1. PIC 2001 Michael Strauss The University of Oklahoma Recent Results on Jet Physics and  s XXI Physics in Collision Conference Seoul, Korea June 28, 2001 Presented by Michael Strauss The University of Oklahoma

2. PIC 2001 Michael Strauss The University of Oklahoma Outline Introduction and Experimental Considerations Jet and Event Characteristics –Low E T Multijet Studies –Subjet Multiplicities Cross Sections –Three-to-Two Jet Ratio –Ratio at Different Center-of-Mass Energies –Inclusive Production –DiJet Production

3. PIC 2001 Michael Strauss The University of Oklahoma Motivation for Studying Jets Investigates pQCD –Compare with current predictions –pQCD is a background to new processes Investigates parton distribution functions (PDFs) –Initial state for all proton collisions Investigates physics beyond the Standard Model pdf ? Compositeness ? d 2  dE T d  ETET Central  region

4. PIC 2001 Michael Strauss The University of Oklahoma Developments in Jet Physics Inclusion of error estimates in the PDFs calculation of virtual corrections Progress toward NNLO predictions covariance matrices More rigorous treatment of experimental errors jet algorithms workshop More consistent E T calculations between experiments at the Tevatron (with proton initial states)

5. PIC 2001 Michael Strauss The University of Oklahoma R=  2 +  2 Cone Definition R=0.7 in  Merging and splitting of jets required if they share energy R sep required to compare theoretical predictions to data (R sep is the minimum separation of 2 partons to be considered distinct jets) Cone Definition of Jets Centroid found with 4-vector addition 2R 1.3R  = -ln[tan(  /2)]

6. PIC 2001 Michael Strauss The University of Oklahoma k T Definition of Jets k T Definition cells/clusters are combined if their relative k T 2 is “small” (D=1.0 or 0.5 is a scaling parameter) min(d ii, d ij ) = d ij  Merge min(d ii, d ij ) = d ii  Jet Infrared Safe Same definition for partons, Monte Carlo and data Allows subjet definitions

7. PIC 2001 Michael Strauss The University of Oklahoma k T and Cone Algorithm Use CTEQ4M and Herwig Match k T jets with cone jets 99.9% of Jets have  R<0.5 p T of k T algorithm is slightly higher DO Preliminary

8. PIC 2001 Michael Strauss The University of Oklahoma k T Algorithm and Subjets For subjets, define “large” k T (y cut = 10 -3 ) Increasing y cut

9. PIC 2001 Michael Strauss The University of Oklahoma Jet Selection Criteria Central Tracking EM Calorimeter Hadronic Calorimeter Inner Muon Magnet Outer Muon e  jet  noise Typical selections on EM fraction, hot cells, missing E T, vertex position, etc. > 97% efficient > 99% pure

10. PIC 2001 Michael Strauss The University of Oklahoma Jet Energy Corrections Response functions Noise and underlying event “Showering” Resolutions: Uncertainty on E T Estimated with dijet balancing or simulation d 2  dE T d  ETET d 2  dE T d  ETET no distinction between jets of different kinds Observed Cross Section Important for cross section measurement

11. PIC 2001 Michael Strauss The University of Oklahoma Jet and Event Quantities Low E T Multijet Studies Subjet Multiplicity

12. PIC 2001 Michael Strauss The University of Oklahoma D  Low E T Multijet events At high-E T, NLO QCD does quite well, but the number of jets at low-E T does not match as well. (Comparison with Pythia) Each jet’s E T >20 GeV. Theory normalized to 2-jet data >40 GeV. Looking also at Jetrad and Herwig E T of Leading Jet

13. PIC 2001 Michael Strauss The University of Oklahoma D  Low E T Multijet events Strong p T ordering in DGLAP shower evolution may suppress “spectator jets” in Pythia BFKL has diffusion in log(p T ) (DATA-THEORY)/THEORY

14. PIC 2001 Michael Strauss The University of Oklahoma D  Subjet Multiplicity Using K T Algorithm Perturbative and resummed calculations predict that gluon jets have higher subjet multiplicity than quark jets, on average. Linear Combination: = f g M g + (1-f g ) M Q Mean Jet Multiplicity Quark Jet Fraction Gluon Jet Fraction Monte Carlo DO Preliminary

15. PIC 2001 Michael Strauss The University of Oklahoma D  Subjet Multiplicity Using K T Algorithm Assume M g, M Q independent of √s Measure M at two √s energies and extract the g and Q components DO Preliminary

16. PIC 2001 Michael Strauss The University of Oklahoma D  Subjet Multiplicity Using K T Algorithm Raw Subjet MultiplicitiesExtracted Quark and Gluon Mutiplicities Higher M  more gluon jets at 1800 GeV DO Preliminary

17. PIC 2001 Michael Strauss The University of Oklahoma D  Subjet Multiplicity Using K T Algorithm Coming soon as a PRD HERWIG prediction =1.91±0.16(stat) Largest uncertainty comes from the gluon fractions in the PDFs

18. PIC 2001 Michael Strauss The University of Oklahoma ZEUS Subjet Multiplicity Comparison at hadron level Unfolded using Ariadne MC NLO QCD describes dataSensitive to  s

19. PIC 2001 Michael Strauss The University of Oklahoma  s from ZEUS Subjets  n sub -1    Proportional to  s Major Systematic Errors  Model dependence (2-3%)  Jet energy scale (1-2%) Major Theoretical Errors  Variation of renormalization scale

20. PIC 2001 Michael Strauss The University of Oklahoma Cross Sections Inclusive cross sections Rapidity dependence K T central inclusive R 32 630/1800 ratio of jet cross sections Di-Jets  s Conclusions

21. PIC 2001 Michael Strauss The University of Oklahoma Jet Cross Sections How well are pdf’s known? Are quarks composite particles? What are appropriate scales? What is the value of  s ? Is NLO (  s 3 ) sufficient?

22. PIC 2001 Michael Strauss The University of Oklahoma CTEQ Gluon Distribution Studies Momentum fraction carried by quarks is very well known from DIS data Fairly tight constraints on the gluon distribution except at high x Important for high E T jet production at the Tevatron and direct photon production

23. PIC 2001 Michael Strauss The University of Oklahoma Experimental Differential Cross Section Theoretical cross section Physics variables are  and x Detector measures E T and  Counting experiment with detector inefficiencies

24. PIC 2001 Michael Strauss The University of Oklahoma CDF Inclusive Jet Cross Section PRD 64, 032001 (2001) 0.1 < |  | < 0.7 Complete  2 calculation

25. PIC 2001 Michael Strauss The University of Oklahoma x-Q 2 Measured Parameter Space x Q 2 (GeV 2 ) From D  Inclusive Cross Section Measurement

26. PIC 2001 Michael Strauss The University of Oklahoma D  Inclusive Jet Cross Section Five rapidity regions Largest systematic uncertainty due to jet energy scale Curves are CTEQ4M PRL 86, 1707 (2001) E T (GeV)  d 2  dE T d  (fb/GeV)

27. PIC 2001 Michael Strauss The University of Oklahoma D  Inclusive Jet Cross Section CTEQ4HJ CTEQ4M MRSTg  MRST

28. PIC 2001 Michael Strauss The University of Oklahoma Gluon PDF Conclusions  2 determined from complete covariance matrix Best constraint on gluon PDF at high x Currently being incorporated in new global PDF fits

29. PIC 2001 Michael Strauss The University of Oklahoma Inclusive Cross Section Using K T Algorithm Predictions IR and UV safe Merging behavior well-defined for both experiment and theory -0.5 <  < 0.5 D = 1.0 D  Preliminary

30. PIC 2001 Michael Strauss The University of Oklahoma Comparison with Theory Normalization differs by 20% or more No statistically significant deviations of predictions from data When first 4 data points ignored, probabilities are 60-80% Strauss The University of Oklahoma D  Preliminary PDF  /dof Prob MRST1.12 31 MRSTg  1.3810 MRSTg  1.1725 CTEQ3M1.56 4 CTEQ4M1.3015 CTEQ4HJ1.1329

31. PIC 2001 Michael Strauss The University of Oklahoma Further k T Developments (since PIC 2001) Parton Hadronization Detected Particles Correction for hadronization explains low E T behavior Single parton Jet With hadronization correction PDF  /dof Prob MRST0.86 71 CTEQ4M1.0644

32. PIC 2001 Michael Strauss The University of Oklahoma CDF  s from Inclusive Cross Section Michael Strauss The University of Oklahoma  s 2 X (0) is LO prediction  s 3 X (0) k 1 is NLO prediction X (0) and k 1 determined from JETRAD MS scheme used Jet cone algorithm used with R sep = 1.3  s determined in 33 E T bins E T (GeV)

33. PIC 2001 Michael Strauss The University of Oklahoma CDF  s from Inclusive Cross Section Michael Strauss The University of Oklahoma Experimental systematic uncertainty Largest at low E T is underlying event Largest at high E T is fragmentation and pion response

34. PIC 2001 Michael Strauss The University of Oklahoma CDF  s from Inclusive Cross Section  scale is the major source of theoretical uncertainty E T /2 <  < 2E T PDF affects  s CTEQ4M minimizes  2 Theoretical uncertainties each ~ 5%

35. PIC 2001 Michael Strauss The University of Oklahoma ZEUS Inclusive Jet Production

36. PIC 2001 Michael Strauss The University of Oklahoma ZEUS Inclusive Jet Production Measured cross section slightly above NLP pQCD in forward section

37. PIC 2001 Michael Strauss The University of Oklahoma Full phase-space High-Q 2 region (Q 2 >500 GeV 2 ) High-E T region (>14 GeV) ZEUS Inclusive Jet Production  s Results: Uses various fits of d  /dQ 2 and d  /dE T

38. PIC 2001 Michael Strauss The University of Oklahoma R 32 : Motivation and Method Study the rate of soft jet emission (20-40 GeV) –QCD multijet production - background to interesting processes –Predict rates at future colliders Improve understanding of the limitations of pQCD –Identify renormalization sensitivity –Does the introduction of additional scales improve agreement with data ? Measure the Ratio with H T for all jets with –E T > 20, 30, 40 GeV for  20 GeV for  <2

39. PIC 2001 Michael Strauss The University of Oklahoma Inclusive R 32 Features: Rapid rise H T <200GeV Levels off at high H T Interesting: 70% of high E T jet events have a third jet above 20 GeV 50% have a third jet above 40 GeV

40. PIC 2001 Michael Strauss The University of Oklahoma R 32 Sensitivity to Renormalization Scale E T >20 GeV,  <2 show greatest sensitivity to scale

41. PIC 2001 Michael Strauss The University of Oklahoma R 32 Results Jet emission best modeled using the same scale i.e. the hard scale for all jets Best scale is that which minimizes  2 for all criteria  R =0.6E T max, for 20 GeV thresholds  R = H T, .3 for all criteria Introduction of additional scales unnecessary. E T >20 GeV,  <2 PRL 86, 1955 (2001)

42. PIC 2001 Michael Strauss The University of Oklahoma Ratio of the scale invariant cross sections : at different cm energies ( 630 and 1800 GeV) Ratio allows substantial reduction in uncertainties (in theory and experiment). May reveal: – Scaling behavior – Terms beyond LO (  s 2 ) xTxT  1 2 0.40.0 QCD Naive Parton model ss  ETET XTXT  s = (E T 3 /2  ) (d 2  /dE T d  vs X T  E T / (  s / 2 ) D  Cross Section Ratio:  (630)/  (1800) vs x T

43. PIC 2001 Michael Strauss The University of Oklahoma D  Inclusive Cross Section  s = 1800 GeV  s = 630 GeV

44. PIC 2001 Michael Strauss The University of Oklahoma Cross Section Ratio  (630)/  (1800) is 10-15% below NLO QCD predictions Top plot: varying choice of pdf has little effect Bottom plot: varying  R scale is more significant Better agreement where  R different at 630 and 1800 (unattractive alternative !) Higher order terms will provide more predictive power! Published in PRL 86, 2523 (2001)

45. PIC 2001 Michael Strauss The University of Oklahoma CDF DiJet Cone of R=0.7 Both Jets: E T >10 GeV Jet 1: 0.1<|  |<0.7 Jet 2: Four  regions 0.1<|  |<0.7 0.7<|  |<1.4 1.4<|  |<2.1 2.1<|  |<3.0 Provides precise information about initial state partons

46. PIC 2001 Michael Strauss The University of Oklahoma CDF DiJet Cross Section PDF  2 /dof MRST 2.68 MRST  3.63 MRST  4.49 CTEQ4M 2.88 CTEQ4HJ 2.43 All < 1% Probability

47. PIC 2001 Michael Strauss The University of Oklahoma ZEUS DiJet k T algorithm used E T > 8 GeV (leading) E T > 5 GeV (other) -1<  <2 (leading) 470<Q 2 <20000 GeV 2 Phys Lett B507, 70 (2001)

48. PIC 2001 Michael Strauss The University of Oklahoma ZEUS DiJet R 2+1 parameterized as: R 2+1 (M Z ) = A 1  s (M Z ) + A 1  s 2 (M Z )

49. PIC 2001 Michael Strauss The University of Oklahoma ZEUS  s Summary Dijets has lowest total error of all Zeus measurements. All measurements consistent with PDG value of 0.1185±20

50. PIC 2001 Michael Strauss The University of Oklahoma Tevatron Run II Run II: E cm = 1.96 TeV,  L  2fb -1 expect: ~100 events E T > 490 GeV and ~1K events E T > 400 GeV Run I: E cm = 1.8 TeV,  L  0.1fb -1 yielded 16 Events E T > 410 GeV Great reach at high x and Q 2, A great place to look for new physics!

51. PIC 2001 Michael Strauss The University of Oklahoma Conclusions from Jet Physics Growing sophistication in jet physics analysis  Error matrices  New jet algorithms  Better corrections  PDF refinements Results generally agree with NLO QCD and PDF’s  Cross section measurements will continue to refine PDF’s   s measurements agree with PDG  Low E T physics still require theoretical refinements Jet physics should continue to provide fruitful developments  High E T region can reveal compositeness and other new physics  Low E T region reveals soft parton distributions in proton  NNLO and other theoretical refinements needed  Results needed for “discovery” measurements