1. Lecture II: parton energy loss at high p T Marco van Leeuwen Utrecht University Jyväskylä Summer School 2008

2. 2 Hard probes of QCD matter Use the strength of pQCD to explore QCD matter Use ‘quasi-free’ partons from hard scatterings to probe ‘quasi-thermal’ QCD matter Interactions between parton and medium: -Radiative energy loss -Collisional energy loss -Hadronisation: fragmentation and coalescence Sensitive to medium density, transport properties Calculable with pQCD Quasi-thermal matter: dominated by soft (few 100 MeV) partons

3. 3 Energy loss in QCD matter radiated gluon propagating parton 22 QCD bremsstrahlung (+ LPM coherence effects) Density of scattering centers: Nature of scattering centers, e.g. mass: radiative vs elastic loss Or no scattering centers, but fields  synchrotron radiation? Transport coefficient Energy loss Energy loss probes:

4. 4 Relativistic Heavy Ion Collider PHENIX STAR Au+Au  s NN = 200 GeV RHIC: variety of beams: p+p, d+Au, Au+Au, Cu+Cu Two large experiments: STAR and PHENIX Smaller experiments: PHOBOS, BRAHMS decomissioned Recent years: Large data samples, reach to high p T

5. 5 STAR and PHENIX at RHIC PHENIX STAR (PHOBOS, BRAHMS more specialised) PHENIX 2  coverage, -1 <  < 1 for tracking + (coarse) EMCal PID by TOF, dE/dx (STAR), RICH (PHENIX) Partial coverage 2 x 0.5 , -0.35 <  < 0.35 Finely segmented calorimeter + forward muon arm Optimised for acceptance (correlations, jet-finding) Optimised for high-pt  0, , e, J/  (EMCal, high trigger rates)

6. 6 Hadron production in p+p and pQCD NLO calculations: W. Vogelsang Star, PRL 91, 172302 Brahms, nucl-ex/0403005  0 and charged hadrons at RHIC in good agreement with NLO pQCD PRL 91, 241803 Perturbative QCD ‘works’ at RHIC energies

7. 7 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

8. 8 Centrality examples This is what you really measure... and this is what you see in a presentation central mid-centralperipheral

9. 9 Centrality dependence of hard processes 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 Total multiplicity: soft processes

10. 10 Direct photons: no interactions PHENIX Direct  spectra Scaled by N coll PHENIX, PRL 94, 232301 Direct  in A+A scales with N coll Centrality A+A initial state is incoherent superposition of p+p for hard probes

11. 11 Testing N coll 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?

12. 12  0 R AA – high-p T suppression Hard partons lose energy in the hot matter  : no interactions Hadrons: energy loss R AA = 1 R AA < 1  0 : R AA ≈ 0.2  : R AA = 1

13. 13 Two extreme scenarios p+p Au+Au pTpT 1/N bin d 2 N/d 2 p T Scenario I P(  E) =  (  E 0 ) ‘Energy loss’ Shifts spectrum to left Scenario II P(  E) = a  (0) + b  (E) ‘Absorption’ 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

14. 14 Energy loss spectrum Brick L = 2 fm,  E/E = 0.2 E = 10 GeV Typical examples with fixed L  E/E> = 0.2 R 8 ~ R AA = 0.2 Different theoretical approximation (ASW, WHDG) give different results – significant? Significant probability to lose no energy (P(0)) Broad distribution, large E-loss (several GeV, up to  E/E = 1) Theory expectation: mix of partial transmission+continuous energy loss – Can we see this in experiment?

15. 15 Parton energy loss and R AA modeling Qualitatively: `known’ from e + e - known pQCDxPDF extract Parton spectrum Fragmentation (function) Energy loss distribution This is what we are after Need deconvolution to extract P(  E) Parton spectrum and fragmentation function are steep  non-trivial relation between R AA and P(  E)

16. 16 Determining the medium density PQM (Loizides, Dainese, Paic), Multiple soft-scattering approx (Armesto, Salgado, Wiedemann) Realistic geometry GLV (Gyulassy, Levai, Vitev), Opacity expansion (L/ ), Average path length WHDG (Wicks, Horowitz, Djordjevic, Gyulassy) GLV + realistic geometry ZOWW (Zhang, Owens, Wang, Wang) Medium-enhanced power corrections (higher twist) Hard sphere geometry AMY (Arnold, Moore, Yaffe) Finite temperature effective field theory (Hard Thermal Loops) For each model: 1.Vary parameter and predict R AA 2.Minimize  2 wrt data Models have different but ~equivalent parameters: Transport coeff. Gluon density dN g /dy Typical energy loss per L:  0 Coupling constant  S PHENIX, arXiv:0801.1665, J. Nagle WWND08

17. 17 Medium density from R AA PQM = 13.2 GeV 2 /fm +2.1 - 3.2 ^ GLV dN g /dy = 1400 +270 - 150 WHDG dN g /dy = 1400 +200 - 375 ZOWW  0 = 1.9 GeV/fm +0.2 - 0.5 AMY  s = 0.280 +0.016 - 0.012 Data constrain model parameters to 10-20% Method extracts medium density given the model/calculation Theory uncertainties need to be further evaluated e.g. comparing different formalisms, varying geometry But models use different medium parameters – How to compare the results?

18. 18 Some pocket formula results Large differences between models GLV/WHDG: dN g /dy = 1400 T(  0 ) = 366 MeV PQM: (parton average) T = 1016 MeV AMY: T fixed by hydro (~400 MeV),  s = 0.297

19. 19 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

20. 20 Naive picture for di-hadron measurements P T,jet,1 P T,jet,2 Fragment distribution (fragmentation fuction) Out-of-cone radiation: P T,jet2 < P T,jet1 Ref: no Eloss In-cone radiation: P T,jet2 = p T,jet1 Softer fragmentation Naive assumption for di-hadrons: p T,trig measures P T,jet So, z T =p T,assoc /p T,trig measures z

21. 21 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 Near side associated trigger Away side associated trigger

22. 22 d-Au Au-Au Medium density from di-hadron measurement I AA constraint D AA constraint D AA + scale uncertainty J. Nagle, WWND2008 associated  trigger  0 =1.9 GeV/fm single hadrons Medium density from away-side suppression and single hadron suppression agree Theory: ZOWW, PRL98, 212301 Data: STAR PRL 95, 152301 8 < p T,trig < 15 GeV z T =p T,assoc /p T,trig (Experiment and theory updates in the works)

23. 23 Conclusion so far Hard probes experimentally accessible at RHIC –Luminosity still increasing, so more to come? N coll scaling seen for , total charm xsec Large suppression of light hadrons  parton energy loss We have a dense, strongly interacting system in Heavy Ion collisions at RHIC But how dense? All models say: T > 300 MeV, but large spread

24. 24 Path length dependence I Centrality Au+Au Cu+Cu In-plane Out of plane, density increase with centrality Vary L and density independently by changing Au+Au  Cu+Cu Change L in single system in-plane vs out of plane Collision geometry

25. 25 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

26. 26 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

27. 27 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

28. 28 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

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

30. 30 R AA vs reaction plane angle Azimuthal modulation, path length dependence largest in ASW-BDMPS Data prefer ASW-BDMPS C. Vale, PHENIX, QM09 But why? – No clear answer yet

31. 31 Path length III: ‘surface bias’ Near side trigger, biases to small E-loss Away-side large L Away-side suppression I AA samples different path-length distribution than inclusives R AA

32. 32 L scaling: elastic vs radiative T. Renk, PRC76, 064905 R AA : input to fix densityRadiative scenario fits data; elastic scenarios underestimate suppression Indirect measure of path-length dependence: single hadrons and di-hadrons probe different path length distributions Confirms L 2 dependence  radiative loss dominates

33. 33 Summary of L-dependence Centrality, system size dependence as expected (   N part ) Angle-dependence under study more subtle, needs work R AA vs I AA indicates L 2 dependence  radiative E-loss

34. 34 Heavy quark suppression PHENIX nucl-ex/0611018, STAR nucl-ex/0607012 Djordjevic, Phys. Lett. B632, 81 Armesto, Phys. Lett. B637, 362 Measured suppression of non- photonic electrons larger than expected Using non-photonic electrons light M.Djordjevic PRL 94 Wicks, Horowitz et al, NPA 784, 426 Expected energy loss Expect: heavy quarks lose less energy due to dead-cone effect Most pronounced for bottom Radiative (+collisional) energy loss not dominant? E.g.: in-medium hadronisation/dissociation (van Hees, et al)

35. 35 Light flavour reference Armesto, Cacciari, Salgado et al. Note again: R AA and I AA fit same density

36. 36 Heavy Quark comparison No minimum – Heavy Quark suppression too large for ‘normal’ medium density

37. 37 B D X.Y. Lin, hep-ph/0602067 Charm/bottom separation Idea: use e-h angular correlations to tag semi-leptonic D vs B decay D → e + hadrons B peak broader due to larger mass Extract B contribution by fitting:

38. 38 Charm/bottom separation Combine r B and R AA to extract R AA for charm and bottom

39. 39 I: Djordjevic, Gyulassy, Vogt and Wicks, Phys. Lett. B 632 (2006) 81; dN g /dy = 1000 II: Adil and Vitev, Phys. Lett. B 649 (2007) 139 III: Hees, Mannarelli, Greco and Rapp, Phys. Rev. Lett. 100 (2008) 192301 p T > 5 GeV/c R AA for c  e and b  e B.Biritz QM09 Combined data show: electrons from both B and D suppressed Large suppression suggests additional energy loss mechanism (resonant scattering, dissociative E-loss)

40. 40 Use e-K invariant mass to separate charm and bottom Signal: unlike-sign near-side correlations Subtract like-sign pairs to remove background Use Pythia to extract D, B yields arXiv:0903.4851 hep-ex D/B from e-K correlations B → e + D D → e + K

41. 41 Charm-to-Bottom Ratio PHENIX p+p measuments agree with pQCD (FONLL) calculation arXiv:0903.4851 hep-ex

42. 42 Equalibration of rare probes Rare probes: not chemically equilibrated in the jet spectrum. Example 1: flavor not contained in the medium, but can be produced off the medium (e.g. photons) –Need enough yield to outshine other sources of N rare. Example 2: flavor chemically equilibrated in the medium –E.g. strangeness at RHIC –Coupling of jets (flavor not equilibrated) to the equilibrated medium should drive jets towards chemical equilibrium. R. Fries, QM09

43. 43 Equilibration process: jet conversion W. Liu, R.J. Fries, Phys. Rev. C77 (2008) 054902 hard parton path length L Quark gluon Flavour of leading parton changes through interactions with medium

44. 44 R AA for , K and p p T (GeV) STAR preliminary R AA (K) ~ 0.4 at high p T > 5.0 GeV Consistent with jet conversion calculations

45. 45 Summary Large suppression of high-p T hadron production  partons lose energy 4 different theoretical frameworks (radiative E-loss) –Can all describe single hadron suppression (and often di- hadron suppression) –T = 300 - 1000 MeV Path length dependence –R AA vs reaction plane not fully understood? –RAA, IAA simultaneous fit: Strong indication of L 2 dependence  radiative dominates Heavy quarks –Expected to lose less energy (dead cone effect) Not observed ‘A lot of ins, a lot of outs’ – The Dude

46. 46 Extra slides

47. 47 Transport and medium properties 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 (see previous talk: Steinberg) (Majumder, Muller, Wang) Lattice QCD:  /s < 0.1 A quantitative understanding of hot QCD matter is emerging (Meyer)

48. 48 Kaons in p+p Charged and neutral kaons are extended up to 15 GeV/c in p+p collisions. Charged and neutral kaons are consistent. Phys. Rev. C 75 (2007) 64901 STAR preliminary

49. 49 Quark vs gluon energy loss Energy Loss when jet pass the medium, which is characterized by    Color charge effect of parton energy loss in heavy ion collisions.   ddpd d Nd N R T pp T AB bin AB / /1 2 2  QM08 arXiv: 0804.4760 STAR preliminary EgEg EqEq ~ 9/4 In pQCD: Suppression for proton >  hard parton path length L Quark

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