Jet Quenching and Jet Finding

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

2. Fragmentation and parton showers mF MC event generators implement ‘parton showers’ Longitudinal and transverse dynamics High-energy parton (from hard scattering) Hadrons Q ~ mH ~ LQCD large Q2 Analytical calculations: Fragmentation Function D(z, m) z=ph/Ejet Only longitudinal dynamics

3. Jet Quenching High-energy parton (from hard scattering) Hadrons • How is does the medium modify parton fragmentation? • Energy-loss: reduced energy of leading hadron – enhancement of yield at low pT? • 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?

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

5. Testing volume (Ncoll) scaling in Au+Au Direct g spectra PHENIX, PRL 94, 232301 PHENIX Centrality Scaled by Ncoll Direct g in A+A scales with Ncoll A+A initial state is incoherent superposition of p+p for hard probes

6. p0 RAA – high-pT suppression : no interactions RAA = 1 Hadrons: energy loss RAA < 1 : RAA = 1 0: RAA≈ 0.2 Hard partons lose energy in the hot matter

7. Two extreme scenarios (or how P(DE) says it all) Scenario I P(DE) = d(DE0) Scenario II P(DE) = a d(0) + b d(E) 1/Nbin d2N/d2pT ‘Energy loss’ ‘Absorption’ p+p Downward shift Au+Au Shifts spectrum to left pT P(DE) encodes the full energy loss process RAA not sensitive to energy loss distribution, details of mechanism

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 (p0)

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 kT • in-cone  broadening of jet-profile Ejet kT~m l fragmentation after energy loss?

10. Jet reconstruction algorithms Two categories of jet algorithms: • Sequential recombination kT, anti-kT, Durham • Define distance measure, e.g. dij = min(pTi,pTj)*Rij • Cluster closest • Cone • Draw Cone radius R around starting point • Iterate until stable h,jjet = <h,j>particles 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 For a complete discussion, see: http://www.lpthe.jussieu.fr/~salam/teaching/PhD-courses.html

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. Collinear safety Illustration by G. Salam Note also: detector effects, such as splitting clusters in calorimeter (p0 decay)

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

14. Clustering algorithms – kT algorithm

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

16. kT algorithm demo

17. kT algorithm properties • Everything ends up in jets • kT-jets irregular shape • Measure area with ‘ghost particles’ • kT-algo starts with soft stuff • ‘background’ clusters first, affects jet • Infrared and collinear safe • Naïve implementation slow (N3). Not necessary  Fastjet Alternative: anti-kT Cambridge-Aachen:

18. Cone algorithm • Jets defined as cone • Iterate until stable:(h,j)Cone = <h,j>particles in cone • Starting points for cones, seeds, e.g. highest pT particles • Split-merge prescription for overlapping cones

19. Cone algorithm demo

20. Seedless 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 (h,j) Limiting cases occur when two particles are on the edge of the cone

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

22. Split-merge procedure • Overlapping cones unavoidable • Solution: split-merge procedureEvaluate Pt1, Pt,shared • If Pt,shared/Pt1> fmerge jets • Else split jets (e.g. assign Pt,shared to closest jet or split Pt,shared according to Pt1/Pt2) f = 0.5 … 0.75 Jet1 Jet1 Jet2 Jet2 Merge: Pt,shared large fraction of Pt1 Split: Pt,shared small fraction of Pt1

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

24. Current best jet algorithms • Only three good choices: • kT algorithm (sequential recombination, non-circular jets) • Anti-kT algoritm (sequential recombination, circular jets) • SISCone algorithm (Infrared Safe Cone) + some minor variations: Durham algo, differentcombination 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. Speed matters G. Salam, arXiv:0906.1833 At LHC, multiplicities are largeA lot has been gained from improving implementations

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

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

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

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

30. Background estimate from jets Single event: pT vs area r = pT/area Background level Jet pT grows with area Jet energy density r ~ independent of h M. Cacciari, arXiv:0706.2728

31. Example of dpT distribution SIngle particle ‘jet’ pT=20 GeV embedded in 8M real events Response over ~5 orders of magnitude • Gaussian fit to LHS: • LHS: good representation • RHS: non-Gaussian tail • Centroid non-zero(~ ±1 GeV) • contribution to jet energy scale uncertainty Response over range of ~40 GeV (sharply falling jet spectrum)

32. Unfolding background fluctuations Pythia Pythia smeared Pythia unfolded dPT distribution: ‘smearing’ of jet spectrum due to background fluctuations unfolding Large effect on yields Need to unfold Simulation Test unfolding with simulation – works

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

34. RAA at LHC • pronounced pT dependence • of RAA at LHC • sensitivity to details of the energy loss distribution

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

37. Jet fragmentation

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

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

40. Di-Jet fragmentation

41. Summary

42. Extra slides

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/q4 • 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 L2 dependence)

44. Energy loss spectrum Typical examples with fixed L <DE/E> = 0.2 R8 ~ RAA = 0.2 Brick L = 2 fm, DE/E = 0.2 E = 10 GeV Significant probability to lose no energy (P(0)) Broad distribution, large E-loss (several GeV, up to DE/E = 1) Theory expectation: mix of partial transmission+continuous energy loss – Can we see this in experiment?

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

46. Determining ASW: HT: AMY: Bass et al, PRC79, 024901 Large density: AMY: T ~ 400 MeV Transverse kick: qL ~ 10-20 GeV All formalisms can match RAA, but large differences in medium density 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 At RHIC: DE large compared to E, differential measurements difficult