Jet Corrections Group at CDF

Generic Jet Energy Corrections at CDF
A journey from calorimeter to partons...

Conveners: Monica D'Onofrio

The primary goal of jet energy corrections group is to determine the energy correction to scale the measured energy of the jet energy back to the energy of the final state particle level jet. Additionally, there are corrections to associate the measured jet energy to the parent parton energy, so that direct comparison to the theory can be made. Currently, the jet energy scale is the major source of uncertainty in the top quark mass measurement and inclusive jet cross section.
The CDF jet energy corrections are divided into different levels to accommodate different effects that can distort the measured jet energy, such as, response of the calorimeter to different particles, non-linearity response of the calorimeter to the particle energies, un-instrumented regions of the detector, spectator interactions, and energy radiated outside the jet clustering algorithm. Depending on the physics analyses, a subset of these corrections can be applied.

The CDF detector has been upgraded for Run II. All systems, except central calorimeter and muon system, were replaced. The data acquisition electronic and simulation and reconstruction software was re-written.
For central calorimeter, the ADC integration gate was reduced from 600 ns to 132 ns, clipping the tails of the signal. In addition, the material in front of the calorimeter increased due to the new tracking system. Both of these effect reduce the observed energy in the calorimeter. We compared photon-jet Pt difference measured in Run II with Run I data and found that Run II jet energy scale is [-2.8 +/- 0.4 (stat) +/- 0.8 (sys)]% lower than Run I, consistent with the drop expected from extra material and shorter integration gate.
We tuned the Run II calorimeter simulation to the single particle response measured in Run II ppbar collisions at low momenta (p<20 GeV) and test beam measurement at higher momenta (p>20 GeV). This tuning takes care of above changes in detector at least at low momenta. In the central calorimeter, we achieve an uncertainty about 50% smaller than initial CDF Run II estimate and slightly better than final Run I estimate. As a result of having a better CDF simulation, the Run II jet energy scale uncertainties in the non-central regions have been decrease up to a factor of 5. The jet energy scale uncertainty is the dominant systematic uncertainty on the CDF measurement of the top quark mass. We expect to be able to decrease the uncertainty from this source on the top quark mass in the near future.

Absolute Scale
The jet energy measured in the calorimeter needs to be corrected for any non-linearity and energy loss in the un-instrumented regions of each calorimeter. Since there are no high statistics calibration processes at high Et, this correction is extracted from Monte Carlo. The simulation of the calorimeter needs to accurately describe the response to single particles (pions, protons, neutrons, etc). The Monte Carlo fragmentation needs to describe the particle spectra and densities of the data for all jet Et. We measure the fragmentation and single particle response in data and tune the Monte Carlo to describe it. The correction is obtained mapping the total Pt of the hadron-level jet to the Pt of the calorimeter-level jet. The hadron-level jet consists of particles within a cone of the same size as and within Delta R<0.4 of the calorimeter-level jet. The main systematic uncertainties on the absolute scale are obtained by propagating the uncertainties on the single particle response (E/p) and the fragmentation. Smaller contributions are included from the comparison of data and Monte Carlo simulation of the calorimeter response close to tower boundaries in azimuth, and from the stability of the calorimeter calibration with time.

Relative Scale
Since the central calorimeters are better calibrated and understood, this correction scales the forward calorimeters to the central calorimeter scale. This correction is obtained using Pythia and data di-jet events. The transverse energy of the two jets in a 2->2 process should be equal. This property is used to scale jets outside the 0.2<|eta|<0.6 region to jets inside the region. This region is chosen since it is far away the cracks or non-instrumented regions. This results in a correction as a function of pseudo-rapidity and Pt. After corrections, the response of the calorimeter is almost flat with respect to pseudo-rapidity. We vary the selection requirements and fitting procedure and take the deviation of the calorimeter response versus eta from a straight line as a systematic uncertainty. The difference between data and PYTHIA is already accounted for by the uncertainties from our other studies of fragmentation and out-of-cone energy, so we do not include it again as a systematic here. We find good agreement of the relative response of the calorimeter between PYTHIA di-jet production and data. We do not observe such good response with HERWIG di-jet, the origin of these discrepancies is under study.

Photon+jet balance. Cone 0.4. Pythia, Herwig and data

Di-jet balance cone size 0.4 and cone 0.7. Pythia and data

Multiple interactions
The energy from different ppbar interactions during the same bunch crossing falls inside the jet cluster, increasing the energy of the measured jet. This correction (UEM) subtracts this contribution in average. The correction is derived from minimum bias data and it is parameterized as a function of the number of vertexes in the event. The systematic uncertainty from this correction is 15%. The sources of uncertainties are the differences observed with different topologies and the luminosity dependence.

Underlying event (spectator partons)
The underlying event is defined as the energy associated with the spectator partons in a hard collision event. Depending on the details of the particular analysis, this energy needs to be subtracted from the particle-level jet energy. The UE energy was measured from minimum bias data requiring events only one vertex. The uncertainty is 30% of the underlying event correction.

Out-of-Cone
It corrects the particle-level energy for leakage of radiation outside the clustering cone used for jet definition, taking the "jet energy" back to "parent parton energy". We measure the energy flow between cones of size 0.4 and 1.3. Since the Monte Carlo must describe the jet shape of the data, the systematic is again taken from the difference between data and Monte Carlo for different topologies.

Total Systematic Uncertainties
The total systematic uncertainties in the central calorimeter (0.2<|eta|<0.6) are shown below. For non-central jets, the total uncertainty is obtained adding in quadrature the relative (eta-dependent) and the central uncertainties. The central uncertainties (0.2<|eta|<0.6) are of the same order than Run I. The CDF simulation has greatly improved since Run I, therefore in the non-central regions the Run II uncertainties are smaller even by a factor of 4 in some regions. At low PT, the main contribution is from the out-of-cone uncertainty, while at high PT is from the absolute jet energy scale. Reducing the uncertainty at low PT requires a better understanding of the differences between data and Monte Carlo in samples like photon+jet. A better CDF simulation and larger statistics to determine the uncertainties should reduce the uncertainties at high PT.
We improved the CDF simulation and now understand part of the origin of the differences between data and Monte Carlo. As consequence, comparing to the jet energy scale from 2004, the error decreased in about a factor of 2 in the central region and by more than 5 in other regions.

PT = 15 GeV
Systematic Uncertainty (%) PT = 100 GeV
Systematic Uncertainty (%)

Multiple ppbar Interactions 0.4 0.05

Absolute Jet Energy Scale 1.8 2.2

Underlying Event 1.0 0.1

Out of Cone + Splash-out 7.0 1.5

Relative(|eta|<0.2) 1.5
0.5

Relative(0.2<|eta|<0.6) 0.5
0.5

Relative(0.6<|eta|<0.9) 1.5
0.5

Relative(0.9<|eta|<1.4) 1.5
0.5

Relative(1.4<|eta|<2.0) 1.5
0.5

Relative(2.0<|eta|) 3.0
2.0

Tests
PT balance between photon and jet in photon+jet Herwig, Pythia, and data samples after applying all jet corrections for different cone sizes. The PT balance after all corrections is zero, as expected, showing that the corrections work well in this PT range.

Data, Pythia, Herwig
PT balance between photon and jet in photon+jet Herwig, Pythia, and data samples before applying jet corrections for Cone 0.4 jets in different eta regions. In the central region (0.2<|eta|<0.6), we observe a 3% difference between data, Pythia, and Herwig. We find that these discrepancies are covered by the central and relative uncertainties. This sample is used as a cross-check and to determine systematic uncertainties. To reduce the systematic uncertainties even further we need a better understanding of the origin of this 3% discrepancy.

PT balance between photon and jet in photon+jet Herwig, Pythia, and data samples before applying jet corrections for different cone size jets in all eta regions (0.0<|eta|<2.0)

Absolute Scale	The jet energy measured in the calorimeter needs to be corrected for any non-linearity and energy loss in the un-instrumented regions of each calorimeter. Since there are no high statistics calibration processes at high Et, this correction is extracted from Monte Carlo. The simulation of the calorimeter needs to accurately describe the response to single particles (pions, protons, neutrons, etc). The Monte Carlo fragmentation needs to describe the particle spectra and densities of the data for all jet Et. We measure the fragmentation and single particle response in data and tune the Monte Carlo to describe it. The correction is obtained mapping the total Pt of the hadron-level jet to the Pt of the calorimeter-level jet. The hadron-level jet consists of particles within a cone of the same size as and within Delta R<0.4 of the calorimeter-level jet. The main systematic uncertainties on the absolute scale are obtained by propagating the uncertainties on the single particle response (E/p) and the fragmentation. Smaller contributions are included from the comparison of data and Monte Carlo simulation of the calorimeter response close to tower boundaries in azimuth, and from the stability of the calorimeter calibration with time.
Relative Scale	Since the central calorimeters are better calibrated and understood, this correction scales the forward calorimeters to the central calorimeter scale. This correction is obtained using Pythia and data di-jet events. The transverse energy of the two jets in a 2->2 process should be equal. This property is used to scale jets outside the 0.2<\|eta\|<0.6 region to jets inside the region. This region is chosen since it is far away the cracks or non-instrumented regions. This results in a correction as a function of pseudo-rapidity and Pt. After corrections, the response of the calorimeter is almost flat with respect to pseudo-rapidity. We vary the selection requirements and fitting procedure and take the deviation of the calorimeter response versus eta from a straight line as a systematic uncertainty. The difference between data and PYTHIA is already accounted for by the uncertainties from our other studies of fragmentation and out-of-cone energy, so we do not include it again as a systematic here. We find good agreement of the relative response of the calorimeter between PYTHIA di-jet production and data. We do not observe such good response with HERWIG di-jet, the origin of these discrepancies is under study. Photon+jet balance. Cone 0.4. Pythia, Herwig and data Di-jet balance cone size 0.4 and cone 0.7. Pythia and data
Multiple interactions	The energy from different ppbar interactions during the same bunch crossing falls inside the jet cluster, increasing the energy of the measured jet. This correction (UEM) subtracts this contribution in average. The correction is derived from minimum bias data and it is parameterized as a function of the number of vertexes in the event. The systematic uncertainty from this correction is 15%. The sources of uncertainties are the differences observed with different topologies and the luminosity dependence.
Underlying event (spectator partons)	The underlying event is defined as the energy associated with the spectator partons in a hard collision event. Depending on the details of the particular analysis, this energy needs to be subtracted from the particle-level jet energy. The UE energy was measured from minimum bias data requiring events only one vertex. The uncertainty is 30% of the underlying event correction.
Out-of-Cone	It corrects the particle-level energy for leakage of radiation outside the clustering cone used for jet definition, taking the "jet energy" back to "parent parton energy". We measure the energy flow between cones of size 0.4 and 1.3. Since the Monte Carlo must describe the jet shape of the data, the systematic is again taken from the difference between data and Monte Carlo for different topologies.

	PT = 15 GeV Systematic Uncertainty (%)	PT = 100 GeV Systematic Uncertainty (%)
Multiple ppbar Interactions	0.4	0.05
Absolute Jet Energy Scale	1.8	2.2
Underlying Event	1.0	0.1
Out of Cone + Splash-out	7.0	1.5
Relative(\|eta\|<0.2)	1.5	0.5
Relative(0.2<\|eta\|<0.6)	0.5	0.5
Relative(0.6<\|eta\|<0.9)	1.5	0.5
Relative(0.9<\|eta\|<1.4)	1.5	0.5
Relative(1.4<\|eta\|<2.0)	1.5	0.5
Relative(2.0<\|eta\|)	3.0	2.0