1. 1 High-p T probes of QCD matter Marco van Leeuwen, Utrecht University

2. 2 Part II: in-medium energy loss Nuclear geometry, N bin scaling –photons –charm High-p T measure of energy loss –Single, di-hadrons – first quantitative steps Differential tests of energy loss –Path-length dependence –Heavy vs light (charm/beauty) –Quark vs gluon (baryon/meson)

3. 3 Nuclear geometry: N part, N bin, L,  b N part : n A + n B (ex: 4 + 5 = 9 + …) N bin : n A x n B (ex: 4 x 5 = 20 + …) Two limits: - Complete shadowing, each nucleon only interacts once,   N part - No shadowing, each nucleon interact with all nucleons it encounters,  N bin Soft processes: long timescale, large   tot  N part Hard processes: short timescale, small ,  tot  N bin Transverse view Eccentricity Path length L, mean Density profile  :  part or  coll x y L

4. 4 Centrality dependence in A+A d  /dN ch 200 GeV Au+Au Rule of thumb for A+A collisions (A>40) 40% of the hard cross section is contained in the 10% most central collisions Binary collisions weight towards small impact parameter

5. 5 Testing N bin scaling I: direct photons Direct  in p+p agree with pQCD q + g  q +  PHENIX, PRL 94, 232301 Direct  in A+A scales with N coll Centrality R AA =1 (N coll scaling) for incoherent superposition of p+p collisions Production through q + q  g + 

6. 6 Testing N bin scaling II: Charm PRL 94 (2005) NLO prediction: m ≈ 1.3 GeV, reasonably hard scale at p T =0 Total charm cross section scales with N bin in A+A Scaling observed in PHENIX and STAR – scaling error in one experiment?

7. 7 Energy loss in QCD matter  : R AA = 1  0, h ± : R AA ≈ 0.2 Au+Au 200 GeV, 0-5% central ‘nuclear modification factor’ D. d’Enterria Hard partons lose energy in the hot matter High-p T hadron production suppressed in Au+Au collisions  : no interactions Hadrons: energy loss R AA = 1 R AA < 1

8. 8 Two extreme scenarios p+p Au+Au pTpT 1/N bin d 2 N/d 2 p T Scenario I P(  E) =  (  E 0 ) ‘typical energy loss’ Shifts spectrum to left Scenario II P(  E) = a  (0) + b  (E) ‘partial transmission’ Downward shift (or how P(  E) says it all) P(  E) encodes the full energy loss process R AA not sensitive to details of mechanism … need more differential probes

9. 9 Radiative energy loss in QCD Energy loss process characterized by a single constant Transport coefficient Transport coefficient is a fundamental parameter of QCD matter Energy loss kT~kT~ pQCD expectation Transport coefficient sets medium properties Non-perturbative: is a Wilson loop (Wiedemann) (Liu, Rajagopal, Wiedemann) e.g. N=4 SUSY: From AdS/CFT (Baier et al)

10. 10 from inclusive hadron suppression R AA: ~ 5-15 GeV 2 /fm Eskola et al. ‘04 Large uncertainty – inclusive hadrons insensitive

11. 11 Intermediate p T – not only fragmentation Large baryon/meson ratio in Au+Au ‘intermediate p T ‘ M. Konno, QM06 High p T : Au+Au similar to p+p  Fragmentation dominates p/  ~ 1,  /K ~ 2 Baryon/meson = 0.2-0.5

12. 12 Di­hadron correlations associated  trigger 8 < p T trig < 15 GeV p T assoc > 3 GeV Use di-hadron correlations to probe the jet-structure in p+p, d+Au Near side Away side and Au+Au Combinatorial background

13. 13 Di-jet kinematics k T measures di-jet acoplanarity J T distribution measures transverse jet profile P L,h distribution measures longitudinal jet profile Use z=p L,h /E jet or  = ln(E jet /p L,h )  approx indep of E jet P T,jet1 P T,jet2 k T,xy P Th1 JTJT P Th2 P out P L,h Di-hadron correlations: naïvely assume P Th1 ~P Tjet1 : z T = pT,h2 /p Th1 P out ~ J T Not a good approximation!

14. 14 Generic expectations from energy loss Longitudinal modication: –out-of-cone  energy lost, suppression of yield, di-jet energy imbalance –in-cone  softening of fragmentation Transverse modification –out-of-cone  increase acoplanarity k T –in-cone  broadening of jet-profile kT~kT~ E jet fragmentation after energy loss?

15. 15 p T assoc > 3 GeV p T assoc > 6 GeV d+Au Au+Au 20-40% Au+Au 0-5% Suppression of away-side yield in Au+Au collisions: energy loss High-p T hadron production in Au+Au dominated by (di-)jet fragmentation Highest p T : focus on fragmentation

16. 16 Di­hadron yield suppression No suppression Suppression by factor 4-5 in central Au+Au Away-side: Suppressed by factor 4-5  large energy loss Near side Away side STAR PRL 95, 152301 8 < p T,trig < 15 GeV Yield of additional particles in the jet Yield in balancing jet, after energy loss Near side: No modification  Fragmentation outside medium? Note: per-trigger yields can be same with energy-loss

17. 17 Extracting the transport coefficient Zhang, H et al, nucl-th/0701045 Di-hadrons provide stronger constrain on density Extracted transport coefficient from singles and di-hadrons consistent 2.8 ± 0.3 GeV 2 /fm  2 -minimum narrower for di-hadrons Di-hadron suppression Inclusive hadron suppression Di-hadrons Inclusive hadrons

18. 18 Model dependence of Different calculational frameworks C. Loizides hep-ph/0608133v2 2.8 ± 0.3 GeV 2 /fm Di-hadrons Inclusive hadrons Zhang, H et al, nucl-th/0701045 Multiple soft scattering (BDMPS, Wiedemann, Salgado,…)‏ Twist expansion (Wang, Wang,…)‏ Different approximations to the theory give significantly different results Uncertainties: -Formalism for QCD radiation -Geometry (density profile)

19. 19 Need to ask critical questions! Brian Cole, QM08 summary: Scrutinise theory, experiment and interpretation What do we know? What do we not know? How can we improve? Good understanding needed to communicate our results with other scientists (e.g. particle physicists)

20. 20 Interpreting di-hadron measurements Scenario I: Some lose all, Some lose nothing Scenario II: All lose something Di-hadron measurement: Away-side yield is (semi-)inclusive, so does not measure fluctuations of energy loss Multi-hadron measurements potentially more sensitive All is encoded in energy loss distribution P(  E)

21. 21 A closer look at azimuthal peak shapes No away-side broadening: -No induced radiation -No acoplanrity (‘multiple-scattering’)   Induced acoplanarity (BDMPS): Vitev, hep-ph/0501225 Broadening due to fragments of induced radiation 8 < p T (trig) < 15 GeV/c p T (assoc)>6 GeV

22. 22 More detailed tests of energy loss Path length dependence –Elastic (L) vs radiative (L 2 ) –Measurements wrt centrality, reaction plane, v 2 Mass dependence –Heavy quarks  dead cone effect Quark/gluon differences –Color factors

23. 23 L scaling: elastic vs radiative T. Renk, PRC76, 064905 R AA : input to fix densityExpect small away-side suppression in elastic scenario Indirect measure of path-length dependence: single hadrons and di-hadrons probe different path length distributions

24. 24 Path length I: centrality dependence Modified frag: nucl-th/0701045 - H.Zhang, J.F. Owens, E. Wang, X.N. Wang 6 < p T trig < 10 GeV Away-side suppressionR AA : inclusive suppression B. Sahlmüller, QM08 O. Catu, QM2008 Inclusive and di-hadron suppression seem to scale with N part Some models expect scaling, others (PQM) do not Comparing Cu+Cu and Au+Au

25. 25 N part scaling? PQM - Loizides – private comunication Geometry (thickness, area) of central Cu+Cu similar to peripheral Au+Au PQM: no scaling of with N part

26. 26 Path length II: R AA vs L PHENIX, PRC 76, 034904 In Plane Out of Plane 3<p T <5 GeV/c LL R AA as function of angle with reaction plane Suppression depends on angle, path length

27. 27 R AA L  Dependence Au+Au collisions at 200GeV Phenomenology: R AA scales best with L  Little/no energy loss for L   < 2 fm ? 0-10% 50-60% PHENIX, PRC 76, 034904

28. 28 Path Length III: v 2 at high-p T PQM: Dainese, Loizides, Paic, Eur Phys J C38, 461 Models tend to predict low v 2 v 2 for  0 Agreement improves for high-p T Promising measurements, not much new in recent years Main issue: how do jets influence the event-plane (non-flow)

29. 29 Modelling azimuthal dependence A. Majumder, PRC75, 021901 R AA p T (GeV) R AA R AA vs reaction plane sensitive to geometry model Awaiting more detailed model-data comparison

30. 30 Heavy-light difference Expect: dead-cone effect Armesto plot Armesto et al, PRD71, 054027 Below 10 GeV: charm loses 20-30% less energy than u,d Bottom loses ~80% less Expected suppression of D mesons ~0.5 times light hadrons light M.Djordjevic PRL 94 (2004) Wicks, Horowitz et al, NPA 784, 426

31. 31 Charm R AA (using non-phot electrons) PHENIX nucl-ex/0611018 STAR nucl-ex/0607012 Djordjevic, Phys. Lett. B632 81 (2006) Armesto, Phys. Lett. B637 362 (2006) Measured suppression of non- photonic electrons larger than expected Larger medium density? Note: c/b ratio important

32. 32 Heavy flavour (charm) II New PHENIX data plot? Radiative energy loss underestimates v 2 HF PHENIX, nucl-ex/0611018 Next step: charm v 2 Note: most HF measurements at RHIC indirect (electrons), upgrades under way for direct charm (beauty) measurements

33. 33 QCD : For SU(3) : N c = 3 C A = 3, C F = 4/3 C F ~ strength of a gluon coupling to a quark C A ~ strength of the gluon self coupling T F ~ strength of gluon splitting into a quark pair C A /C F =9/4 Color factors Color factors measured at LEP Expect gluons radiate ~ twice more energy than quarks

34. 34 PYTHIA (by Adam Kocoloski) gg qq gq Subprocesses and quark vs gluon p+pbar dominantly from gluon fragmentation

35. 35 PRL 97, 152301 (2006) STAR Preliminary, QM08 Curves: X-N. Wang et al PRC70(2004) 031901 Baryon & meson NMF STAR Preliminary Comparing quark and gluon suppression Protons less suppressed than pions, not more No sign of large gluon energy loss

36. 36 Quark vs gluon suppression + renk plot WHDG Renk and Eskola, PRC76,027901 GLV formalism BDMPS formalism Quark/gluon difference larger in GLV than BDMPS (because of cut-off effects  E < E jet ?) ~10% baryons from quarks, so baryon/meson effect smaller than gluon/quark Are baryon fragmentation functions under control? Conclusion for now: some homework to do...

37. 37 So, where are we? Single hadron and di-hadron suppression give similar medium density –Favour L 2 dependence – radiative Path length dependence –Centrality dependence and A-dependence constrain medium density models –Measurements wrt reaction plane pursued – some open issues Heavy quark suppression similar to light quarks Baryon suppression less or similar to mesons –No sign of quark/gluon difference Specific predictions lead to specific questions That’s how we make progress in science! Lots of data available. Time for a ‘global fit’ of the medium properties at RHIC?

38. 38 Properties of medium at RHIC Broad agreement between different observables, and with theory pQCD: 2.8 ± 0.3 GeV 2 /fm (Baier)   23 ± 4 GeV/fm 3 T  400 MeV Transport coefficient Total E T Viscosity (model dependent)   = 0.3-1fm/c  ~ 5 - 15 GeV/fm 3 T ~ 250 - 350 MeV (Bjorken) From v 2 (Majumder, Muller, Wang) Lattice QCD:  /s < 0.1 A quantitative understanding of hot QCD matter is emerging (Meyer)

39. 39 Extra slides

40. 40 (fm/c) log t pTpT 11010 7 (GeV) hadron decays hadron gas sQGP hard scatt jet Brems. Cartoon only: sources of , mean p T vs time (dashed: hadrons) jet-thermal jet fragmentation Direct photon history Direct photons are emitted at all stages then surviving unscathed strongly (  s, almost transparent to medium) Cartoon from G. David, Hard Probe 2006 Good Write-up to read: nucl-ex/0611009

41. 41 Sources of Radiation in A+A (interaction of jet and medium) Compton scattering of hard scattered and thermal partons (Jet-photon conversion) –A recent calculation predicted yields for radiative and collisional E-loss case –This itself probes the matter on similar way as jets do. New way to look at photons? Bremsstrahlung from hard scattered partons in medium C. Gale, NPA774(2006)335 Turbide et al., PRC72, 014906 (2005) R. Fries et al., PRC72, 041902 (2005) Turbide et al., arXiv:0712.0732 Liu et al., arXiv:0712.3619, etc.. Hard scattered partons interact with thermal partons in matter

42. 42 A theory: F. Arleo (JHEP 0609 (2006) 015) Isospin effect, in addition to jet-quenching(BDMPS) and shadowing. Jet-photon conversion is not taken into account Low pT region is underestimated because of lack of jet-photon conversion? Direct photons in 200GeV Au+Au Remember the extended “highlight plots” from PHENIX –Consistent with old published result up to ~ 12GeV/c Direct photons suppressed at very high pT?

43. 43 Nuclear geometry: Glauber theory for p+A Normalized nuclear density  (b,z): Nuclear thickness function Inelastic cross section for p+A: Hard processes with large momentum transfer: short coherence length  successive NN collisions independent p+A is incoherent superposition of N+N collisions

44. 44  Drell-Yan /A in p+A at SPS Glauber scaling of hard process cross sections in p(  )+A Experimental tests of Glauber scaling: M.May et al, Phys Rev Lett 35, 407 (1975 )  inel for 7 GeV muons on nuclei A 1.00 A Small/hard cross sections in p+A scale as A 1.0 NA50 Phys Lett B553, 167

45. 45 Glauber Scaling for A+A b-dependent nuclear overlap function: b Hard process rate for restricted impact parameter range: is suitably averaged over impact parameter distribution of events Number of binary nucleon-nucleon collisions in A+B:

46. 46 Jet-medium Enhancement tested… …allowing a quantative test of Jet-medium enhancement predictions At high p T data favors standard suppression predictions, not enhancement