R AA at 4 GeV: smooth evolution with √s NN Agrees with energy loss models

9. Two possible mechanisms of radiative e-loss plus collisional e-loss High energy limit: energy loss by gluon radiation. Two limits: (a) Thin medium: virtuality q 2 controlled by initial hard scattering (LQS, GLV) (b) Thick medium: virtuality q 2 controlled by rescattering in medium (BDMPS) Trigger on leading hadron (e.g. in R AA ) favors case (a). Low to medium jet energies: Collisional energy loss is competitive! Especially when the parent parton is a heavy quark (c or b). q q L qq g L

10. Radiative energy loss in QCD BDMPS approximation: multiple soft collisions in a medium of static color charges  E independent of parton energy (finite kinematics  E~log(E))  E  L 2 due to interference effects (expanding medium  E~L) Medium-induced gluon radiation spectrum: Total medium-induced energy loss: Transport coefficient: Baier, Schiff and Zakharov, AnnRevNuclPartSci 50, 37 (2000)

11. Extracting qhat from hadron suppression data R AA : qhat~5-15 GeV 2 /fm

12. What does qhat measure? Equilibrated gluon gas: number density  ~T 3 energy density  ~T 4  qhat+modelling  energy density pQCD result: c~2 (  S ? quark dof? …) sQGP (multiplicities+hydro): c~10 R. Baier, Nucl Phys A715, 209c Hadronic matter QGP ~RHIC data Model uncertainties

13. q-hat at RHIC Pion gas QGP Cold nuclear matter sQGP? ? ? RHIC data

14. BDMPS(ASW) vs. GLV Baier, Dokshitzer, Mueller, Peigne, Schiff, Armesto, Salgado, Wiedemann, Gyulassy, Levai, Vitev  Rough correspondence: (Wiedemann, HP2006)  BDMPS GLV Medium-induced radiation spectrum Salgado and Wiedemann PRD68 (2003) 014008  30-50 x cold matter density

15. What do we learn from R AA ? ~15 GeV  E=15 GeV Energy loss distributions very different for BDMPS and GLV formalisms But R AA similar! Renk, Eskola, hep-ph/0610059 Wicks et al, nucl-th/0512076v2 BDMPS formalism GLV formalism Need more differential probes

16. R AA for  0 : medium density I C. Loizides hep-ph/0608133v2 I. Vitev W. Horowitz Use R AA to extract medium density: I. Vitev: 1000 < dN g /dy < 2000 W. Horowitz: 600 < dN g /dy < 1600 C. Loizides: 6 < < 24 GeV 2 /fm Statistical analysis to make optimal use of data Caveat: R AA folds geometry, energy loss and fragmentation

17. Application to Heavy Ion Collisions: Initial Results Strong suppression in Au+Au collisions, no suppresion in d+Au: Effect is due to interactions between the probe and the medium Established use as a probe of the density of the medium Conclusion (at the time): medium is dense (50-100x nuclear matter density) PHENIX: Phys. Rev. Lett. 91 (2003) 072301 STAR: Phys. Rev. Lett. 91 (2003) 072304 PHOBOS: Phys. Rev. Lett. 91 (2003) 072302 BRAHMS: Phys. Rev. Lett. 91 (2003) 072303 Binary collision scalingp+p reference

18. Central R AA Data Increasing density The Limitations of R AA: “Fragility ” Surface bias leads effectively to saturation of R AA with density Challenge: Increase sensitivity to the density of the medium K.J. Eskola, H. Honkanken, C.A. Salgado, U.A. Wiedemann, Nucl. Phys. A747 (2005) 511 A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38(2005) 461

19. What can we learn about Energy Loss? Fractional effective energy loss: S loss (MJT) “Effective” because of surface bias when analyzing single particle spectra PHENIX  0 Spectrum Renk and Eskola, hep-ph/0610059 8 < p T < 15 GeV/c PHENIX, nucl-ex/0611007

20. Calibrated Interaction? Grey Probes Problem: interaction with the medium so strong that information lost: “Black” Problem: interaction with the medium so strong that information lost: “Black” Significant differences between predicted R AA, depending on the probe Significant differences between predicted R AA, depending on the probe Experimental possibility: recover sensitivity to the properties of the medium by varying the probe Experimental possibility: recover sensitivity to the properties of the medium by varying the probe Wicks et al, nucl-ex/0512076

21. Interpreting Correlations Geometric biases: Hadrons: surface Di-hadrons: tangential, but depending on Eloss can probe deeply Charm-hadron, and especially Beauty-hadron(B): depends on Eloss Note: b and c produced in pairs, B and C decay into multiple hadrons Gamma-hadrons: Precise kinematics, back to surface Beyond reaction of probe to medium, also reaction of medium to probe T. Renk, nucl-ex/0602045

22. pedestal and flow subtracted 4 < p T,trig < 6 GeV/c, 2< p T,assoc < p T,trig Di-Jets through Hadron-Hadron Correlations “Disappearance of away-side jet” in central Au+Au collisions 0-5% Escaping Jet “Near Side” Lost Jet “Far Side” STAR, PRL 90 (2003) 082302 I AA  (Jet-correlated Yield in AA) / (Jet-correlated Yield in pp)

23. Evolution of Jet Structure At higher trigger p T (6 < p T,trig < 10 GeV/c), away-side yield varies with p T,assoc For lower p T,assoc ( 1.3 < p T,assoc <1.8 GeV/c), away-side correlation has non-gaussian shape  becomes doubly-peaked for lower p T,trig pedestal and flow subtracted 4 < p T,trig < 6 GeV/c, 2 < p T,assoc < p T,trig M. Horner, QM 2006

24. “Reappearance of away-side jet” With increasing trigger p T, away-side jet correlation reappears 4 < p T,trig < 6 GeV/c, 2< p T,assoc < p T,trig STAR, Phys. Rev. Lett. 97 (2006) 162301

25. Dijets from dihadrons NOT background subtracted: no ambiguities from background model At high trigger p T, high associated p T : clear jet-like peaks seen on near and away side in central Au+Au 8 < p T (trig) < 15 GeV/c p T (assoc)>6 GeV STAR PRL 97 (2006) 162301 d+Au 1/N trig dN/d(  ) Au+Au 20-40%Au+Au 0-5%

26. Surface Bias of Di-Jets? Renk and Eskola, hep-ph/0610059 8 < pT,trig< 15, 4< pT,assoc< 6 GeV/c 8 < pT,trig< 15 GeV/c STAR, Phys. Rev. Lett. 97 (2006) 162301

27. Comparison of I AA to R AA I AA = Yield(0-5% Au+Au) Yield(d+Au) In the di-jets where trigger p T is 8-15 GeV/c, the suppression is same as for single particles as a function of p T = Near-side I AA = Away-side I AA 8 < p T (trig) < 15 GeV/c D. Magestro, QM 2005

28. Modification of Clean Signals Away-side yield strongly suppressed (almost) to level of R AA No dependence on z T in measured range No modification in shape in transverse or longitudinal direction The jets you can see cleanly are also in some sense the least modified STAR PRL 97 (2006) 162301

29. Near-side Yields vs. z T After subracting the RidgeM. Horner, QM 2006

30. Away-side Yields vs. z T M. Horner, QM 2006

31. Away-side suppression as a function of p T,trig M. Horner, QM 2006 Away-side I AA Away-side suppression reaches a value of 0.2 for trigger p T > 4 GeV/c, similar to single- particle suppression I AA  (Jet-correlated Yield in AA) / (Jet-correlated Yield in pp)

32. Where does the energy go? Lower the associated p T to search for radiated energy Lower the associated p T to search for radiated energy Additional energy at low p T BUT no longer collimated into jets Additional energy at low p T BUT no longer collimated into jets Active area: additional handles on the properties of the medium? Mach shocks, Cherenkov cones … e.g. Renk and Ruppert, Phys. Rev. C 73 (2006) 011901 PHENIX preliminary Leading hadrons Medium away near M. Horner, QM2006 STAR, Phys. Rev. Lett. 95 (2005) 152301 p T (GeV/c) AA/pp STAR preliminary 0-12% 200 GeV Au+Au

33.  -  Correlations Phys. Rev. C73 (2006) 064907 mid-central Au+Au p t < 2 GeV d+Au, 40-100%Au+Au, 0-5% 3 < p T (trig) < 6 GeV 2 < p T (assoc) < p T (trig) 0.8< p t < 4 GeV STAR PRC 75(2007) 034901  / √  ref In Au+Au: broadening of the near- side correlation in  In Au+Au: broadening of the near- side correlation in  Seen in multiple analyses Seen in multiple analyses  Number correlations at low p T  PRC73 (2006) 064907  P T correlations at low p T, for multiple energies  Major source of p T fluctuations  J. Phys. G 32, L37 (2006)  J. Phys. G 34, 451 (2007)  Number correlations at intermediate p T  PRC 75, 034901 (2007)  Number correlations with trigger particles up to 8 GeV/c trigger particles up to 8 GeV/c  D. Magestro, HP2005  J. Putschke, QM2006

34. Near-side Correlation Additional long-range correlation in  Au+Au 20-30% the “ridge” Coupling of high p T partons to longitudinal expansion - Armesto et al, PRL 93 (2004) QCD magnetic fields- Majumder et al, hep- ph/0611035 In recombination framework: Coupling of shower partons to thermal partons undergoing longitudinal expansion- Chiu & Hwa Phys. Rev. C72:034903,2005 Radial flow + trigger bias – S.A. Voloshin, Nucl. Phys. A749, 287 (2005) J. Putschke, QM 2006 Au+Au 0-10% STAR preliminary

35. Study near-side yields Study away-side correlated yields and shapes Components  near-side jet peak  near-side ridge  v2 modulated background Strategy: Subtract  from  projection: isolate ridge-like correlation Definition of “ridge yield”: ridge yield := Jet+Ridge(  )  Jet(  ) Can also subtract large .     3<p t,trigger <4 GeV p t,assoc. >2 GeV Au+Au 0-10% preliminary  Two-Component Ansatz

36.  (J+R) |  |<1.7 J = near-side jet-like corrl. R = “ridge”-like corrl. v 2 modulated bkg. subtracted  (J+R) |  |<1.7 flow (v 2 ) corrected Extracting near-side “jet-like” yields 1 Au+Au 20-30% 2 2  (J+R) -  (R) const bkg. subtracted  (J) |  |<0.7   (J) no bkg. subtraction const bkg. subtracted  (J) |  |<0.7 J. Putschke, QM 2006

37. The  “Ridge” + “Jet” yield vs Centrality 3<p t,trigger <4 GeV p t,assoc. >2 GeV Au+Au 0-10% preliminary Jet+Ridge (  ) Jet (  ) Jet  ) yield ,  ) N part “ Jet ” yield constant with N part J ö rn Putschke, QM2006 Reminder from p T <2 GeV:  elongated structure already in minbias AuAu  elongation in p-p  to  elongation in AuAu. STAR, PRC 73, 064907 (2006)  / √  ref

38. STAR preliminary “Jet” spectrum vs. “Ridge” spectrum “jet” slope “ridge” slope inclusive slope J. Putschke, QM 2006 STAR preliminary

39. Ridge Yield p t,assoc. > 2 GeV STAR preliminary Ridge yield persists up to highest trigger p T and approximately constant yield J. Putschke, QM 2006

40. Particle production in jet distinctly different than in medium Associated particle production (B/M ratio) similar in ridge and medium and about a factor 2-3 different than in the jet. Ridge and medium have similar production mechanism ? Recombination ?  /K~1  /K~0.5

41. Extending the ridge: correlations to  =5 Trigger: 3<p T trig <4 GeV/c, A.FTPC: 0.2<p T assoc < 2 GeV/c, A.TPC: 0.2<p T assoc < 3 GeV/c Trigger on mid-  associated particle high  (reverse of FMS) Near-side correlation: consistent with zero (within large v 2 errors) Away-side correlations are very similar (when scaled) Energy loss picture is the same for mid- and forward  ? AuAu 0-10% AuAu 0-5% AuAu 60-80% STAR Preliminary 2.7<|  assoc |<3.9 Levente Molnar, QM2006 STAR Preliminary

42. STAR preliminary 0-12% 200 GeV Au+Au How to interpret shape modifications? Hard-soft: away-side spectra approaching the bulk. Deflected jets, Mach-cone shock waves, Cherenkov radiation, completely thermalized momentum conservation, or … ? Medium away near deflected jets away near Medium mach cone  M. Horner, QM2006 STAR Collaboration, PRL 95,152301 (2005)

43. STAR preliminary 0-12% 200 GeV Au+Au Hard-soft correlations Hard-soft: away-side spectra approaching the bulk. Inclusive in top 5%?  Three-particle correlation – N.N. Ajitanand, J. Ulery Medium away near deflected jets away near Medium mach cone STAR, PRL 95,152301 (2005) 4 < pT,trig< 6 GeV/c

44. Three particle correlations Two Analysis Approaches: Cumulant Method Unambiguous evidence for true three particle correlations. Two-component Jet+Flow-Modulated Background Model Within a model dependent analysis, evidence for conical emission in central Au+Au collisions p T trig =3-4 GeV/c p T assoc =1-2 GeV/c off-diagonal projection d+Au 0-12% Au+Au  =(  1  2 )/2 Δ2Δ2 Δ1Δ1 Δ1Δ1 0-12% Au+Au: jet v 2 =0 Δ2Δ2 C. Pruneau, QM2006 J. Ulery, HP2006 and poster, QM2006

45. What other handles do we have? Centrality, trigger and associated p T,….. ….Reaction plane In-plane Out-plane STAR 4 < p T,trig < 6 GeV/c, 2 < p T,assoc < p T,trig STAR, Phys. Rev. Lett. 93 (2004) 252301

46. Another handle:  -jet  q Photon-jet measurement is, in principle, sensitive to full medium Bias to where away-side jet is close to surface? Together with di-jet measurement for comparison  Another differential observable Increasing ratio of direct photons to decay photons with centrality due to hadron suppression at high p T PHENIX, Phys. Rev. Lett. 94, 232301 (2005) Wang et al., Phys.Rev.Lett. 77 (1996) 231-234

47. 1/N trig dN/d   (rad) Another handle:  -jet Current Results from Run-4 Au+Au collisions: J. Jin, QM 2006 T. Dietel, QM 2005  q

48. Summary Limited information extracted from single-particle p T spectra Limited information extracted from single-particle p T spectra  Effective fractional energy loss reaches 20% for most central collisions  Initial energy density ~ 15 GeV/fm 3 from radiative energy loss models Di-Jets (those that are observed) may have less surface bias Di-Jets (those that are observed) may have less surface bias Photon-Jet Measurement will complement the di-jet for more complete probe Photon-Jet Measurement will complement the di-jet for more complete probe Heavy-flavor suppression not consistently described by theoretical models with light meson suppression – need elastic energy loss Heavy-flavor suppression not consistently described by theoretical models with light meson suppression – need elastic energy loss