Inclusive Cross Section using the K T algorithm at the Tevatron

1. Inclusive Cross Section using the KT algorithm at the Tevatron Olga Norniella IFAE-Barcelona Corfu summer Institute on EPP 2005

2. Jet @ Tevatron Jet production jet jet • Higher jet with respect to RunI • Increased pT range for jet production • Stringent test of p-QCD • Over 9 order of magnitude Highest dijet mass so far: Mass 1.3 TeV • Sensitivity to distances ~ 10-19 m • Tail sensitive to new physics and PDFs ET = 666 GeV h = 0.43 ET = 633 GeV h = -0.19

3. Run I cross section vs  RunI D0 measurement NLO QCD (JETRAD, CTEQ4M) CTEQ5/CTEQ6 Measurements in the forward region allow to constrain the gluon distribution Big uncertainty still remains for high-x gluons

4. Jet measurements Jets measured with calorimeter • Complex detector properties • Non-linear response to hadrons • Different response to electrons and hadrons • Un-instrumented regions • Large fluctuation in deposited energy • Some of the particles do not reach the calorimeter • A good understanding of the calorimeter response becomes crucial • Jet energy scale and resolution

5. Calorimeter response • CDF scintillating time with lead/iron absorbers ||<3.6 • Not compensated (non-linear response to hadrons) • Coarse granularity • New plug • Resolution ElectronssE / E = 13.5% /ÖE (central) sE / E = 16% /ÖE (plug) Charged PionssE / E ~ 80% /ÖE

6. Jet Energy scale • Measured E/p using single particles - Charged pions, ’s (J/Psi and W decays) - Z->ee mass is used to set absolute EM scale • E/p used to tune the simulation •  GFLASH parameterization of the showering in the calorimeter • -jet balance used to checkthe jet energy scale • Systematic uncertainties • Calorimeter simulation - Residual differences between dataand simulation in the response of the calorimeter to single particles (E/p) • Fragmentation - Spectra of the particles inside jets • Stability - Calibration fluctuation with time

7. KT algorithm • KT Algorithm preferred by theory • Separate jets according to their relative transverse momentum - • Infrared/collinear safe to all order in p-QCD (relevant for NNLO) • No merging/splitting parameter needed Successfully used at LEP and HERA jet Photoproduction at HERA jet Relatively new in hadron colliders more difficult environment(Underlying Event, Multiple pp interactions) -

8. Event Selection • Measurements based on 385 pb-1 of CDF Run II data • Event Selection • Jets defined with KT algorithm (D=0.5, 0.7, 1.0)  • Primary vertex position |VZ| < 60 cm • Missing ET significance ETmiss /  ET < min (2+5/400*PTjet (leading jet), 7) • Jets in different  regions Region 1 : ||< 0.1(90o crack) Region 2 : 0.1 < ||< 0.7 (Central Calorimeter) Region 3 : 0.7< ||< 1.1(Central Cal. + 30o crack) Region 4 : 1.1 < ||< 1.6(30o crack + Plug Cal.) Region 5 : 1.6 < ||< 2.1(Plug Cal.) • Pythia MC samples used to correct the measurements

9. MC studies: Dijet Balance • To study the jet response relative to central calorimeter region where the MC provides a proper description of the data Central Region: Calorimeter + Tracking Jet Calorimeter response well understood (within  2-3% energy scale) Trigger Jet Central Probe Jet • Dijet events PT > 10 Gev/c • Definitions -> PTMean = (PTTrig + PTProb)/2 -> PTF = (PTProb - PTTrig)/PTMean ->  = (2+ <PTF> )/(2- <PTF>) Event by event:  = PTProb /PTTrig In some rapidity regions the MC has to be corrected forcing data =MC

10. detector detector MC Studies: Bisector Method • To study the jet energy resolution The PT unbalance between the jets is sensitive to physic (ISR) and detector effects PERP axis PTJet1 • Dijet events PT > 10 Gev/c PTPERP  • Definitions PT//  // axis (bisector) ->  = |(Jet1- Jet2)/2| -> PT// =  (PTJet1+ PTJet2) cos() PTJet2 -> PTPERP = (PTJet1- PTJet2) sin() Transverse Plane • Relevant variables • // = rms of PT// distribution physics effects PERP = rms of PTPERP distribution  detector + physics effects • D = √(2PERP - 2//)

11. Bisector method results |Jet| < 0.1 1.6 < |Jet| < 2.1 Ddata= DMC Ddata DMC In some rapidity regions the jet energy resolution is corrected in the MC to force Ddata= DMC After applying corrections to the MC based on Dijet Balance and Bisector Method studies the MC is ready to be used to correct the raw measurement

12. Corrections From calorimeter to hadron level - • Multiple pp interaction correction To remove contributions from multiple interactions per bunch crossing • Average pT correction (based on MC) To correct in average the energy measuredin the calorimeter to take into accountnon-compensation and dead material • Unfolding correction (based on MC) To take into account smearing/resolution effects For comparison to NLO pQCD calculations, the theory has to be corrected for UE/Hadronization (model dependent) • Underlying Event contribution • Fragmentation into hadrons

13. Multiple pp interaction correction + 0.70 0.7 = 1.62 GeV/c - 0.46 • PT contribution (D ) to the PTJet for each additional primary vertex  ~1-2 GeV/c Important at low PT PTRAW(corrected) = PTRAW - 0.7  (Num.vert – 1) - • At high instantaneous luminosity the contribution from multiple pp interactions change the shape of the cross section - The fraction 0.7 is extracted from ratioof cross sections for two subsamples high luminosity/low luminosity Not corrected ratio corrected PTJet

14. Average PT correction PT jet measured in the calorimeter is affected by detector response PTCal < PThad Hadron level • Reconstruct jets at Calorimeter and Hadron level • Match pair of CAL-HAD jets in  -  space Calorimeter level • < PTHAD-PTRAW> vs <PTRAW> |Jet| < 0.1 1.6 < |Jet| < 2.1

15. Unfolding Procedure • The measured jet spectrum is corrected back to the hadron level NJet Hadron level • Bin-by-bin unfolding factors Ci = (PTJet bin i) NJet Calorimeter level • Apply unfolding factors to the measured PT spectrum Njets UNFOLDED = Ci Njets DATA Reasonable dependence on PTJet |Jet| < 0.1 1.6 < |Jet| < 2.1 • The MC is re-weighted to make the measurements independentof the PDF used

16. Systematic Uncertainties • Jet Energy Scale • Energy scale varied in MC according to uncertainty estimated ~2-3% • ~10% at low PTJet and ~40 to 60% at high PTJet • Unfolding • Sensitivity to PT spectrum: ratio of unfolding factors obtained from nominal and weighted Pythia• Sensitivity to fragmentation model: ratio of unfolding factors obtained from weighted Herwig and weighted Pythia |Jet| < 0.1 • ~ 5 to 10 % low PT and < 10% high PTJet • Jet EnergyResolution • 8%uncertainty on the jet momentum resolution • ~2 to 8% - • Multiple pp interactions • Correction changed within its uncertainty • < 3% • Selection Cuts • Variation of the cuts 1.6 < |Jet| < 2.1 • ~ 2%

17. NLO calculations • JETRAD CTEQ61 package • R = F = Maximum Jet PT/2 • NLO uncertainties • ScaleR = F = Maximum Jet PT • Preliminary estimation of the uncertainties associated to the PDFs Use the four sets corresponding to plus and minus deviations of eigenvectors 5 and 15 Eigenvector 15 related to gluon PDF which dominates the uncertainty - Final uncertainties will be computed taking into account all the 40 PDF sets

18. NLO corrections • UE / Hadronization corrections • Correct the NLO pQCD calculations for Underlying Event and Fragmentation in order to compare to data jet jet  (Hadron Level Pythia Tune A with MPI) C HAD (PTJet, Jet) = (PTJet, Jet)  (Parton Level Pythia Tune A no MPI)

19. jet jet KT Jets vs D D = 0.5 D = 0.7 D = 1.0

20. Jets cross sections

21. Data/Theory In all the rapidity regions there is a good agreement between measurements and NLO pQCD calculations

22. Summary & Conclusions • Inclusive jet cross section measured using 385 pb-1 of CDF Run II data for jets with PT 54 GeV/c in five rapidity regions: |Jet|< 0.1 ; 0.1<|Jet|< 0.7 ; 0.7 < |Jet|< 1.1 ; 1.1 < |Jet|< 1.6 ; 1.6 < |Jet|< 2.1 • Using the KT algorithm • Fully corrected to the hadron level • Good agreement with theory, NLO pQCD corrected for UE / Hadronization • The KT algorithm works fine in hadron colliders • These measurements will be used to further constrainthe PDFs (gluon at high x)