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Lecture III: jets

Lecture III: jets. Marco van Leeuwen, Utrecht University. Lectures for Helmholtz School Feb/March 2011. Generic expectations from energy loss. Longitudinal modification: out-of-cone  energy lost, suppression of yield, di-jet energy imbalance in-cone  softening of fragmentation

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Lecture III: jets

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  1. Lecture III: jets Marco van Leeuwen, Utrecht University Lectures for Helmholtz School Feb/March 2011

  2. 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?

  3. Medium modification of fragmentation MLLA calculation: good approximation for soft fragmentation extended with ad-hoc implementation medium modifications Borghini and Wiedemann, hep-ph/0506218 pThadron ~2 GeV for Ejet=100 GeV =ln(EJet/phadron) z 0.37 0.14 0.05 0.02 0.007 Note small x large z Suppression at high z, enhancement at low z

  4. Fragmentation functions Qualitatively: Fragmentation functions sensitive to P(DE) Distinguish GLV from BDMPS?

  5. Modified fragmentation functions Small-z enhancement from gluon fragments (only included in HT, not important for RAA) A. Majumder, MvL, arXiv:1002.2206 Differences between formalisms large, both magnitude of supresion and z-dependence Can we measure this directly? Jet reconstruction

  6. Jet shapes q-Pythia, Eur Phys J C 63, 679 Energy distribution in sub-jets Energy loss changes radial distribution of energy Several ‘new’ observables considered Discussion: sensitivity  viability … ongoing

  7. Fixing the parton energy with g-jet events  Input energy loss distribution T. Renk, PRC74, 034906 Away-side spectra in g-jet Eg = 15 GeV Nuclear modification factor Away-side spectra for g-jet are sensitive to P(DE) g-jet: know jet energy  sensitive to P(DE) RAA insensitive to P(DE)

  8. g-jet in Au+Au Use shower shape in EMCal to form p0 sample and g-rich sample Combinatorial subtraction to obtain direct-g sample

  9. Direct-g recoil suppression  8 < ET,g < 16 GeV STAR, arXiv:0912.1871 DAA(zT) IAA(zT) = Dpp(zT) Large suppression for away-side: factor 3-5 Reasonable agreement with model predictions NB: gamma pT = jet pT still not very large

  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. Di-jet kinematics Pout PTh2 PL,h PT,jet1 PTh1 PT,jet2 JT kT,xy Di-hadron correlations: naïvely assume PTh1~PTjet1: zT = pT,h2/pTh1 Pout ~ JT Not a good approximation! kT measures di-jet acoplanarity JT distribution measures transverse jet profile PL,h distribution measures longitudinal jet profile Use z=pL,h/Ejet or x = ln(Ejet/pL,h)  approx indep of Ejet

  28. Relating jets and single hadrons High-pT hadrons from jet fragmentation Qualitatively: • Inclusive hadrons are suppressed: • Suppression of jet yield (out-of-cone radiation) RAAjets < 1 • Modification of fragment distribution (in-cone radiation) softening of fragmentation function and/or broadening of jet structure

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

  30. 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

  31. 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’

  32. 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

  33. Background subtraction STAR Preliminary Background energy density (GeV) multiplicity Background density at RHIC:60-100 GeV Strong dependence on centrality Fluctuations remain after subtraction: RMS up to 10 GeV

  34. 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)

  35. 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

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

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

  38. Jet R dependence p+p G. Soyez, arXiv:1101.2665 R=0.2/R=0.4 ratio agrees with Pythia, Herwig Hadronisation effects important NLO QCD not enough

  39. Jet R dependence Au+Au STAR, M. Ploskon, QM09 RAA depends on jet radius: Small R jet is single hadron Jet broadening due to E-loss?

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

  41. Di-jet spectra Jet IAA Away-side jet yield suppressed  partons absorbed E. Bruna, STAR, QM09 STAR Preliminary ... due to large path length (trigger bias) STAR Preliminary 41

  42. Emerging picture from jet results • Jet RAA ~ 1 for sufficiently large R – unbiased parton selection • Away side jet fragmentation unmodified – away-side jet emerges without E-loss • Jet IAA ~ 0.2 – Many jets are absorded (large E-loss) Study vs R, E to quantify P(DE) and broadening

  43. Jet broadening II Qualitatively, two different possible scenarios Diffuse broadening Hard radiation/splitting Radiated energy ‘uniformly’ distributed Radiated energy directional • Different measurements: • R(0.2/0.4) • Transverse jet profile • May have different sensitivities Interesting idea: sub-jet structure; so far no studies available

  44. Jet-hadron correlations 1.0 < pT < 2.5 GeV 0.1 < pT < 1.0 GeV Jet anti-kT, R=0.4, pTcut = 2 GeV pTrec = 20 (10) GeV J. Putschke STAR, INT workshop pT > 2.5 GeV ‘Trigger’ jet: reconstruction bias (e.g. large charged fraction) Look at recoil jet Broadening at low pT Suppression-enhancement (high-low pT)

  45. Jet-hadron correlations Yield Width Redistribution of fragments in longitudinal momentum Soft radiation at larger angle NB: no correction for trigger bias (jet energy), jet energy resolution (background fluctuations)

  46. Extra slides

  47. Unfolding background fluctuations Formally: Definition of dpT Measured distribution Response due to background fluctuations Jet Signal AS: Signal jet area AB: Background jet area AC: some suitably large cutoff area Measured distribution In practice: Corrected Spectrum Regularizedinverse

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