1. Jet Quenching and Jet Finding Marco van Leeuwen, UU

2. 2 Fragmentation and parton showers large Q 2 Q ~ m H ~  QCD FF Analytical calculations: Fragmentation Function D(z,  ) z=p h /E jet Only longitudinal dynamics High-energy parton (from hard scattering) Hadrons MC event generators implement ‘parton showers’ Longitudinal and transverse dynamics

3. 3 Jet Quenching 1)How is does the medium modify parton fragmentation? Energy-loss: reduced energy of leading hadron – enhancement of yield at low p T ? Broadening of shower? Path-length dependence Quark-gluon differences Final stage of fragmentation outside medium? 2)What does this tell us about the medium ? Density Nature of scattering centers? (elastic vs radiative; mass of scatt. centers) Time-evolution? High-energy parton (from hard scattering) Hadrons

4. 4 Medium-induced radition If <  f, multiple scatterings add coherently Zapp, QM09 L c =  f,max propagating parton radiated gluon Landau-Pomeranchuk-Migdal effect Formation time important Radiation sees length ~  f at once Energy loss depends on density: and nature of scattering centers (scattering cross section) Transport coefficient

5. 5 Testing volume (N coll ) scaling in Au+Au 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

6. 6  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

7. 7 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 energy loss distribution, details of mechanism

8. 8 Jet reconstruction Single, di-hadrons: focus on a few fragments of the shower  No information about initial parton energy in each event Jet finding: sum up fragments in a ‘jet cone’ Main idea: recover radiated energy – determine energy of initial parton Feasibility depends on background fluctuations, angular broadening of jets Need: tracking or Hadron Calorimeter and EMCal (  0 )

9. 9 Generic expectations from energy loss Longitudinal modification: –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?

10. 10 Jet reconstruction algorithms Two categories of jet algorithms: Sequential recombination k T, anti-k T, Durham –Define distance measure, e.g. d ij = min(p Ti,p Tj )*R ij –Cluster closest Cone –Draw Cone radius R around starting point –Iterate until stable ,  jet = particles For a complete discussion, see: http://www.lpthe.jussieu.fr/~salam/teaching/PhD-courses.html Sum particles inside jet Different prescriptions exist, most natural: E-scheme, sum 4-vectors Jet is an object defined by jet algorithm If parameters are right, may approximate parton

11. 11 Collinear and infrared safety Illustration by G. Salam Jets should not be sensitive to soft effects (hadronisation and E-loss) -Collinear safe -Infrared safe

12. 12 Collinear safety Note also: detector effects, such as splitting clusters in calorimeter (  0 decay) Illustration by G. Salam

13. 13 Infrared safety Infrared safety also implies robustness against soft background in heavy ion collisions Illustration by G. Salam

14. 14 Clustering algorithms – k T algorithm

15. 15 k T algorithm Calculate –For every particle i: distance to beam –For every pair i,j : distance Find minimal d –If d iB, i is a jet –If d ij, combine i and j Repeat until only jets Various distance measures have been used, e.g. Jade, Durham, Cambridge/Aachen Current standard choice:

16. 16 k T algorithm demo

17. 17 k T algorithm properties Everything ends up in jets k T -jets irregular shape –Measure area with ‘ghost particles’ k T -algo starts with soft stuff –‘background’ clusters first, affects jet Infrared and collinear safe Naïve implementation slow (N 3 ). Not necessary  Fastjet Alternative: anti-k T Cambridge-Aachen:

18. 18 Cone algorithm Jets defined as cone Iterate until stable: ( ,  ) Cone = particles in cone Starting points for cones, seeds, e.g. highest p T particles Split-merge prescription for overlapping cones

19. 19 Cone algorithm demo

20. 20 Seedless cone Limiting cases occur when two particles are on the edge of the cone 1D: slide cone over particles and search for stable cone Key observation: content of cone only changes when the cone boundary touches a particle Extension to 2D ( ,  )

21. 21 IR safety is subtle, but important G. Salam, arXiv:0906.1833

22. 22 Split-merge procedure Overlapping cones unavoidable Solution: split-merge procedure Evaluate P t1, P t,shared –If P t,shared /P t1 > f merge jets –Else split jets (e.g. assign P t,shared to closest jet or split P t,shared according to P t1 /P t2 ) Jet1 Jet2 Merge: P t,shared large fraction of P t1 Jet1 Jet2 Split: P t,shared small fraction of P t1 f = 0.5 … 0.75

23. 23 Note on recombination schemes E T -weighted averaging: Simple Not boost-invariant for massive particles Most unambiguous scheme: E-scheme, add 4-vectors Boost-invariant Needs particle masses (e.g. assign pion mass) Generates massive jets

24. 24 Current best jet algorithms Only three good choices: –k T algorithm (sequential recombination, non-circular jets) –Anti-k T algoritm (sequential recombination, circular jets) –SISCone algorithm (Infrared Safe Cone) + some minor variations: Durham algo, different combination schemes These are all available in the FastJet package: http://www.lpthe.jussieu.fr/~salam/fastjet/ Really no excuse to use anything else (and potentially run into trouble)

25. 25 Speed matters At LHC, multiplicities are large A lot has been gained from improving implementations G. Salam, arXiv:0906.1833

26. 26 Jet algorithm examples Cacciari, Salam, Soyez, arXiv:0802.1189 simulated p+p event

27. 27 Jet reco p+p 200 GeV, p T rec ~ 21 GeV p+p: no or little background Cu+Cu: some background STAR PHENIX

28. 28 Jet finding in heavy ion events  η p t per grid cell [GeV] STAR preliminary ~ 21 GeV FastJet:Cacciari, Salam and Soyez; arXiv: 0802.1188 http://rhig.physics.yale.edu/~putschke/Ahijf/A_Heavy_Ion_Jet-Finder.html Jets clearly visible in heavy ion events at RHIC Use different algorithms to estimate systematic uncertainties: Cone-type algorithms simple cone, iterative cone, infrared safe SISCone Sequential recombination algorithms k T, Cambridge, inverse k T Combinatorial background Needs to be subtracted

29. 29 Jet finding with background By definition: all particles end up in a jet With background: all  -  space filled with jets Many of these jets are ‘background jets’

30. 30 Background estimate from jets M. Cacciari, arXiv:0706.2728 Single event: p T vs area  = p T /area Jet p T grows with area Jet energy density  ~ independent of  Background level

31. 31 Example of  p T distribution Response over ~5 orders of magnitude Response over range of ~40 GeV (sharply falling jet spectrum) SIngle particle ‘jet’ p T =20 GeV embedded in 8M real events Gaussian fit to LHS: LHS: good representation RHS: non-Gaussian tail Centroid non-zero(~ ±1 GeV)  contribution to jet energy scale uncertainty

32. 32 Unfolding background fluctuations unfolding Pythia Pythia smeared Pythia unfolded Simulation  P T distribution: ‘smearing’ of jet spectrum due to background fluctuations Large effect on yields Need to unfold Test unfolding with simulation – works

33. 33 RAA at LHC ALICE, H. Appelshauser, QM11

34. 34 RAA at LHC pronounced p T dependence of R AA at LHC  sensitivity to details of the energy loss distribution

35. 35 Jets at LHC LHC: jet energies up to ~200 GeV in Pb+Pb from 1 ‘short’ run Large energy asymmetry observed for central events

36. 36 Jet RCP at LHC Significant suppression of reconstructed jets in AA Out to large pT~250 GeV No indication of rise vs pT like single hadrons  Significant out-of-cone radiation ATLAS, B, Cole, QM11

37. 37 Jet fragmentation

38. 38 Di-jet (im)balance CMS, arXiv:1102.1957 Jet-energy asymmetry Large asymmetry seen for central events ATLAS, arXiv:1011.6182 (PRL), QM update

39. 39 Di-jet (im)balance CMS, arXiv:1102.1957

40. 40 Di-Jet fragmentation

41. 41 Summary

42. 42 Extra slides

43. 43 Four theory approaches Multiple-soft scattering (ASW-BDMPS) –Full interference (vacuum-medium + LPM) –Approximate scattering potential Opacity expansion (GLV/WHDG) –Interference terms order-by-order (first order default) –Dipole scattering potential 1/q 4 Higher Twist –Like GLV, but with fragmentation function evolution Hard Thermal Loop (AMY) –Most realistic medium –LPM interference fully treated –No finite-length effects (no L 2 dependence)

44. 44 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 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?

45. 45 Geometry Density profile Profile at  ~  form known Density along parton path Longitudinal expansion dilutes medium  Important effect Space-time evolution is taken into account in modeling

46. 46 Determining Bass et al, PRC79, 024901 ASW: HT: AMY: Large density: AMY: T ~ 400 MeV Transverse kick: qL ~ 10-20 GeV All formalisms can match R AA, but large differences in medium density At RHIC:  E large compared to E, differential measurements difficult After long discussions, it turns out that these differences are mostly due to uncontrolled approximations in the calculations  Best guess: the truth is somewhere in-between

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