1. Hard probes: High-p T and jets Marco van Leeuwen, Utrecht University Topical lectures NIKHEF 24-26 June 2009

2. 2 Plan of Lecture Introduction Main results at high p T Interpretation: extracting medium density, T Path length L dependence Focus on what we know so far; mainly RHIC results Tomorrow: Intermediate p T Jet finding Jet measurements at RHIC The future: LHC

3. 3 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

4. 4 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:

5. 5 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

6. 6 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)

7. 7 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

8. 8 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

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 However: -Theory curve does not match d+Au: need to evaluate systematics -Experimental uncertainties will decrease in near future Data: STAR PRL 95, 152301 8 < p T,trig < 15 GeV z T =p T,assoc /p T,trig

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? Quantitative interpretation still ‘under construction’ ‘A lot of ins, a lot of outs’ – The Dude

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 Awaiting more detailed model-data comparison

30. 30 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

31. 31 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

32. 32 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

33. 33 Summary Jet-fragmentation fragmentation dominant at high p T Hadron production suppressed by factor 4-5 Single vs di-hadrons indicate L 2 dependence  radiative E-loss Detailed connection to geometry still outstanding

34. 34 Extra slides

35. 35 Particle Data Group topical reviews http://pdg.lbl.gov/2009/reviews/contents_sports.html http://pdg.lbl.gov/2009/reviews/contents_sports.html QCD and jets: CTEQ web page and summer school lectures http://www.phys.psu.edu/~cteq/ http://www.phys.psu.edu/~cteq/ Handbook of Perturbative QCD, Rev. Mod. Phys. 67, 157–248 (1995) http://www.phys.psu.edu/~cteq/handbook/v1.1/handbook.ps.gz http://www.phys.psu.edu/~cteq/handbook/v1.1/handbook.ps.gz QCD and Collider Physics, R. K. Ellis, W. J. Sterling, D.R. Webber, Cambridge University Press (1996) An Introduction to Quantum Field Theory, M. Peskin and D. Schroeder, Addison Wesley (1995) Introduction to High Energy Physics, D. E. Perkins, Cambridge University Press, Fourth Edition (2000) General QCD references http://www.lpthe.jussieu.fr/~salam/fastjet/

36. 36 Heavy Ion references RHIC overviews: P. Jacobs and X. N. Wang, Prog. Part. Nucl. Phys. 54, 443 (2005) B. Mueller and J. Nagle, Ann. Rev. Nucl. Part. Sci. 56, 93 (2006) RHIC experimental white papers BRAHMS: nucl-ex/0410020 PHENIX: nucl-ex/0410003 PHOBOS: nucl-ex/0410022 STAR: nucl-ex/0501009 LHC Yellow Reports

37. 37 QCD NLO resources PHOX family (Aurenche et al) http://wwwlapp.in2p3.fr/lapth/PHOX_FAMILY/main.html http://wwwlapp.in2p3.fr/lapth/PHOX_FAMILY/main.html MC@NLO (Frixione and Webber) http://www.hep.phy.cam.ac.uk/theory/webber/MCatNLO/ http://www.hep.phy.cam.ac.uk/theory/webber/MCatNLO/ You can use these codes yourself to generate the theory curves! And more: test your ideas on how to measure isolated photons or di-jets or... http://nagyz.web.cern.ch/nagyz/Site/NLOJet++.html

38. 38 Energy loss in a QCD medium + alternative scenarios, e.g. shock wave Energy loss and fragmentation Unmodified fragmentation after energy loss Fragmentation in the medium completely modified A more complete picture FragmentationIn-medium energy loss Or in-medium fragmentation Or Time-scales matter Hadron formation time Lower p T assoc : measure radiation fragments Lower p T trig : explore timescale

39. 39 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

40. 40 Nuclear modification factor D. d’Enterria Hard partons lose energy in the hot matter  : no interactions Hadrons: energy loss R AA = 1 R AA < 1 Yield per collision  0 : R AA ≈ 0.2  : R AA = 1 Nuclear modification factor C. Vale, K. Okada, Hard Probes 2008

41. 41  0 at lower energies  0 production at lower energies (ISR, fixed target FNAL) not well described Good description at RHIC energies Soft jets at lower √s not well controlled? C. Bourelly and J. Soffer, hep-ph/0311110