1. Jet Physics at the Tevatron Sally Seidel University of New Mexico XXXVII Rencontres de Moriond For the CDF and D0 Collaborations

2. An overview of selected jet studies by CDF and D0 in 2001-2. 1. Jets at CDF and D0 2. Inclusive Jet Production (CDF) 3. Inclusive Jet  and E T Dependence (D0) 4.  s from Inclusive Jet Production (CDF) 5. Inclusive Jet Cross Section using the k T Algorithm (D0) 6. Ratios of Multijet Cross Sections (D0) 7. Subjet Multiplicity of g and q Jets using the k T Algorithm (D0) 8. Charged Jet Evolution and the Underlying Event (CDF)

3. Jet distributions at colliders can: signal new particles + interactions test QCD predictions improve parton distribution functions

4. CDF (D0) data quality and reconstruction requirements: |z vertex | < 60 (50) cm to maintain projective geometry of calorimeter towers. 0.1 (0.0)  |  detector |  0.7 (0.5) for full containment of energy in central barrel. To reject cosmic rays + misvertexed events, define = missing E T. Require (CDF) < (30 GeV or 0.3E T leading jet, whichever is larger). (D0) Reconstruct jets using a cone algorithm with cone radius Apply EM/HA + jet shape cuts to reject noise fakes.

5. Next correct for Pre-scaling of triggers. Detection efficiencies (typically 94 –100%). underlying event + multiple interactions. “smearing” of the data: the effects of detector response and resolution. If > 1 primary vertex: choose vertex with 2 highest E T jets. (CDF). choose 2 vertices with max track multiplicity, then choose the one with minimum.(D0)  No correction is made for jet energy deposited outside the cone by the fragmentation process, as this is included in the NLO calculations to which the data are compared.

6. The Inclusive Jet Cross Section, E·d 3  /dp 3 CDF For jet transverse energies achievable at the Tevatron, this probes distances down to 10 -17 cm.  This is what’s measured.

7. (88.8 pb -1 ) (20.0 pb -1 ) The CDF result for unsmeared data:

8. New in this analysis: compare raw data to smeared theory. This uncouples the systematic shift in the cross section associated with smearing from the statistical uncertainty on the data. Consider only uncorrelated uncertainties first. Develop a  2 fitting technique that includes experimental uncertainties, to quantify the degree to which each theory reproduces the data.

9. Define where: n d = observed # jets in bin i n t = predicted # jets in bin i  t = uncertainty on prediction s k,t = shift in k th systematic for t th theoretical prediction Term 1: uncorrelated scatter of points about a smooth curve Term 2:  2 penalty from systematic uncertainties

10. Begin with n t 0 : nominal prediction by theory t. Smear prediction separately for each systematic uncertainty k to get smeared prediction n t k. The systematic uncertainty in bin i is then Predicted # jets in bin i is Use this n t (i) to calculate (uncorrelated) statistical uncertainty. The s k are chosen to minimize total  2 using MINUIT.

11. Example resulting  2 values: CTEQ4M: 63.4 CTEQ4HJ: 46.8 MRST: 49.5 This suggests that CTEQ4HJ best describes the data. But combinations of the 8 systematics can cancel. To study this, redo the fit separately for every combination of systematics. For: NO systematics:  2 = 94.2 4 systematics: best  2 = 47.6 8 systematics: best  2 = 46.8 The normalization systematic can be cancelled by shape systematics.

12. To extract confidence levels: Generate fake raw data (“pseudo- experiments”) using CTEQ4HJ. Predict nominal # entries for each of the 33 bins. Vary each prediction with 33 (statistical) + 8 (systematic) random numbers. Assume systematics are gaussian but E T dependent. Repeat for other PDF’s. Fit each pseudo-experiment to the nominal PDF prediction using  2.

13. Calculate  2 between data and smeared theory. Integral of the distribution above this  2 is the CL.

14. Results, for 33 dof: CTEQ4HJ: 10% CL MRST: 7% CL (relatively high value because normalization systematic is cancelled by shape systematics). All other PDF’s: < 5% CL CTEQ4M: 1.4% CL, change in agreement with data above 250 GeV cannot be accounted for.

15. CDF conclusion on inclusive jet cross section measurement: predictions using CTEQ4HJ have best agreement with data in both shape and normalization before considering systematics. when systematics are included, some combinations cancel out to produce only small changes in the spectrum shape. CTEQ4HJ provides the best prediction, followed by MRST. CDF Run Ib data are consistent with Run Ia and with NLO QCD given the flexibility allowed by current knowledge of PDF’s. CDF is also consistent with D0.

16. The Inclusive Jet Cross Section versus Pseudorapidity and E T D0 Extends the kinematic range beyond previous measurements:

17. D0 result, with cone algorithm, for 95 pb -1 at 1800 GeV:

18.  2 Comparison of D0 data and theory: i.) Define ii.) Construct the C ij by analyzing the correlation of uncertainties between each pair of bins. (Bin-to-bin correlations for representative bins are ~ 40% + positive.) iii.) There are 90  -E T bins.

19. Conclusions: PDF  2 /dofProbability CTEQ4HJ0.660.99 MRSTg  0.950.63 CTEQ4M1.030.41 MRST1.260.05

20. Measurement of  s from Inclusive Jet Production CDF The cross section and  s are related at NLO by: In the Tevatron E T regime, non-perturbative contributions are negligible. 1 1 S.D. Ellis et al., PRL 69, 3615 (1992).

21. Procedure: The and k 1 are calculated with JETRAD 1 for given 2 matrix elements, in the scheme. Clustering and cuts are applied directly to the partons. The 33 E T bins provide independent measurements at 33 values of  R =  F. Evolve the measured  s values: 1 W. Giele et al., PRL 73, 2019 (1994) and Nucl. Phys. B403, 633 (1993) 2 R.K. Ellis and J. Sexton, Nucl. Phys. B 269, 445 (1986).

22. Result, for 87 pb -1, with CTEQ4M : Average of results is  s =  s evolution verified for 40 < E T < 250 GeV : 27 values of  s (M Z ) are E T -independent. E T (GeV)

23. Theoretical uncertainties due to: E T /2 <  < 2E T : PDF:5% (extracted  s values are consistent with those in PDF’s.) 1.3 < R sep < 2.0:2-3%

24. The Inclusive Jet Cross Section using the k T Algorithm D0 The k T algorithm differs from the cone algorithm because Particles with overlapping calorimeter clusters are assigned to jets unambiguously. Same jet definitions at parton and detector levels: no R sep parameter needed. NNLO predictions remain infrared safe.

25. The k T algorithm successively merges pairs of nearby objects (partons, particles, towers) in order of increasing relative p T. Parameter D controls the end of merging, characterizes jet size. Every object is uniquely assigned to one jet. Infrared + collinear safe to all orders.

26. D0 k T Algorithm 1 : 1) For each object i with p Ti, define d ii = (p Ti ) 2 2) For each object pair i, j, define (  R ij ) 2 = (  ij ) 2 + (  ij ) 2 d ij = min[(p Ti ) 2,(p Tj ) 2 ]·(  R ij ) 2 /D 2 3) If the min of all d ii and d ij is a d ij, i and j are combined; otherwise i is defined as a jet. 4) Continue until all objects are combined into jets. 5) Choose D = 1.0 to obtain NLO prediction identical to that for R = 0.7 cone. 1 Based on S.D. Ellis and D. Soper, PRD 48. 3160 (1993).

27. k T jets do not have to include all objects in a cone of radius D, and may include objects outside cone. D0 result for 87 pb -1, unsmeared data, |  |<0.5, statistical errors only:

28. Theory below data by 50% at low p T, by (10 - 20)% for p T > 200 GeV/c. NLO predictions with k T and cone are within 1%. Cross section measured with k T is 37% higher than with cone.

29. Effect of final state hadronization studied with HERWIG: For 24 d.o.f.,  2 calculated with covariance technique: PDF  2 /dofProb. MRST + hadr.1.000.46 CTEQ4HJ + hadr.1.010.44 MRST1.120.31 MRSTg  1.170.25 CTEQ4M1.300.15 MRSTg  1.380.10

30. Ratios of Multijet Cross Sections D0 This study measures as a function of. Compare to JETRAD with CTEQ4M for several choices of renormalization scale using a  2 covariance technique.

31. Re call  F controls infrared divergences;  R controls ultraviolet. Assume  R =  F. Test four options:  R = for leading 2 jets and (a)  R = also for third jet. (b)  R = E T for third jet. (c)  R = 2E T for third jet.  R = 0.6 E T max for all 3 jets.

32. Result, for 10 pb -1 :

33. No prediction accurately describes the data throughout the full kinematic region. A single  R assumption is adequate: introduction of additional scales does not improve agreement with data.  R = 0.3 is consistent with the data.

34. Subjet Multiplicity of Gluon and Quark Jets Reconstructed with the k T Algorithm D0 This study examines p T and direction of k T jets event-by-event comparison of k T and cone multiplicity structure of quark and gluon jets

35. Calibration of jet momentum: To find p environ (from U noise, multiple interactions, pile-up) : overlay HERWIG events with zero-bias (random crossing) events at various luminosities. Observation: p environ for (D = 1.0) k T is 50-75% higher (i.e., 1 GeV/jet) than for (R = 0.7) cone.

36. To find p underlying : (1) overlay HERWIG events with minimum-bias (coincidence in hodoscopes) data at low luminosity (negligible environment) (2) overlay HERWIG events with zero- bias events at low luminosity (3) subtract: (1) - (2). Observation: p underlying for (D = 1.0) k T is 30% higher than for (R = 0.7) cone.

37. To find R: (1) calibrate EM energy scale with Z, J,  0 decays (2) require p T conservation in  -jet events: R consistent for k T and cone jets.

38. Comparison of k T and cone jet reconstruction for 2 leading jets in 69k Run 1b events: 99.94% of jets reconstructed within  R < 0.5.

39. systematically higher than by 3-6%:

40. Subjets Reapply k T algorithm to each jet, using its preclusters, until all remaining objects have These are subjets, defined by fractional p T and separation in space. Multiplicity M depends on: color factor (gluon > quark) y cut : y cut = 0  M = # preclusters y cut = 1  M = 1 Choose y cut = 10 -3.

41. Select gluon-enriched and quark- enriched data samples: PDF data show that fraction of gluon jets decreases with x  p T /. Select jets with same p T at = 630 GeV and = 1800 GeV for 2-jet events.

42. Use HERWIG with CTEQ4M to predict gluon jet fraction f. LO calculation is algorithm-independent. Identify reconstructed jets with type of nearest parton. Gluon jet fractions for 55 < p T < 100 GeV/c: f 1800 :0.59 f 630 :0.33

43. Multiplicity M measured in the data is related to gluon jet multiplicity M g and quark jet multiplicity M q by: For M g, M q independent of, Correct result for shower detection effects in calorimeter.

44. Mean subjet multiplicities: gluon jets: 2.21  0.03 quark jets: 1.69  0.04 after unsmearing,

45. Charged Jet Evolution and the Underlying Event CDF A two-part analysis: Data are compared to HERWIG, ISAJET, and PYTHIA for observables associated with the leading charged jet: the hard scatter. global observables used to study the behavior of the underlying event.

46. The data: minimum bias (one interaction each with forward + backward beam-beam counters) and charged jets with |  | p T > 0.5 GeV/c. measured in the central tracker:  p T /p T 2  0.002 (GeV/c) -1 impact parameter cut, vertex cut, to ensure 1 primary vertex. no correction for track finding efficiency (92% correction applied to models).

47. The models: p t hard > 3 GeV/c, to guarantee  2  2 ‹  total inelastic All assume superposition of the hard scatter the underlying event: beam-beam remnants, initial state radiation, and multiple parton scattering but different models for underlying event...

48. HERWIG: soft collision between 2 beam “clusters.” ISAJET: “cut Pomeron” similar to soft min bias. Independent fragmentation allows tracing of particles to origin: beam-beam, initial state rad, hard scatter + final state rad. PYTHIA: non-radiating beam remnants + multiple parton interactions with different effective minimum p T options: 0, 1.4, and 1.9 GeV/c. No independent fragmentation: cannot distinguish initial from final state radiation but can distinguish beam-beam.

49. The standard CDF jet algorithm based on calorimeter towers is not directly applicable to charged particles. A naive jet algorithm is used because it can be applied at low p T : define jet as a circular region with radius Order all charged particles by p T. Start with particle with p T max, include in the jet all particles within R = 0.7. Recalculate centroid after each addition. Go to next highest p T particle and construct new jet around its R = 0.7. Continue until all particles are in a jet. Jet can extend beyond |  | < 1.

50. Results on the leading jet: The QCD hard scattering models describe these observables for the leading (highest ) charged jet well: multiplicity of charged particles size radial distribution of charged particles and p T around jet direction momentum distribution of charged particles Charged particle clusters evident in the minimum bias data above p T  2 GeV/c  a continuation of the high p T jets in the jet trigger samples.

51. To study the underlying event, global observables and are correlated with angle  relative to axis of leading jet. Region transverse to leading jet (normal to the plane of the 2  2 parton hard scatter) is most sensitive to beam-beam fragments and initial state radiation.

52. Observation: and grow rapidly with p T leading, then plateau at p T leading > 5 GeV/c. Plateau height in transverse direction is half height in direction of leading jet.

53. PYTHIA 6.115 best model for in tranverse region but over-estimates in direction of leading jet. ISAJET shows right activity but wrong p T dependence:

54. ISAJET uses independent fragmentation (too many soft hadrons when partons overlap) and leading log picture without color coherence (no angle ordering within the shower):

55. HERWIG + PYTHIA model hard scatter (esp. initial state radiation) component of underlying event best:

56. HERWIG lacks adequate :

57. Summary: Many interesting and significant results from D0 and CDF in Inclusive jets  s k T algorithm Multijet production Particle evolution Underlying event On to Run II!