1. Jet Physics at CDF Sally Seidel University of New Mexico APS’99 24 March 1999

2. 1. Jets at CDF 2. The Inclusive Jet Cross Section 3. The Dijet Mass Cross Section 4. The Differential Dijet Cross Section

3. CDF: A multi-purpose detector for studying hadronic collisions at the Fermilab Tevatron:

4. The motivation: Jet distributions at colliders can: signal new particles test QCD predictions check parton distribution functions

5. The data: CDF reconstructs jets using an iterative cone algorithm with cone radius Jet energies are corrected for calorimeter non-linearity uninstrumented regions contributions from spectator partons

6. The iterative cone algorithm: Examine all calorimeter towers with E T > 1 GeV. Form preclusters from continuous groups of towers with monotonically decreasing E T. If a tower is outside a window of 7 x 7 towers from the seed of its cluster, start a new precluster with it. For each precluster, find the E T -weighted centroid with R = 0.7. Define the centroid to be the new cluster axis. Save all towers with E T > 100 MeV within R = 0.7 about the new axis. Iterate until the tower list is stable.

7. The Inclusive Jet Cross Section For jet transverse energies in the range 40 < E T < 440 GeV: this probes distances down to 10 -17 cm. The analysis: –For luminosity (88.8 ± 4.1) pb -1 –Trigger on jet-like events: accept 4 triggers with uncorrected E T thresholds at 20, 50, 70, and 100 GeV; correct for pre-scaling

8. C –Apply data quality requirements:  z vertex  < 60 cm to maintain projective geometry of calorimeter towers 0.1 < |  detector | < 0.7 for full containment of energy in central barrel E total < 1800 GeV to reject accelerator loss events Define E T = E  sin  and = missing E T. Require to reject cosmic rays –Correct (“unsmear”) observed E T for energy degradation and calorimeter resolution

9. Calculate the cross section: where N = number of events L = luminosity  range is 1.2 and  E T bins have width 5 - 80 GeV Compare to EKS (Ellis, Kunszt, Soper) NLO calculation with CTEQ4M pdf and renormalization/factorization scale  = E T jet /2

14. Systematic uncertainties (all uncorrelated) on the inclusive jet cross section: i. Calorimeter response to high-p T charged hadrons ii. Calorimeter response to low-p T charged hadrons iii. Energy scale stability (1%) iv. Jet fragmentation model used in the simulation v. Energy of the underlying event in the jet cone (30%) vi. Calorimeter response to electrons + photons vii. Modelling of the jet energy resolution function viii. Luminosity (4.1%)

16. The Dijet Mass Cross Section Many classes of new particles have a larger branching fraction to just 2 partons than to modes containing a lepton or a W/Z…so this can be a powerful way to search for new particles. The analysis: For luminosity (85.9 ± 4.1) pb -1 Trigger on jet-like events Select events with  2 jets, both with |  event | < 2.

17. Define  *  (  1 -  2 )/2, then require   e 2|  *| < 5. This is the same as |cos  *| = |tanh  *| < 2/3 where  * is the Rutherford scattering angle: Apply the data quality cuts. Correct for trigger efficiency, |z vertex | cut efficiency, resolution, and calorimeter effects.

18. Define the dijet mass: Calculate the cross section: where: N = number of events, corrected for prescaling L = luminosity  M jj = 10% mass bins (consistent with detector resolution) Compare to JETRAD (Giele, Glover, Kosower) NLO calculation with CTEQ4M +  = E T max /2. Two partons are merged if they are within R sep = 1.3  R.

19. The dijet mass cross section compared to JETRAD with CTEQ4M:

20. Compare results to data + JETRAD with other pdf’s: Changing  from 0.5 E T max to 0.25 E T max changes the normalization by 25%.

25. Compare CDF and D0 results for CTEQ4M (D0 examines |  | < 1 with no requirement on cos  *)

26. Systematic uncertainties on the dijet mass cross section (17-34%, asymmetric + E T -dependent): Absolute energy scale (14-31%): Calorimeter calibration: 1.3-1.8% over the E T range Jet fragmentation model: 1.2-1.7% over the E T range Calorimeter stability: 1% of E Energy of the underlying event: 1 GeV Unsmearing: Parameterization of the resolution function: 1-9% depending on M jj Variation between analytic and MC procedure: ±4% Detector simulator energy scale: 2-8%

27. Relative jet energy scale (5-9% depending on M jj and considering all instrumented regions): Other uncertainties: luminosity: 4.1% prescale factors: 1.7-3.5% depending on trigger used. |z vertex | cut efficiency: 1% trigger efficiency: < 1% depending on the statistics of the turn-on region of the trigger.

29. The Dijet Differential Cross Section The rapidity dependence of the cross section probes the parton momentum fractions. The analysis: For luminosity (86.0 ± 4.1) pb -1 Trigger on jet-like events; select events with  2 jets Apply data quality cuts

30. Order the jets by E T. Define: The “leading jet”: with highest E T. Require that it has 0.1 40 GeV. The “probe jet”: with second highest E T. Require that it has E T2 > 10 GeV. Correct jet energies for calorimeter effects; require E T1 > 35 GeV. Classify events according to probe jet ,  2 : 0.1 < |  2 | < 0.7 0.7 < |  2 | < 1.4 1.4 < |  2 | < 2.1 2.1 < |  2 | < 3.0

31. Correct (“unsmear”) measured  Correct for trigger efficiency, prescale, and vertex-finding efficiency For events in each of the 4  2 classes, calculate the cross section: N = number of events, corrected for prescale L = luminosity E T1 bins are consistent with detector resolution Compare to JETRAD for 3 pdf’s +  = E T max /2

34. Sources of systematic errors on the dijet differential cross section: Same as for inclusive cross section +  resolution

35. Probing the high-x, high-Q 2 regime: Notice that for a two-body process, and so these data examine a range in (x,Q 2 ) including that where an excess was observed at HERA: