1. Lecture IV: Jet finding techniques and results Marco van Leeuwen Utrecht University Jyväskylä Summer School 2008

2. 2 Parton energy from  -jet and jet reconstruction Qualitatively: `known’ from e + e - known pQCDxPDF extract Full deconvolution large uncertainties (+ not transparent) Fix/measure E jet to take one factor out Two approaches:  -jet -Jet reconstruction  Second-generation measurements at RHIC – first generation at LHC?

3. 3 Perturbative QCD processes Hadron production Heavy flavours Jet production –e + e - → jets –p(bar)+p → jets Direct photon production Measurement difficulty Theory difficulty

4. 4 Fixing the parton energy with  -jet events T. Renk, PRC74, 034906  -jet: know jet energy  sensitive to P(  E) R AA insensitive to P(  E) Nuclear modification factor Away-side spectra in  -jet E  = 15 GeV Away-side spectra for  -jet are sensitive to P(  E)  Input energy loss distribution

5. 5  -jet in Au+Au Use shower shape in EMCal to form  0 sample and  -rich sample Combinatorial subtraction to obtain direct-  sample

6. 6 STAR Preliminary I AA (z T ) = D AA (z T ) D pp (z T ) Direct-  recoil suppression Large suppression for away-side: factor 3-5 Results agree with model predictions Uncertainties still sizable Some improvements expected for final results Future improvements with increased RHIC luminosity J. Frantz, Hard Probes 2008 A. Hamed, Hard Probes 2008  8 < E T,  < 16 GeV E T,  2 < p T assoc < 10 GeV

7. 7 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

8. 8 Collinear and infrared safety Illustration by G. Salam Jets should not be sensitive to soft effects (hadronisation and E-loss) -Collinear safe -Infrared safe

9. 9 Collinear safety Note also: detector effects, such as splitting clusters in calorimeter (  0 decay) Illustration by G. Salam

10. 10 Infrared safety Infrared safety also implies robustness against soft background in heavy ion collisions Illustration by G. Salam

11. 11 Clustering algorithms – k T algorithm

12. 12 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:

13. 13 k T algorithm demo

14. 14 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

15. 15 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

16. 16 Cone algorithm demo

17. 17 IR safety is subtle, but important G. Salam, arXiv:0906.1833

18. 18 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 ( ,  )

19. 19 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 tshared large fraction of P t1 Jet1 Jet2 Split: P tshared small fraction of P t1 f = 0.5 … 0.75

20. 20 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

21. 21 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)

22. 22 Speed matters At LHC, multiplicities are large A lot has been gained from improving implementations G. Salam, arXiv:0906.1833

23. 23 Relating jets and single hadrons High-p T hadrons from jet fragmentation Qualitatively: Single hadrons are suppressed: -Suppression of jet yield (out-of-cone radiation) R AA jets < 1 -Modification of fragment distribution (in-cone radiation) softening of fragmentation function and/or broadening of jet structure

24. 24 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

25. 25 p+pAu+Au central STAR Preliminary Jet spectra STAR Preliminary Note kinematic reach out to 50 GeV Jet energy depends on R, affects spectra k T, anti-k T give similar results Take ratios to compare p+p, Au+Au

26. 26 Jet R AA at RHIC Jet R AA >> 0.2 (hadron R AA ) Jet finding recovers most of the energy loss  measure of initial parton energy M. Ploskon, STAR, QM09 Some dependence on jet-algorithm? Under study…

27. 27 Radius dependence R AA depends on jet radius: Small R jet is single hadron M. Ploskon, STAR, QM09 Jet broadening due to E-loss?

28. 28 Fragmentation functions STAR Preliminary p t,rec (AuAu)>25 GeV 20<p t,rec (AuAu)<25 GeV Use recoil jet to avoid biases Suppression of fragmentation also small (>> 0.2) E. Bruna, STAR, QM09

29. 29 Di-jet spectra 29 Elena Bruna for the STAR Collaboration - QM09 STAR Preliminary E. Bruna, STAR, QM09 Jet I AA Away-side jet yield suppressed  partons absorbed... due to large path lentgh (trigger bias)

30. 30 Emerging picture from jet results Jet R AA ~ 1 for sufficiently large R – unbiased parton selection Away side jet fragmentation ummodified – away-side jet emerges without E-loss Jet I AA ~ 0.2 – Many jets are absorded (large E-loss) Study vs R, E to quantify P(  E) and broadening

31. 31 Modeling in-medium fragmentation From C. Salgado

32. 32 Sudakov prescription From C. Salgado

33. 33 Sudakov prescription From C. Salgado

34. 34 Sudakov MC implementation Used by most MC event generators (PYTHIA, HERWIG) From C. Salgado

35. 35 Full MC event From C. Salgado

36. 36 MC results Q-PYTHIA N. Armesto et al, arXiv:0907.1014 Softening of fragmentation (p T -spectra) Broadening Caveat: all plot are parton-level. Effect of hadronisation may be large

37. 37 Summary Jet-finding,  -jet to fix parton energy  Sensitivity to P(  E), jet broadening  -hadron results agree with prediction Need more statistics for P(  E) Jet-algorithm requirements: Infrared and Collinear safe Jet results from RHIC: –Can recover full parton energy (R=0.4) –Indicate large broadening –Away-side jet I AA ~ 0.2, jet absorption? Full event MC genartors are being developed  important reference/benchmark for jet-analyses

38. 38 Extra slides

39. 39 Direct-  recoil yields A. Hamed, Hard Probes 2008 Run 4 p+p/Au+Au @ 200 GeV M. Nguyen, Quark Matter 2006 Direct-  –jet measurements being pursued by STAR and PHENIX Requires large data samples Suppression of away-side yield visible Similar to di-hadrons, but now with selected parton energy 