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Production and Evolution of High Energy Jets Outline (both lectures) A look at the data

Day 1. Day 2. Production and Evolution of High Energy Jets Outline (both lectures) A look at the data Theoretical framework Inclusive Jet Cross sections Multijet Events Double Parton Scattering Underlying Event Clustering algorithms Structure inside jets

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Production and Evolution of High Energy Jets Outline (both lectures) A look at the data

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  1. Day 1 Day 2 Production and Evolution of High Energy Jets Outline (both lectures) A look at the data Theoretical framework Inclusive Jet Cross sections Multijet Events Double Parton Scattering Underlying Event Clustering algorithms Structure inside jets Overall Theme: Interplay of Theory and Measurements Brenna Flaugher CTEQ Summer School 2002

  2. Simple view of a proton - antiproton collision jet y detector x  p p z • Pseudo-rapidity: • = - ln tan /2 Simple translation (additive) under longitudinal boosts jet • 2→2 scattering: • Two partons are produced from the collision of a • parton in each of the incoming hadrons • Initial partons have a fraction, x, of proton (antiprotion) • longitudinal momentum and small ~0 transverse momentum. • Each outgoing parton forms one jet • Events are characterized by x and Q2, where Q is the total momentum transfer ~ ETjet Brenna Flaugher CTEQ Summer School 2002

  3. Jets at Fermilab Hadron Collider • Fermilab Tevatron collides protons and antiprotons at √s = 1.96 GeV (was 1.8 TeV in Run 1) • These collisions produce the highest energy jets (ET~500 GeV) • Probes proton structure to smallest distance scales  = hc/Mc2 = 197MeVfm/500 GeV = 4x10-17cm p Hadronic Electromagnetic Jet ET =Sum of towers = 415 GeV p Brenna Flaugher CTEQ Summer School 2002

  4. Regions Covered by Different Measurements • Tevatron data overlaps and extends reach of DIS (talks by Jose Repond) • This talk concentrates on jet production at the Tevatron. Brenna Flaugher CTEQ Summer School 2002

  5. What is a Jet? • Jets are the clusters of particles produced by the scattered partons • Particles (mostly hadrons) are produced nearly collinear to parent parton • Underlying Event: Remnants of incoming hadrons leave some low energy particles too. These are randomly distributed, not in clusters • Fundamental concept: Sum up all the daughter particles and you approximate the properties of the scattered parton Brenna Flaugher CTEQ Summer School 2002

  6. End view of the two-jet event in CDF Azimuthal angle  Tracks in magnetic field Can measure momentum of charged particles in tracking chambers. Neutral particles e.g (π0) are measured only by the calorimeters Brenna Flaugher CTEQ Summer School 2002

  7. More complicated events: three-jet event ET = 328 GeV η = 0.21 φ = 2.5o ET = 123 GeV η = 0.23 φ = 170.4o ET = 173 GeV η = -0.57 φ = 192.4o Brenna Flaugher CTEQ Summer School 2002

  8. A five-jet event Brenna Flaugher CTEQ Summer School 2002

  9. 6 - jet events Brenna Flaugher CTEQ Summer School 2002

  10. From Partons to Jets Leading Log Approximation (LLA): sum leading contributions to all orders (from ~collinear radiation of quarks and gluons around original parton) Leading Order Theory Uses 2→2 matrix elements Parton Shower Only two jets in final state Only one parton/jet Brenna Flaugher CTEQ Summer School 2002

  11. From Partons to Jets Cont. • Hadronization: Each parton in the “shower” is converted into colorless hadrons • The hadrons are measured in the tracking chambers and calorimeters • Sum of the momentum and energy of all the particles in a “cluster” → “particle level jet” ≈ scattered parton Clustering (or Jet) algorithms : Rules for combining measured energy into Jets Brenna Flaugher CTEQ Summer School 2002

  12. Comparisons between Data and Theory • Overall rate of jet production ( cross sections) • Valid over full ET range (Jet ET 20 GeV – 500 GeV)? • Match data for different √s ? • Look for something new and unexpected which increases the rate of jet production over the predicted rates • rate of multi( 3, 4, 5...) jet events, can QCD predict these higher order processes? • Details of event structure • Jet shapes • Structure inside jets • Multiple parton interactions • Use Monte Carlo programs (e.g. ISAJET) to generate hadrons from LO predictions, and a detector simulation to derive corrections to data • Compare corrected data to pQCD parton level predictions • Theory: no dependence on empirical parton shower or hadronization models • Data: can minimize and quantify dependence of corrections on modeling Brenna Flaugher CTEQ Summer School 2002

  13. Theoretical predictions at the parton level : fa/A(xa ,F): Parton Momentum Distributions (PDF) – probability to find parton of type a in hadron A with momentum fraction xa F: 4-momentum transfer or “factorization scale” of interation • :partonic level cross section  Brenna Flaugher CTEQ Summer School 2002

  14. Rapidity and Pseudo-rapidity y scattered parton x  z antiproton proton Rapidity (y): bcosq = tanh y where b = p/E Pseudorapidity (): high energy limit (m«pT, β → 1) Rapidity and Pseudo-rapidity are simply additive under longitudinal boosts Brenna Flaugher CTEQ Summer School 2002

  15. Parton momentum fractions x1 and x2 can not exceed unity η = -ln tan θ/2 x1 = (eη1 + eη2) ET/√s x2 = (e-η1 + e-η2) ET/√s xT = 2ET/s and xT2 <x1x2<1 As xT → 1, x1 and x2 are tightly constrained boost = ½ (1 +2) *= ½ (1 -2) Lab = *+boost 1 1 CM Lab θ* 2 2 Brenna Flaugher CTEQ Summer School 2002

  16. Kinematic Variables • Transverse Energy ET: • ET= m2 + px2 + py2 = Esinθ • = E2- pz2 • Energy E: E2 = m2 + p2 = ET cosh η • Momentum p: • p2 = px2 + py2 + pz2 • Longitudinal momentum • pz = E tanh η • = ET sinh η • Transverse Momentum pT • pT= px2 + py2 = psinθ • Invariant Mass for di-jet event: • M122 = (p1 + p2)2 • =m12 +m22 + 2(E1E2-p1·p2) • For m1, m2 0 • M122 → 2ET1ET2(coshΔη – cosΔφ) Brenna Flaugher CTEQ Summer School 2002

  17. Phase Space Boundaries for 2 2 Scattering s = 2 TeV and Jet ET = 100,200 and 400 GeV 2 • phase space shrinks • as ET increases • for1 ~ -2 , boost → 0 • for1 ~ 2 , M122~ 4ET2 1 Brenna Flaugher CTEQ Summer School 2002

  18. Leading Order Two-Jet Cross Section At leading order ET1 =ET2 =ET • where, • fi(x,F) (i = g, q, q) is the PDF • |Mij|is lowest order matrix element for ij2 partons • summed and averaged over initial and final states • s(R) is the strong coupling constant • F is the factorization scale • R is the renormalization scale Usually assume F= R =  ~ ET/2 Many processes contribute: Brenna Flaugher CTEQ Summer School 2002

  19. Lowest order matrix elements Matrix elements for Averaged (summed) over initial (final) state colors and spins: where s = (p1 + p2)2, t = (p1 - p3)2 and u = ( p2-p3)2 are the Mandelstam variables Brenna Flaugher CTEQ Summer School 2002

  20. Quark and Gluon contributions to cross section xT = 2ET/s Solid: s = 2 TeV Dashed: s = 14 TeV • Lowest ET jets from • Tevatron are ~20 GeV • or xT ~ 0.02 • gluon initial states dominate • Highest ET jets are • ~500 GeV or xT~ 0.5 • qq dominates, • but qg still ~20% of total Fraction of total Brenna Flaugher CTEQ Summer School 2002

  21. The single effective subprocess approximation • All the matrix elements have similar shape • Can approximate the parton momentum distributions fi(x,F) (i = g, q, q) as a single effective subprocess: And the lowest order cross section can be written as: Brenna Flaugher CTEQ Summer School 2002

  22. Parton Luminosity • In the single effective subprocess approximation the parton-parton luminosity (x1F(x1,µ)x2F(x2,µ) ) can be written as a function of boost and * • For ET =100 GeV and √s = 2TeV • largest luminosity is when x1 and • x2 are equally small boost ~ * =0 • As |boost| or |*| increases • luminosity decreases rapidly x1F(x1,µ)x2F(x2,µ) boost Brenna Flaugher CTEQ Summer School 2002

  23. Digression on the scales F and R • F and Rare artifacts of working at fixed order in perturbation theory. • The predictions should not depend on the choice of scales (Data doesn’t!) • The renormalization scale Rshows up in the strong coupling constant because itis introduced when the bare fields are redefined in terms of the physical fields • The factorization scale Fis introduced when absorbing the divergence from collinear radiation into the PDFs • Can choose any value for F and R • Typical choice F = R~ ET/2 of the jets • Dependence of predictions on scale indicates potential size of higher order contributions • Dependence on scale should get smaller as higher order terms are included • Usually study predictions with range  = ET/4 to 2ET Brenna Flaugher CTEQ Summer School 2002

  24. Digression on the scales F and R cont. αs2 for differentR compared toR= ET for different F compared to F = ET at η1 = η2 =0 Ratio Dependence of LO on choice of scales flat at ~ 10% level for =ET/2 but normalization uncertain at ~±50% level Brenna Flaugher CTEQ Summer School 2002

  25. Inclusive Jet Cross Section Measurements • Fundamental and “simple” test of QCD predictions • Include all jets in the event within a given η range • Can search for signs of composite quarks Brenna Flaugher CTEQ Summer School 2002

  26. Inclusive Jet Cross Section and Compositeness • Compositeness Scale: c • c =  pointlike quarks • c = finite → substructure • at mass scale of c • Hypothesis: Quarks are bound states of preons which interact via new strong interaction The composite interactions are represented by a contact term: • Compositeness: • enhances the jet • cross section • has different ang. • dist. from QCD Brenna Flaugher CTEQ Summer School 2002

  27. Measurements of Inclusive Jet Cross Section • In the 80’s, only Leading Order 2→2 predictions were available • High energy Jet data was just becoming available • AFS √s = 63 GeV – initial hints of 2-jet structures • UA1 and UA2: √s = 546 and 630 GeV , (ET ~20-150 GeV) • CDF 1987 √s = 1800 (ET ~30-250 GeV) • Obviously in the data there were events with more than 2 jets! • Try to make data and theory look more alike: • Parton shower Monte Carlo program ISAJET – FF fragmentation, LLA • Tune parameters of parton shower and hadronization to give agreement with data – minimizes dependence of corrections on details of the model. • Defined clustering algorithms which could make data look like 2→2 process • Summed energy in a large cones R = 1 – 1.2 (cone algorithm) • Summed neighboring towers (nearest-neighbor algorithm) Brenna Flaugher CTEQ Summer School 2002

  28. Uncertainties • LO Theory: • PDFs – derived from global fits to data (See talk by Walter Giele) • Choice of scale for evaluation of αs and PDFs • higher order corrections • Total uncertainty ranged from a factor of 2 to a factor of 10 depending on ET • Experimental: Measurement uncertainties • energy scale (could be a whole talk by itself) • luminosity • corrections to go from measured jets to partons (e.g. energy that escaped the cone or jet cluster) • underlying event (extra energy that leaked into cluster) Brenna Flaugher CTEQ Summer School 2002

  29. Inclusive Jet Cross Sections from the 80’s UA1 Unc. ~ 70% ± 50% jet corr. ± 40% jet calib ± 10% aging ± 15% lum Λc >400 GeV UA2 Unc. ~32% ± 25% Frag. model ± 15% jet id ± 11% calib ± 5% lum Λc >825 GeV Theory uncertainties mainly on normalization – compositeness limits set based on shape at high ET • CDF 1987 data • Exp. Unc. • 70% @ 30 GeV • 34% @ 250 GeV • Λc >700 GeV While data and theory agreed qualitativly, large uncertainties existed in both theoretical predictions and in experimental measurements Brenna Flaugher CTEQ Summer School 2002

  30. NLO 2→2 Theory predictions Late 80’s NLO parton level predictions became available Aversa et al PLB 210,225 (1988), S.Ellis, Kuntz, Soper, PRL 62,2188(1989) ( EKS) 1 loop, 2 parton final state same kinematics as LO 1 parton = jet tree level, 3 parton final state or 2+1 parton final state Now have possibility of combining partons to form a jet. Predictions sensitive to size of jet and way in which partons are combined Brenna Flaugher CTEQ Summer School 2002

  31. NLO 2→2 Theory predictions • Dependence on the choice of scale reduced from factor of 2 to ±~ 30%, more precise comparison to data possible • Ushered in a new era of Jet identification • Could use the same algorithm to cluster partons into jets as is used to cluster towers of energy in the detector • Should minimize difference between data and theory predictions due to technical differences • Led to SNOWMASS accord • cone algorithm to be used by CDF, D0 and Theory • detailed rules for combining towers (partons) into jets • No out-of-cone energy correction! (part of NLO prediction) • still have to estimate and subtract UE energy • Other algorithms also exist – will be described later Brenna Flaugher CTEQ Summer School 2002

  32. SNOWMASS Algorithm • Choose a seed tower from a list of high ET towers (partons) • Define a cone of radius R around the seed tower Towers (partons) within the cone are associated with the jet. Calculate new cluster centroid: loop over towers again until stable set of towers is reached. Finally: Snowmass studies (1992) found that for a cone size of 0.7 out-of-cone energy ~ underlying event Brenna Flaugher CTEQ Summer School 2002

  33. Inclusive cross section compared to NLO • CDF collected data in 1989: • 4pb-1 √s = 1800 GeV • 8nb-1 √s = 546 GeV • Compared to NLO predictions – still uncertain due to scale and PDFs, but better than LO • Statistical uncertainty dominated above about 200 GeV ET • Set new limit on Λc>1.4 TeV • CDF also measured jet cross section for different cone sizes and looked at Jet shapes for 100 GeV Jets • Interplay between data and theory! Brenna Flaugher CTEQ Summer School 2002

  34. Jet cross section dep. on cone size • Jet cross section for • cone sizes 0.4, 0.7, 1.0. • PRL 68 1104 (1992)) • Jet ET = 100 GeV • Best agreement with very small scale ET/4 • Introduce ad-hoc parameter Rsep which scales radius for parton merging: ΔRparton = Rsep R effectively reduces parton cone size • Snowmass: Rsep = 2 µ = ET/2 solid µ= ET short dash µ=ET/4 long dash Rsep = 1.3 Theory: PRL 69, 3615 (1992) Brenna Flaugher CTEQ Summer School 2002

  35. Jet Shape Measurement Data:PRL 70, 713 (1993) Thy: PRL 69, 3615 (1992) Jet ET = 100 GeV Measure energy inside subcones around jet axis Rsep = 1.3 µ = ET/2 solid µ= ET short dash µ=ET/4 long dash ET/4 give worst agreement Rsep = 1.3 gives best agreement with data F(r) = ET(r)/ET(R) Brenna Flaugher CTEQ Summer School 2002

  36. Snowmass didn’t specify how to separate close jets (not an issue with partons) • CDF merged close jets if 75% of smaller jet energy overlapped • otherwise separated based on distance from centroids • At parton level jets are separated if ΔR>2Rcone ET = 123 GeV η = 0.23 φ = 170.4o ΔR = 0.88 ET = 173 GeV η = -0.57 φ = 192.4o Brenna Flaugher CTEQ Summer School 2002

  37. Separation between jets in CDF data • In data look at separation between leading 3 jets • Plot the minimum separation between the two closest clusters • 50% separated at 1.3 R • 100% separated at 1.6R Rsep of 1.3 makes sense! Explains better match between data and theory (divided by R) Brenna Flaugher CTEQ Summer School 2002

  38. Effect of Rsep on NLO 2→2 Inclusive Jet Cross Section Predictions • Cross section for Rsep =2 is larger than for Rsep = 1.3 by ~ flat 5% • Lessons: • Inc. cross section is not very sensitive to Rsep, but more detailed comparisons pointed out difference between analysis of data and theory • Details of clustering algorithms are important for precise comparisons between data an theory Brenna Flaugher CTEQ Summer School 2002

  39. More implications of NLO: Phase space • The Parton momentum fractions at NLO are: ET= 50 GeV √s = 1.8 TeV where ET1 > ET2>ET3 etc. • Since ET2 can now be < ET1, • |η2| can increase compared to LO • Adding more partons (e.g.NNLO) • further increases allowed range • Still have sharp cutoff on η1 • η2 can be bigger than η1 η2 η1 Brenna Flaugher CTEQ Summer School 2002

  40. Compare LO and NLO predictions K factor = NLO/LO ~10% for |η|<1.5, away from PS boundaries Large corrections for large | η2| →stay away from there, theory not reliable at LO or NLO η Brenna Flaugher CTEQ Summer School 2002

  41. Scale dependence LO where L = log(µR/ET) and bi are the beta functions NLO NNLO NNLO coefficient C is unknown. Curves show guesses C=0 (solid) C=±B2/A (dashed) Dependence on choice of scale is reduced as higher orders are included Usual range d/dET at ET = 100 GeV µR /ET Brenna Flaugher CTEQ Summer School 2002

  42. Another digression on the scale • Addition of NLO terms reduced dependence of prediction on scale when choice ranged from ET/4 to 2ET • But, since ET1 and ET2 are no longer required to be equal we now have to think about which ET should be used for the scale • µ  ET of each jet in the event • Many scales per event • Cross section is proportional to αs(ET)n, can extract αs from inc. xsec. • µ  ET1 = Maximum Jet ET in the event • one scale per event • can implement in event generator (JETRAD does this) • Can write the theory both ways: Two programs used by CDF and D0 • EKS – analytic NLO program uses µ  ET • JETRAD – event generator uses µ  ETMAX Brenna Flaugher CTEQ Summer School 2002

  43. Effect of Scale on NLO 2→2 Inclusive Jet Cross Section Predictions Brenna Flaugher CTEQ Summer School 2002

  44. CDF Run 1A Inclusive Cross Section (1996) • Excess observed above 200GeV • In 1996 all PDFs gave roughly same shape • Motivated discussions of new physics as well and PDF uncertainties Brenna Flaugher CTEQ Summer School 2002

  45. PDF uncertainties 2000 Ratio of inclusive jet cross section for different PDFs compared to CTEQ4M • Turns out PDFs are very flexible, even at high ET • ~30% changes in shape are OK • Pretty much squelched discussions of new physics • Ended ~15 year history of using Inc. cross section for compositeness search. • Need more constraints on PDFs!! Brenna Flaugher CTEQ Summer School 2002

  46. Alternate Variables: Mass and Angle • can write cross section in terms of dijet mass M12 and the center of mass scattering angle θ* : M122 = 4ET2cosh2η* cos θ* = tanh η* t = - (1-cos θ* )s/2 • Typically measure • dijet mass spectrum: d/dMJJ • by integrating over a fixed angular range • angular distibution : d/dcosθ* • for intervals of dijet mass Brenna Flaugher CTEQ Summer School 2002

  47. Angular Distribution – Not sensitive to PDFS • Dominant subprocesses have similar shape for angular distribution d/dcosθ* with different weights • Can use to test for compositeness with smaller theoretical uncertainties • Measure angular distribution directly • Measure dijet mass in different angular regions and • take ratios to cancel PDF uncertainties Brenna Flaugher CTEQ Summer School 2002

  48. Angular Distribution and quark substructure QCD is dominated by ~ 1/(1-cos θ*)2 Contact terms by ~ ~ 1/(1+cos θ*)2 Difference in forward η region is hard to measure Change to a better angular variable: d/dχ Much more sensitive to contact term large difference from QCD in central region Brenna Flaugher CTEQ Summer School 2002

  49. Limits on Quark Substructure D0 Run IB results Brenna Flaugher CTEQ Summer School 2002

  50. Limits on Quark Substructure Brenna Flaugher CTEQ Summer School 2002

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