1. Marco van Leeuwen, Marta Verweij, Utrecht University Energy loss in a realistic geometry

2. 2 Soft QCD matter and hard probes Use the strength of pQCD to explore QCD matter Hard-scatterings produce ‘quasi-free’ partons  Initial-state production known from pQCD  Probe medium through energy loss Heavy-ion collisions produce ‘quasi-thermal’ QCD matter Dominated by soft partons p ~ T ~ 100-300 MeV Sensitive to medium density, transport properties

3. 3 Plan of talk Energy loss in a brick: reminder of main differences between formalisms How do these carry over to full geometry Surface bias? Can we exploit full geometry, different observables to constrain/test formalisms? Case study: R AA vs I AA Some results for LHC

4. 4 The Brick Problem Gluon(s) Compare energy-loss in a well-defined model system: Fixed-length L (2, 5 fm) Density T, q Quark, E = 10, 20 GeV  kTkT

5. 5 Energy loss models Multiple soft scattering approximation ASW-MS Opacity expansions (OE)  ASW-SH  (D)GLV Phys.Rev.D68 014008 Nucl.Phys.A784 426 AMY, HT only in brick part (discussed at JET symposium)

6. 6 Some (overly) simple arguments This is a cartoon! Hadronic, not partonic energy loss No quark-gluon difference Energy loss not probabilistic P(  E) Ball-park numbers:  E/E ≈ 0.2, or  E ≈ 2 GeV for central collisions at RHIC  0 spectra Nuclear modification factor PHENIX, PRD 76, 051106, arXiv:0801.4020 Note: slope of ‘input’ spectrum changes with p T : use experimental reach to exploit this

7. 7 Energy loss distributions TECHQM ‘brick problem’ L = 2 fm,  E/E = 0.2 E = 10 GeV ‘Typical for RHIC’ Not a narrow distribution:  Significant probability for  E ~ E  Conceptually/theoretically difficult Significant probability to lose no energy P(0) = 0.5 – 0.6 ASW: Armesto, Salgado, Wiedemann WHDG: Wicks, Horowitz, Dordjevic, Gyulassy

8. 8 Large impact of P(0); broad distribution Spread in  E reduces suppression (R AA ~0.6 instead of 0.2) 〈  E/E 〉 not very relevant for R AA at RHIC Quarks only R AA with  E/E= 0.2

9. 9 R n to summarize E-loss n: power law index n ~ 8 at RHIC  R 8 ~ R AA Use R n to characterise P(  E) (Brick report uses R 7, numerical differences small)

10. 10 Suppression vs For all models: Use temperature T to set all inputs TECHQM preliminary Gluon gas N f = 0

11. 11 Single gluon spectrum For all models this is the starting point P(∆E) originates from spectrum of radiated gluons Models tuned to the same suppression factor R 7 Gluon spectrum different for ASW-MS and OE TECHQM preliminary

12. 12 Energy loss probability P(∆E) is generated by a Poisson convolution of the single gluon spectrum: 3 distinct contributions:  p 0 = probability for no energy loss = e - 〈 Ngluons>  p(∆E) = continuous energy loss = parton loses ∆E  ∆E > E: parton is absorbed by the medium

13. 13 Outgoing quark spectrum Outgoing quark spectrum:  x E = 1 - ∆E/E  x E = 0: Absorbed quarks  x E = 1: No energy loss Suppression factor R 7 dominated by:  ASW-MS: partons w/o energy loss  OEs: p 0 and soft gluon radiation TECHQM preliminary Can we measure this? Continuous part of energy loss distribution more relevant for OE than MS

14. 14 Geometry Density profile Density along parton path Longitudinal expansion 1/  dilutes medium  Important effect Space-time evolution Wounded Nucleon Scaling with optical Glauber Formation time:  0 = 0.6 fm

15. 15 Effective medium parameters PQM: ASW-MS:  c, R Generalisation , : GLV, ASW-OE: GLV, ASW-OE

16. 16 Medium as seen by parton Path average variables which characterize the energy loss. Exercise:  Parton is created at x 0 and travels radially through the center of the medium until it leaves the medium or freeze out has taken place.

17. 17 Medium as seen by parton Different treatment of large angle radiation cut-off: qperp<E Now: Partons in all directions from all positions Medium characterized by  c and L ASW-MSDGLV

18. 18 Medium as seen by parton Medium characterized by typical gluon energy  c and path length L Radially outward from surface Radially outward from intermediate R Radially inward from surface ASW-MS DGLV

19. 19 Medium as seen by parton ASW-MSDGLV There is no single ‘equivalent brick’ that captures the full geometry Some partons see very opaque medium (R 7 < 0.05) R 7 isolines

20. 20 Why measure I AA ? Bias associated particle towards longer path length Probe different part of medium Trigger to larger parton p t Probe different energy loss probability distribution Associate Trigger Single hadron

21. 21 Surface bias I ASW-MSWHDG rad 22% surviving partons 48% surviving partons OE more surviving partons → more fractional energy loss OE probe deeper into medium  E < E: Surviving partons

22. 22 Surface bias II: L trig vs L assoc For R AA and I AA different mean path length. P t Trigger > P t Assoc Triggers bias towards smaller L Associates bias towards longer L L eff [fm]

23. 23 R AA vs I AA : Trigger bias Parton spectra resulting in hadrons with 8<p t hadron <15 GeV for without (vacuum) and with (ASW-MS/WHDG) energy loss. I AA : conditional yield Need trigger hadron with p T in range   E < E I AA selects harder parton spectrum

24. 24 R AA and I AA at RHIC Models fitted to R AA using modified  2 analysis 1  uncertainty band indicated q 0 for multiple-soft approx 4x opacity expansion (T 0 factor 1.5)

25. 25 Brick vs full geometry Brick: Full geometry Factor between MS and OE larger in full geom than brick OE give larger suppression at large L NB: large L  R 7 < 0.2 in full geom

26. 26 R AA and I AA at RHIC R AA – fitted I AA – predicted Measured I AA (somewhat) larger than prediction Differences between models small; DGLV slightly higher than others I AA < R AA due to larger path length – difference small due to trigger bias

27. 27 R AA and I AA at LHC 50 < p t,Trig < 70 GeV Using medium density from RHIC R AA increases with p T at LHC larger dynamic range  E/E decreases with p T I AA : decrease with p T,assoc Slopes differ between models

28. 28 R AA and I AA at LHC Reduced p T dependence Slope similar for different models I AA < R AA Some p T dependence? 50 < p t,Trig < 70 GeV Density 2x RHIC

29. 29 LHC estimates RHIC best fits

30. 30 Conclusion Energy loss models (OE and MS) give different suppression at same density For R 7 = 0.25, need L=5, T=300-450 MeV or L=2, T=700-1000 MeV Full geometry: Large paths, large suppression matter Surface bias depends on observable, energy loss model Measured I AA above calculated in full geometry At LHC: p T -dependence of R AA  sensitive to P(  E | E) Only if medium density not too large R AA, I AA limited sensitivity to details of E-loss mode (P(E)) Are there better observables? Jets: broadening, or long frag?  -hadron

31. 31 Extra slides

32. 32 Where does the log go?

33. 33 Single gluon spectrum P(∆E) originates from spectrum of radiated gluons. ASW-MS and ASW-SH the same at large. WHDG smooth cutoff depending on E parton. Opacity expansions more soft gluon radiation than ASW-MS. N gluons,ASW-SH ~ N gluons,WHDG 〈〉 ASW-SH > 〈〉 WHDG N gluons,ASW-MS < N gluons,OE TECHQM preliminary

34. 34 Suppression Factor in a brick Hadron spectrum if each parton loses energy: Weighted average energy loss: For RHIC: n=7 R 7 approximation for R AA. p t ' = (1-) p t

35. 35 Multi gluon spectrum 1 2 3 4 5 6 7 = N max,gluon Poisson convolution of single gluon to multi gluon spectrum N max,gluon = (2*N gluon +1) Iterations N gluon follows Poisson distribution – model assumption Normalize to get a probability distribution.

36. 36 Geometry of HI collision Woods-Saxon profile Wounded Nucleon Scaling with optical Glauber Medium formation time:  0 = 0.6 fm Longitudinal Bjorken Expansion 1/  Freeze out temperature: 150 MeV Temperature profile Input parton spectrum Known LO pQCD Fragmentation Factor Known from e+e- Energy loss geometry medium Measurement

37. 37 Opacity Expansion Calculation of parameters through Few hard interactions. All parameters scale with a power of T:

38. 38 Schematic picture of energy loss mechanism in hot dense matter path length L kTkT Radiated energy  x  Outgoing quark x   x) 

39. 39 Model input parameters ~