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Jet Physics: Past, Present and Future

Jet Physics: Past, Present and Future. Or – What Have We Learned Recently? (Largely with Joey Huston and Matthias T ö nnesmann ). S. D. Ellis TeV-Scale Physics 7/18/02.

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Jet Physics: Past, Present and Future

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  1. Jet Physics: Past, Present and Future Or – What Have We Learned Recently? (Largely with Joey Huston and Matthias Tönnesmann) S. D. Ellis TeV-Scale Physics 7/18/02

  2. The Goal is 1% strong Interaction Physics (if Run I was ~ 10%) Want to precisely connect • What we can measure, e.g., E(y,) in the detector To • What we can calculate, e.g., arising from small numbers of partons as functions of E, y, Warning: We must all use the same algorithm!! S.D. Ellis: TeV-Scale Physics 7/18/02

  3. Why Jet Algorithms? • We “understand” what happens at the level of partons and leptons, i.e., LO theory is simple. • We want to map the observed (hadronic) final states onto a representation that mimics the kinematics of the energetic partons; ideally on a event-by-event basis. • But we know that the partons shower (perturbatively) and hadronize (nonperturbatively), i.e., spread out. S.D. Ellis: TeV-Scale Physics 7/18/02

  4. Thus we want to associate “nearby” hadrons or partons into JETS • Nearby in angle – Cone Algorithms • Nearby in momentum space – kT Algorithm • But mapping of hadrons to partons can never be 1 to 1, event-by-event! S.D. Ellis: TeV-Scale Physics 7/18/02

  5. Think of the algorithm as a “microscope” for seeing the (colorful) underlying structure - S.D. Ellis: TeV-Scale Physics 7/18/02

  6. Note – 2 logically distinct phases • Identify contents of jet – particles, calorimeter towers or partons – jet IDscheme • Combine kinematic properties of jet contents (e.g., 4-vectors) to find jet kinematic properties – recombination scheme • May not want to do both steps with the same parameters!? S.D. Ellis: TeV-Scale Physics 7/18/02

  7. History – Starting in Snowmass Start over 10 years ago with the “Snowmass Accord” (or the Snowmass Cone Algorithm). Idea was to have an agreed upon algorithm (hence accord) that everyone would use. But, in practice, it was flawed Was not efficient – experimenters used seeds to limit where one looked for jets – this introduces IR sensitivity at NNLO Did not treat issue of overlapping cones – split/merge question S.D. Ellis: TeV-Scale Physics 7/18/02

  8. Snowmass Cone Algorithm • Cone Algorithm – particles, calorimeter towers, partons in cone of size R, defined in angular space, e.g., Snowmass (,) • CONE center - (C,C) • CONE i  C iff • Energy • Centroid S.D. Ellis: TeV-Scale Physics 7/18/02

  9. “Flow vector” • Jet is defined by “stable” cone: • Stable cones found by iteration: start with cone anywhere (and, in principle, everywhere), calculate the centroid of this cone, put new cone at centroid, iterate until cone stops “flowing”, i.e., stable  Proto-jets (prior to split/merge)  unique, discrete jets event-by-event (at least in principle) S.D. Ellis: TeV-Scale Physics 7/18/02

  10. Consider the Snowmass “Potential” • In terms of 2-D vector ordefine a potential • Extrema are the positions of the stable cones; gradient is “force” that pushes trial cone to the stable cone, i.e., the flow vector S.D. Ellis: TeV-Scale Physics 7/18/02

  11. For example, consider 2 partons: yields potential with 3 minima – trial cones will migrate to minimum S.D. Ellis: TeV-Scale Physics 7/18/02

  12. But • Theoretically can look “everywhere” and find all stable cones • Experimentally reduce size of analysis by putting initial cones only at seeds – energetic towers or clusters of towers – thus introducing undesirable IR sensitivity and missing certain possible 2-jets-in-1 configurations • May NOT find 3rd(middle) cone S.D. Ellis: TeV-Scale Physics 7/18/02

  13. History of HIDDEN issues, all of which influence the result • Energy Cut on towers kept in analysis (e.g., to avoid noise) • (Pre)Clustering to find seeds • Energy Cut on precluster towers • Energy cut on clusters • Energy cut on seeds kept Starting with seeds find stable cones by iteration In JETCLU, “once in a seed cone, always in a cone”, the “ratchet” effect S.D. Ellis: TeV-Scale Physics 7/18/02

  14. Overlapping stable cones must be split/merged Depends on overlap parameter fmerge Order of operations matters All of these issues impact the content of the “found” jets • Shape may not be a cone • Number of towers can differ, i.e., different energy • Corrections for underlying event must be tower by tower S.D. Ellis: TeV-Scale Physics 7/18/02

  15. To address these issues, the Run II Study group Recommended Both experiments use • (legacy) Midpoint Algorithm – always look for stable cone at midpoint between found cones • Seedless Algorithm • kT Algorithms • Use identical versions except for issues required by physical differences – all of this in preclustering?? • Use (4-vector) E-scheme variables for jet ID and recombination S.D. Ellis: TeV-Scale Physics 7/18/02

  16. E-scheme (4-vector) • CONE i  C iff • 4-vector • ”Centroid” • Stable (Arithmetically more complex than Snowmass) S.D. Ellis: TeV-Scale Physics 7/18/02

  17. Actually used by CDF and D in run I for cone finding, and approximately equivalent to Snowmass. For jet ET used - • Snowmass (D) – • CDF - • E-Scheme (Run II study proposal) – The differences matters! (in a 1% game) S.D. Ellis: TeV-Scale Physics 7/18/02

  18. 5% Differences!! S.D. Ellis: TeV-Scale Physics 7/18/02

  19. Note that the PDFs are also still different on this scale S.D. Ellis: TeV-Scale Physics 7/18/02

  20. Streamlined Seedless Algorithm • Data in form of 4 vectors in(,) • Lay down grid of cells (~ calorimeter cells) and put trial cone at center of each cell • Calculate the centroid of each trial cone • If centroid is outside cell, remove that trial cone from analysis, otherwise iterate as before • Approximates looking everywhere; converges rapidly • Split/Merge as before S.D. Ellis: TeV-Scale Physics 7/18/02

  21. A NEW issue for Midpoint & Seedless Cone Algorithms • Compare jets found by JETCLU (with ratcheting) to those found by MidPoint and Seedless Algorithms • “Missed Energy” – when energy is smeared by showering/hadronization do not always find 2 partons in 1 cone solutions that are found in perturbation theory, underestimate ET– new kind of Splashout • See Ellis, Huston & Tönnesmann, hep-ph/0111434 S.D. Ellis: TeV-Scale Physics 7/18/02

  22. Lost Energy!? (ET/ET~1%, /~5%) S.D. Ellis: TeV-Scale Physics 7/18/02

  23. Missed Towers – How can that happen? S.D. Ellis: TeV-Scale Physics 7/18/02

  24. Consider a simple model with 2 partons, ET in ratio z and separated in angle by r Look at energy in cone of radius R  Energy Distribution S.D. Ellis: TeV-Scale Physics 7/18/02

  25. No seed NLO Perturbation Theory – r = parton separation, z = E2/E1Rsep simulates the cones missed due to no middle seed Naïve Snowmass With Rsep r r S.D. Ellis: TeV-Scale Physics 7/18/02

  26. Consider the corresponding “potential” with 3 minima, expect via MidPoint or Seedless to find middle stable cone S.D. Ellis: TeV-Scale Physics 7/18/02

  27. But in “real” life the parton’s energy is smeared by hadronization, etc. Simulate with gaussian smearing in angle of width s. Smooths the energy in the cone distribution, larger s, larger effect. First s = 0.1 - Smeared parton energy Energy in cone S.D. Ellis: TeV-Scale Physics 7/18/02

  28. Next s = 0.25 -larger effect, but the desired cones are still “obvious”!? Smeared parton energy Energy in cone S.D. Ellis: TeV-Scale Physics 7/18/02

  29. But it matters for the potential: as we increase wewash out middle minimum and lose middle cone S.D. Ellis: TeV-Scale Physics 7/18/02

  30. Then washout out second minima, find only 1 stable cone S.D. Ellis: TeV-Scale Physics 7/18/02

  31. “Fix” • Use R<R, e.g.,R/2, during stable cone discovery, less sensitivity to energy at periphery • Use R during jet construction  restores right cone, but not middle cone • Helps some with Midpoint algorithm • Does not help with Seedless (need even smaller R ?) still no stable middle cone S.D. Ellis: TeV-Scale Physics 7/18/02

  32. The Fixed potential (in red) S.D. Ellis: TeV-Scale Physics 7/18/02

  33. With Fix S.D. Ellis: TeV-Scale Physics 7/18/02

  34. Consider the number of events versus the jet ET difference for various R' values, distribution ~ symmetric for 1/2 reduction S.D. Ellis: TeV-Scale Physics 7/18/02

  35. Make a second pass to find jets in the “leftovers”, R2nd = R/2, most have previously found “ jet neighbors” Irreducible (JetClu)level at aboutR‘ ~ R/2= R0.25 S.D. Ellis: TeV-Scale Physics 7/18/02

  36. Racheting – Why did it work?Must consider seeds and subsequent migration history of trial cones – yields separate potential for each seed INDEPENDENT of smearing, first potential finds stable cone near 0, while second finds stable cone in middle (even when right cone is washed out)! ~ NLO Perturbation Theory!! S.D. Ellis: TeV-Scale Physics 7/18/02

  37. The “ratcheted” potential function looks like:Note the missing  functions, those terms can be positive far from the seed, hence the “cutoffs” S.D. Ellis: TeV-Scale Physics 7/18/02

  38. BUT .. Want to get rid of seeds, ratcheting and all that!Time for a new idea!! (?)Forget jets event-by-eventUse JEF – Jet Energy Flow • See Tkachov, et al. (circa 1995); Giele & Glover (1997); Sterman, et al. (2001), Berger, et al. hep-ph/0202207 (Snowmass 2001) S.D. Ellis: TeV-Scale Physics 7/18/02

  39. Each event produces a JEF distribution,not discrete jets • Each event = list of 4-vectors • Define 4-vector distribution where the unit vector is a function of a 2-dimensional angular variable • With a “smearing” functione.g., S.D. Ellis: TeV-Scale Physics 7/18/02

  40. We can define JEFs or Corresponding to The Cone jets are the same function evaluated at the discrete solutions of (stable cones) S.D. Ellis: TeV-Scale Physics 7/18/02

  41. Simulated calorimeter data & JEF S.D. Ellis: TeV-Scale Physics 7/18/02

  42. “Typical” CDF event in y, Found cone jets JEF distribution S.D. Ellis: TeV-Scale Physics 7/18/02

  43. Since JEF yields a “smooth” distribution for each event (compared to “non-analytic algorithms), we expect that • The JEF analysis is more amenable to resummation techniques and power corrections analysis in perturbative calculations. • The required multi-particle phase space integrations are largely unconstrained, i.e.,more analytic, and easier (and faster) to implement. • The analysis of the experimental data from an individual event should proceed more quickly (no need to identify jets event-by-event). • Signal to background optimization can now include the JEF parameters (and distributions). S.D. Ellis: TeV-Scale Physics 7/18/02

  44. The trick with JEF is defining observables, e.g. • The probability distribution (for a CDF type rapidity acceptance and CDF ET = E sin definition) is i.e., probabilities  area/R2 • The corresponding number of jets (JEFs) above ET,min, per event, is S.D. Ellis: TeV-Scale Physics 7/18/02

  45. Apply to the previous event and find, where the data points are the CDF found jets Jet ET Jet ET Jet ET S.D. Ellis: TeV-Scale Physics 7/18/02

  46. The JEF definition in NLO yields a cross section much like the usual cone algorithm: S.D. Ellis: TeV-Scale Physics 7/18/02

  47. The mass of a single JEF (jet) is • With probability density • And event occupancy probability S.D. Ellis: TeV-Scale Physics 7/18/02

  48. Applied to a W1 jet in (simulated events) From J.M. Butterworth S.D. Ellis: TeV-Scale Physics 7/18/02

  49. Summary • There are many challenges before we get to 1% precision QCD! The details now matter! • At the same time we have many possible solutions to study! Need to “optimize” Cone & kT algorithms Consider the ETMAX cone? Study the JEF idea • It is essential that we share the details during Run II! (which often did not happen in Run I) S.D. Ellis: TeV-Scale Physics 7/18/02

  50. ETMAX Cone Algorithm • Define a potential without factori.e., just find the maxima of the energy in a cone function (they didn’t get washed out by the smearing) • Make an ET,Jet ordered list of cones: start with largest ET and delete all overlapping cones; continue down the list in same way S.D. Ellis: TeV-Scale Physics 7/18/02

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