DZero Preliminary Jet Energy Scale


Conveners: Aurelio Juste, Christophe Royon



Introduction

Fig 1:  Sketch of the evolution from the hard-scatter parton
           to a jet in the calorimeter.

Many physics measurements at a hadron collider critically depend on an accurate knowledge of the energy of jets resulting from the fragmentation of quarks and gluons generated in the hard scattering process. The precise determination of the jet energy scale is a challenging project, involving corrections for physics, instrumental and jet algorithm-dependent effects (see Fig. 1).

Jets are reconstructed in DZero using the so-called "Run II cone algorithm" [1], using a cone radius Rcone=0.5 or 0.7, and requiring a minimum transverse momentum of 6 GeV. This algorithm is applied both at the stable-particle (particle jets) and the reconstructed calorimeter tower (calorimeter jets) levels.

The goal of the jet energy scale correction is to correct the calorimeter jet energy back to the stable-particle jet level before interaction with the detector. Indeed, during parton evolution some energy can be found at large angles with respect to the original parton direction resulting from hard gluon radiation, which DZero's jet energy scale does not attempt to correct for.

The results presented here are preliminary, as they are based on a rather limited-statistics (~150/pb) data set. Significant improvements, both on statistical and systematic uncertainties are expected for the next version of jet energy scale.




[1] G.C. Blazey et al., Proc. of the QCD and Weak Boson Physics in Run II
     Workshop (Batavia 1999)
, [hep-ex/0005012].
DZero Run II Detector

The DZero Run II detector [2] (see Fig. 2) consists of a magnetic central-tracking system, comprised of a silicon microstrip tracker and a central fiber tracker, both located within a 2 T superconducting solenoidal magnet. Central and forward preshower detectors are positioned just outside of the superconducting coil. The next layer of detection involves three liquid-argon/uranium calorimeters (see Fig. 3): a central section covering |eta| up to ~1.1, and two end calorimeters that extend coverage to |eta|~4.2, all housed in separate cryostats. In addition to the preshower detectors, scintillators between the CC and EC cryostats provide sampling of developing showers at 1.1<|eta|<1.4. Calorimeter readout cells form pseudo-projective towers (see Fig. 4), with each tower subdivided in depth. There are four separate depth layers for the EM modules in the CC and EC, with a total depth of ~20 radiation lengths. There are three (four) finely segmented hadronic layers in the CC (EC), followed by a coarser hadronic layer. The total depth of the CC (EC) is more than 7.2 (8.0) interaction lengths.

The calorimeter themselves remain unchanged from Run I [3]. In Run II, one of the major changes result from  the upgrade of the calorimeter electronics (preamplifier and baseline subtractor boards), required to accomodate the significant reduction in the Tevatron's bunch spacing (from 3600 ns to 396 ns). In contrast to Run I, where the full charge was integrated, now only the charge collected during the first 260 ns after the bunch crossing is integrated. This necessarily results in a higher degree of non-compensation of the calorimeter, which was nearly compensating in Run I. The other major change is the increase in material in front of the calorimeter (~4 radiation lengths) as a result of the upgraded tracking system (silicon tracker, finer tracker, solenoid) and preshower detectors. Both changes directly affect the calorimeter response and energy resolution.




Fig. 2: Diagram of the upgraded DZero detector, as installed in the
   collision call and viewed from inside the Tevatron ring.




[2] DZero Collaboration, V. Abazov et al., "The Upgraded DZero Detector,"
     submitted to Nucl. Instr. Methods Phys. Res. A; [hep-physics/0507191].

[3] S. Abachi et al., Nucl. Instr. Methods Phys. Res. A 338 ( 1994) 185.





Fig. 3: Isometric view of the central and two end calorimeters.


Fig. 4: Schematic view of a portion of the DZero calorimeters showing the transverse
           and longitudinal segmentation pattern. The shading pattern indicates groups of
           cells ganged together for signal readout. The rays indicate pseudorapidity
           intervals from the center of the detector.
Overview of the procedure

The jet energy scale correction procedure (see Fig. 2) involves a number of sub- corrections which are derived (and applied) in a sequential manner. These corrections are estimated separately for collider and simulated (a.k.a. Monte Carlo) data. The first step is to subtract the energy not associated with the hard scatter (e.g. electronics noise or multiple proton interactions in the same bunch crossing).  This is referred to as "Offset correction". The next step, known as "Relative response correction", is to intercalibrate the response in energy of the calorimeter as a function of jet pseudorapidity. At this point, the "Absolute response correction" can be determined, which is the largest in magnitude (~30%), and accounts for effects such as energy loss in uninstrumented detector regions, the lower calorimeter response to hadrons as compared to electrons/photons, etc. Finally, the so-called "Showering correction" takes into account the energy deposited outside (inside) the calorimeter jet cone from particles inside (outside) the particle jet as a result of shower development in the calorimeter, magnetic field bending, etc.

Fig. 2:  Jet energy correction procedure.
Offset correction

The "offset energy" is defined as the energy deposited inside the calorimeter jet cone that is not associated with the hard-scatter. Contributions to offset arise from the so-called "underlying event" (beam remnants and multiple parton interactions), electronics and uraniun noise, energy from previous collisions (pile-up) because of the long shaping time of the calorimeter preamplifier, and multiple proton-antiproton collisions in the same bunch-crossing.

The first step involves the measurement of the per-tower energy density in "minimum-bias" events, defined as those events triggered by the luminosity monitor, and thus signaling the presence of a potential inelastic proton-antiproton collision. The implicit assumption is that all offset energy contributions (including the underlying event) are present in this measurement. The per-tower minimum-bias energy density measurement is performed for different primary vertex multiplicities in order to take into account the instantaneous luminosity dependence.

The offset energy for a jet of radius Rcone at a given pseudorapidity is computed by adding up the estimated energy density from all calorimeter towers nominally within the jet cone (see Figs. 5 and 6).

The main sources of systematic uncertainty include the residual instantaneous luminosity dependence within a given primary vertex multiplicity bin (~10% on the offset correction), and the difference between offset energy outside the jet (as measured in minimum-bias events) and inside the jet as a result of the different impact ofzero-suppression of cell energies.


Fig. 5: Offset energy for Rcone=0.7 jets for different primary vertex
           multiplicities, as a function of jet pseudorapidity from the center
           of the detector (see Fig. 4).

Fig. 6: Offset energy for Rcone=0.5 jets for different primary vertex
           multiplicities, as a function of jet pseudorapidity from the center
           of the detector (see Fig. 4).
Relative response correction

While the DZero calorimeter is fairly uniform within the central calorimeter (CC) and end calorimeter (EC) cryostats (see Fig. 4), the gap between both cryostats (0.5<|eta|<1.8) is not as well instrumented, causing a non-uniformity in response as a function of pseudorapidity. This region is covered by the intercryostat (ICD) and massless gap (MG) detectors. The ICD consists of an array of scintillator tiles located on the EC cryostat wall covering the region 1.1<|eta|<1.4. The MGs are separate single-cell structures installed in the CC and EC between the module end plates and the cryostat wall. The central (endcap) MG covers the region 0.7<|eta|<1.2 (0.7<|eta|<1.3).

The goal of the relative response correction (a.k.a. "eta-intercalibration") is to make the calorimeter uniform versus pseudorapidity before measuring the energy dependence of the response correction. Ideally, after this correction, the whole calorimeter has the same response versus energy (see "Absolute response correction" below).


Fig. 7: Basics of the MPF method.

Fig. 8: Relative response correction in data.

The relative response correction is measured using the Missing Transverse Energy Projection Fraction (MPF) method on samples of photon+jet and dijet events, where the tag object (photon or jet, respectively) is required to be in the CC (|eta|<0.5), and the probe jet can be anywhere in pseudorapidity. The MPF method relates the relative response between probe and tag objects to the observed momentum imbalance in the transverse plane (Missing Transverse Energy or MET) projected in the tag object direction (see Fig. 7).

This correction is determined as a function of tag object transverse momentum, using a fine binning in pseudorapidity (typically ~0.1). The corrections obtained in photon+jet and dijet events are found to be in reasonably good agreement, and are combined for a more precise determination in the whole kinematic range. Photon+jet (dijet) events dominate in the low (high) transverse momentum regions. This correction is determined separately for data and Monte Carlo.

Fig. 8 shows the relative response correction, from the combination of photon+jet and dijet data, for different values of the corrected probe jet energy. As expected, the correction is largest in the 0.5<|eta|<1.8 region.

After full jet energy scale correction (including most importantly the relative and absolute response subcorrections), the relative response correction is remeasured using the MPF method. Ideally, it should be consistent with 1. In practice, small residuals (of up to 2%) are observed, depending on jet energy, resulting from imperfections on the energy-dependent parameterization, eta-interpolation, etc. Fig. 9 illustrates the observed residuals in data, estimated in wide pseudorapidity bins, which are symmetrized and assigned as systematic uncertainty to the relative response correction.
.
Fig. 9: Relative response in data after full jet energy scale correction.
Absolute response correction

The absolute response correction is measured applying the MPF method to selected photon+jet events (see Fig. 7),  after offset and relative response corrections. The photon selection criteria include stringent cuts on the fraction of energy deposited in the electromagnetic (EM) calorimeter, calorimeter- and track-based isolation and shape information on the energy distribution in the third layer of the EM calorimeter as well as the Central PreShower (CPS) detector (for CC photons only). The absolute response measurement is performed using  events with a single photon candidate (|eta|<1.0 or 1.5<|eta|<2.5) and at least one jet, required to be in a back-to-back configuration: DeltaPhi(photon, leading jet)>3.0 radians. This correction is measured separately for data and Monte Carlo photon+jet events.

Fig. 10 shows the measured response for Rcone=0.7 jets in data as a function of the partly-corrected (by offset and relative response) jet energy. As a result of the eta-intercalibration, the response for jet in different pseudorapidity regions is consistent with the response in CC (|eta|<0.5). The lowest (highest) energy points available correspond to the CC (EC). The absolute response is obtained from a global fit to all points.


Fig. 10: Absolute response for Rcone=0.7 jets in data after offset and
relative response corrections, as a function of partly-corrected jet energy.

Figs. 11-13 summarize the fractional uncertainties on the absolute response for data, in different jet pseudorapidity bins. Due to the limited-statistics dataset used (~150/pb), the statistical uncertainty is sizable, especially for high-energy and forward jets. The dominant systematic uncertaities arise from biases related to photon energy scale and purity, the limited understanding of non-gaussian tails in the response distribution, and the sensitivity to the back-to-back topology selection.

Fig. 11: Fractional response uncertainty for jets with |eta|<0.5,
             as a function of partly-corrected jet energy.

Fig. 12: Fractional response uncertainty for jets with 0.8<|eta|<1.5,
             as a function of partly-corrected jet energy.

Fig. 13: Fractional response uncertainty for jets with 1.8<|eta|<2.5,
             as a function of partly-corrected jet energy.
Showering correction

The main goal of the showering correction is to correct for energy leaking outside (inside) the jet cone coming from particles inside (outside) the jet cone. As already pointed out, this correction intends to correct for "detector showering" only (i.e. instrumental effects such as shower development in the calorimeter, magnetic field bending, etc), and not for physics showering resulting for large-angle gluon radiation.

This correction is evaluated separately in data and Monte Carlo using photon+1jet candidate events, and requiring exactly one primary vertex reconstructed (to reduce the impact of multiple interactions). For a given bin of estimated jet energy and pseudorapidity, the first step is compute the jet energy density profile from calorimeter towers as a function of radial distance (in rapidity-phi space) to the jet-axis. After baseline-subtraction (contributed to by the underlying event, noise and pileup), the Monte Carloratio of energy within the jet cone radius to the total energy up to a larger radius (referred to as "jet limit") is defined as the "detector+physics" showering correction (i.e. including both detector and physics showering). The same procedure is repeated in Monte Carlo at the particle level (i.e. without detector effects), yielding the "physics-only" showering correction. Finally, the ratio of "detector+physics" and "physics-only" corrections yields the final showering correction.

Fig. 14 (15) illustrates the showering correction for Rcone=0.7 (0.5) jets in data as a function of corrected (up to absolute response) jet transverse energy for different pseudorapidity values.

The dominant systematic uncertainties (see Figs. 16 and 17) are associated with the baseline subtraction procedure and the choice of the "jet limit" radius, and are estimated in the simulation. Also sizable is the statistical uncertainty related to high jet transverse energy extrapolation, particularly in the forward region, due to the limited available statistics.

Fig. 14: Showering correction for Rcone=0.7 jets in data as
             a function of corrected jet transverse energy.

Fig. 15: Showering correction for Rcone=0.5 jets in data as
  a function of corrected jet transverse energy.

Fig.16: Fractional showering correction uncertainty for Rcone=0.7
            jets in data as a function of corrected jet transverse energy.

Fig.17: Fractional showering correction uncertainty for Rcone=0.5
            jets in data as a function of corrected jet transverse energy.
Total uncertainties

The total fractional jet energy scale uncertainty is illustrated in Figs. 18-20 (21-23) for Rcone=0.7 (0.5) jets in data as a function of uncorrected jet transverse energy, for three different values of jet pseudorapidity. Shown in the figures are also the contributions from each of the subcorrections (relative and absolute response corrections have been lumped together). As it can be appreciated, the contribution to the total uncertainty from response is in general sizable, specially at low and high jet transverse energy. At low transverse energy one of the leading contributions is the understanding of non-gaussian tails in the response distribution. At high transverse energy the main contribution is the limited available statistics to constrain high energy extrapolation of response. Showering-related uncertainties are large at high energy, again due to limited statistics, and for forward jets due to limitations of the current procedure in a detector region with limited detector coverage and large contributions from offset energy.

Improvements in all these areas are expected for the next iteration of jet energy scale determination, which should help further reduce the uncertainties.

Fig. 18: Fractional jet energy scale uncertainty for Rcone=0.7 jets in data
             at eta=0.0, as a function of uncorrected jet transverse energy.

Fig. 19: Fractional jet energy scale uncertainty for Rcone=0.7 jets in data
             at eta=1.0, as a function of uncorrected jet transverse energy.

Fig. 20: Fractional jet energy scale uncertainty for Rcone=0.7 jets in data
             at eta=2.0, as a function of uncorrected jet transverse energy.


Fig. 21: Fractional jet energy scale uncertainty for Rcone=0.5 jets in data
       at eta=0.0, as a function of uncorrected jet transverse energy.

Fig. 22: Fractional jet energy scale uncertainty for Rcone=0.5 jets in data
       at eta=1.0, as a function of uncorrected jet transverse energy.

Fig. 23: Fractional jet energy scale uncertainty for Rcone=0.5 jets in data
       at eta=2.0, as a function of uncorrected jet transverse energy.

Data-to-MC comparison

A last crucial step is the verification of the jet energy scale correction and its uncertainties. The main method used is the so-called "Hemisphere Method", which is typically applied to photon+jets events, although it can also be used in Z+jets and multijet events.

The "Hemisphere Method" starts by dividing the event in two hemispheres according to a line perpendicular to the tag object (e.g. the photon in photon+jet events) direction in the transverse plane. The "Hemisphere" observable (H) is defined as the ratio of the sum of projections of the (corrected) transverse momenta of all objects in the "probe hemisphere" with respect to the "tag hemisphere" (see Fig. 24).



Fig. 24: Basis of the Hemisphere Method.


Ideally, for a perfectly balanced event, H=1. In practice, there are many effects, unrelated to jet energy scale, which can cause a deviation of H from 1: biases from event selection, jet energy resolution, physics out-of-cone, etc. It is very important to disentangle these effects from a potential failure of the jet energy scale correction itself.

In order to validate the absolute jet energy scale, the Hemisphere observable from photon+jets events in data (or full Monte Carlo simulation) is subtracted from the prediction from Monte Carlo at the particle level, including realistic resolution effects, event selection, etc. This allows to cancel many of the non-jet energy scale related biases. In practice, photon+jet events in data have a significant contamination, especially at low transverse momentum, from QCD dijet events with one of the jets faking a photon. In this case, the reconstructed "photon " transverse momentum is a few percent smaller than the underlying particle jet, which will introduce a bias in the estimated imbalance in data. This bias is estimated from the full simulation and a correction applied to the Hemisphere observable in data. If the jet energy scale correction is adequate, the difference of Hemisphere observables should we distributed around 0, and within the quoted jet energy scale uncertainties.

Most physics analyses are not so concerned about the absolute jet energy scale, but rather the relative jet energy scale between data and full Monte Carlo simulation. In this case, the Hemisphere observable from photon+jets events in data (after correcting for the background bias) and Monte Carlo can a-priori be directly compared. Figs. 25-30 show the difference between Hemisphere observable in data and the full simulation (using PYTHIA) for photon+jet events with exactly one photon (|eta|<1.0) and one jet (Rcone=0.7) back-to-back in phi (DeltaPhi(photon,jet)>3.0 radians). The Hemisphere difference is computed as a function of photon transverse momentum and for different bins of jet pseudorapidity. The same comparison for Rcone=0.5 can be found in Figs. 31-36. The observed dispersion is found to be within the quoted total uncertainty (dashed line) for the jet energy scale corrections.

Fig. 25: Difference between data and MC imbalances in
             photon+1jet events, for 0.0<|eta(jet)|<0.4 and Rcone=0.7.

Fig. 26: Difference between data and MC imbalances in
             photon+1jet events, for 0.4<|eta(jet)|<0.8 and Rcone=0.7.

Fig. 27: Difference between data and MC imbalances in
             photon+1jet events, for 0.8<|eta(jet)|<1.2 and Rcone=0.7.

Fig. 28: Difference between data and MC imbalances in
             photon+1jet events, for 1.2<|eta(jet)|<1.6 and Rcone=0.7.

Fig. 29: Difference between data and MC imbalances in
             photon+1jet events, for 1.6<|eta(jet)|<2.0 and Rcone=0.7.

Fig. 30: Difference between data and MC imbalances in
             photon+1jet events, for 2.0<|eta(jet)|<2.4 and Rcone=0.7.


Fig. 31: Difference between data and MC imbalances in
             photon+1jet events, for 0.0<|eta(jet)|<0.4 and Rcone=0.5.

Fig. 32: Difference between data and MC imbalances in
             photon+1jet events, for 0.4<|eta(jet)|<0.8 and Rcone=0.5.

Fig. 33: Difference between data and MC imbalances in
             photon+1jet events, for 0.8<|eta(jet)|<1.2 and Rcone=0.5.

Fig. 34: Difference between data and MC imbalances in
             photon+1jet events, for 1.2<|eta(jet)|<1.6 and Rcone=0.5.

Fig. 35: Difference between data and MC imbalances in
             photon+1jet events, for 1.6<|eta(jet)|<2.0 and Rcone=0.5.

Fig. 36: Difference between data and MC imbalances in
             photon+1jet events, for 2.0<|eta(jet)|<2.4 and Rcone=0.5.






Last updated: June 4, 2006 - juste@fnal.gov