Hsiangnan Li Oct 21 2012 1 Outlines Jet in experiment Jet in theory Jet substructures 2 Introduction Jets are abundantly produced at colliders Jets carry information of hard scattering and parent particles ID: 1044691
Download Presentation The PPT/PDF document "Lecture 3 PQCD for jet physics" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
1. Lecture 3PQCD for jet physicsHsiang-nan LiOct. 21, 20121
2. Outlines Jet in experimentJet in theoryJet substructures 2
3. IntroductionJets are abundantly produced at collidersJets carry information of hard scattering and parent particlesStudy of jets is crucialUsually use event generatorsHow much can be done in PQCDA lot!3
4. Dijet in e+e- annihiation Dijet production is part of total cross sectionBorn cross section is the same as total cross sectionenergy resolution for dijet productionhalf angle of jet coneconstrained phase space for real gluons4
5. NLO correctionsIsotropic soft gluons within energy resolutionCollinear gluons in cone with energy higher than resolution Virtual correctionsDijet cross section is infrared finite, but logarithmically enhancedoverlap of collinear and soft logs5
6. Jet phenomenologyjet as an observable (jet physics)not quarks and gluonsjet substructuresdouble-log enhancement6
7. Jet in experiment 7
8. Jets8
9. Coordinates for jetspseudorapidity9
10. Jet algorithmsComparison of theory with experiment is nontrivialNeed jet algorithmsAlgorithms should be well-defined so that they map experimental measurements with theoretical calculations as close as possibleInfrared safety is important guideline, because Sterman-Weinberg jet is infrared finite 10
11. Types of algorithmsTwo main classes of jet algorithmsCone algorithms: stamp out jets as with a cookie cutter Geometrical methodSequential algorithms: combine parton four-momenta one by one Depend on particle kinematics11
12. Seeded cone algorithmFind stable cones via iterative-cone procedureStart from seed particle i and consider set of particles j with separations smaller than jet coneIf the cone is stable, procedure stops. Otherwise the cone center J is taken as a new seed, and repeat the above procedureA stable cone is a set of particles i satisfying Examples: 12
13. Iterative step 1 13
14. Iterative step 2 14
15. Iterative step 3 15
16. Iterative step 4 16
17. Problem of seeded coneGeometrical algorithm does not differentiate infrared gluons from ordinary gluons Final results (split-merge) depend on soft radiation and collinear splittingVirtual (real) soft gluon contributes to two (single) jet cross section, no cancellation 17
18. Not infrared safeHow abut starting from the hardest particle?Collinear splitting change final resultsVirtual (real) gluon contributes to single (two) jet cross section, no cancellationSeeded cone algorithm is not infrared safe18
19. Sequential algorithmsTake kT algorithm as an example. For any pair of particles i and j, find the minimum ofIf it is diB or djB, i or j is a jet, removed from the list of particles. Otherwise, i and j mergedRepeat procedure until no particles are leftDifferentiate infrared and ordinary gluons 19
20. Step 120
21. Step 221
22. Step 322
23. Step 423
24. Step 5 24
25. start with softer particlesstart with harder particlespTA > pTB 25
26. 26
27. Infrared safetyIn seeded cone algorithmIn kt algorithm, remain two jets---infrared safety27
28. Jet in theory28
29. Factorization of DISMore sophisticated factorization is needed for jet production in DISCross section = H convoluted with PDF and Jet H is defined as contribution with collinear piece for initial state and collinear piece for final state being subtractedBasis for applying PQCD to jet physics29
30. Jet production in DISRestrict phase space of final-state quark and gluon in small angular separationJet production enhanced by collinear dynamics30
31. Wilson linkFeynman rules with are from Wilson linkRepresented by double linescollinear gluon detached and factorizedgo intojet function31
32. Quark Jet functionEikonalization leads to factorization Define jet axis, jet energy, jet invariant massWilson links are needed for gauge invariance of nonlocal matrix elementsLO jetAlmeida et al. 08projector32
33. Gluon jet function Similar definition for gluon jet function33
34. NLO diagramsquark jetgluon jet34
35. Underlying eventsEverything but hard scatteringInitial-state radiation, final-state radiation, multi-parton interaction 35
36. Power countingISR, FSR are leading power, and should be included in jet definitionMPI are sub-leading power: chance of involving more partons in scattering is low. They should be excludedfrom ISRfrom FSR36
37. Pile-up events should be excluded4 pile-upvertices37
38. NLO jet distributionDivergence of NLO quark jet distribution at small MJ38
39. Soft/collinear gluons vs jet massSmall jet mass large jet masspk1k2pk1k239
40. Double logarithmTotal NLO in Mellin space. Double log hints resummationAngular resolution is related to jet mass. When MJ is not zero, particles in a jet can not be completely collimated.Energy resolution is also related to jet mass. When MJ is not zero, the jet must have finite minimal energy Wilson line vector40
41. Resummation Recall low pT spectra of direct photon dominated by soft/collinear radiationsRequire kT resummationJet mass arises from soft/collinear radiations Can be described by resummation!Anti-kT algorithm is preferred in view point of resummationpT41
42. Jet substructures42
43. Boosted heavy particlesLarge Hadron Collider (LHC) provide a chance to search new physicsNew physics involve heavy particles decaying possibly through cascade to SM light particlesNew particles, if not too heavy, may be produced with sufficient boost -> a single jetHow to differentiate heavy-particle jets from ordinary QCD jets?Similar challenge of identifying energetic top quark at LHC43
44. Fat QCD jet fakes top jet at high pTThaler & Wang0806.0023Pythia 8.108Jet invariant mass44
45. Jet substructureMake use of jet internal structure in addition to standard event selection criteriaEnergy fraction in cone size of r,Quark jet is narrower than gluon jet Heavy quark jet energy profile should be different45
46. Jet substructures are finger prints of particlescrucial for particle identification46
47. Various approaches Monte Carlo: leading log radiation, hadronization, underlying eventsFixed order: finite number of collinear/soft radiationsResummation: all-order collinear/soft radiationsCalorimeter-level jets47
48. Why resummation?Monte Carlo may have ambiguities from tuning scales for coupling constantNLO is not reliable at small jet massPredictions from QCD resummation are necessaryTevatron data vs MC predictions N. Varelas 200948
49. Resummation equationUp to leading logs, resummation equation See Lecture 2Regarded as associating soft gluon in Kr in single-log kernel into jet function JThis is anti-kT algorithm!49
50. Predictions for jet mass distributionNLL inresummationNLO ininitial conditionCTEQ6L PDFsLi, Li, Yuan, 201150
51. Energy profilesIf can calculate jet mass in arbitrary jet cone size R, can certainly calculate jet energy in arbitrary jet coneIt is still attributed to soft/collinear radiationsResummation applies51
52. Jet energy functionsJet energy function for quarkJet energy function for gluoninsert step functions52
53. Resummation equationResummation equation for jet profile Have considered N=1 here, corresponding to integration over jet mass (insensitive to nonperturbative physics)Resum from phase space constraint for real gluons53
54. Soft gluon effectSoft real gluon in Kr renders jet axis of other particles inclined by small angleThis jet axis can not go outside of the subconeThis is how real gluons affect r dependence Jet axis of other particlesAxis of total jetInclination angler54
55. Quark jet or gluon jet?It is a quark jet!55
56. Opportunities at LHCIt is a gluon jet! Test new physics models from composition of observed jets, e.g., CDF “W+jj” anomaly56
57. Comparison with CDF dataquark, gluon jets, convoluted with LO hard scattering, PDFsNLO57
58. 58
59. Compasion with CMS data59
60. Higgs jetOne of major Higgs decay modes H -> bb with Higgs mass ~ 125 GeVImportant background g -> bbAnalyze substructure of Higgs jet improves its identificationFor instance, color pull made of soft gluonsGallicchio, Schwartz, 201060
61. Color pullHiggs is colorless, bb forms a color dipoleSoft gluons exchanged between themGluon has color, b forms color dipole with other particles, such as beam particles61
62. Summary Jet substructures can be studied in PQCDStart with Sterman-Weinberg definition, apply factorization and resummation, predict observables consistent with data Fixed-order calculation not reliable at small MJEvent generators have ambiguities Can improve jet identification and new particle search62