Introduction
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Fig 1:
Sketch of the evolution from the hard-scatter parton
to a jet
in the calorimeter.
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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].
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DZero
Run II Detector
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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.
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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.
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Fig. 3: Isometric view of the central and two end calorimeters.
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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.
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Overview
of the procedure
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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.
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Fig. 2: Jet energy correction procedure.
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Offset
correction
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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.
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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).
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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).
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Relative
response correction
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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).
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Fig. 7: Basics of the MPF method.
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Fig. 8: Relative response correction in data.
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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.
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Fig. 9: Relative response in data after full jet energy scale
correction.
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Absolute
response correction
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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.
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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.
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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.
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Fig. 11:
Fractional response uncertainty for jets with |eta|<0.5,
as a function of partly-corrected jet energy.
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Fig. 12:
Fractional response uncertainty for jets with 0.8<|eta|<1.5,
as a function of partly-corrected jet energy.
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Fig. 13:
Fractional response uncertainty for jets with 1.8<|eta|<2.5,
as a function of partly-corrected jet energy.
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Showering
correction
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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.
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Fig. 14:
Showering correction for Rcone=0.7 jets in data as
a function of corrected jet transverse energy.
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Fig. 15: Showering correction for Rcone=0.5 jets in data as
a function of corrected jet transverse energy.
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Fig.16:
Fractional showering correction uncertainty for Rcone=0.7
jets
in data as a function of corrected jet transverse energy.
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Fig.17:
Fractional showering correction uncertainty for Rcone=0.5
jets
in data as a function of corrected jet transverse energy.
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Total
uncertainties
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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.
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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.
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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.
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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.
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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. |
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Data-to-MC
comparison
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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.
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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.
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Fig. 25:
Difference between data and MC imbalances in
photon+1jet events, for 0.0<|eta(jet)|<0.4 and Rcone=0.7.
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Fig. 26:
Difference between data and MC imbalances in
photon+1jet events, for 0.4<|eta(jet)|<0.8 and Rcone=0.7.
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Fig. 27:
Difference between data and MC imbalances in
photon+1jet events, for 0.8<|eta(jet)|<1.2 and Rcone=0.7.
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Fig. 28:
Difference between data and MC imbalances in
photon+1jet events, for 1.2<|eta(jet)|<1.6 and Rcone=0.7.
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Fig. 29:
Difference between data and MC imbalances in
photon+1jet events, for 1.6<|eta(jet)|<2.0 and Rcone=0.7.
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Fig. 30:
Difference between data and MC imbalances in
photon+1jet events, for 2.0<|eta(jet)|<2.4 and Rcone=0.7.
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Fig. 31:
Difference between data and MC imbalances in
photon+1jet events, for 0.0<|eta(jet)|<0.4 and Rcone=0.5.
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Fig. 32:
Difference between data and MC imbalances in
photon+1jet events, for 0.4<|eta(jet)|<0.8 and Rcone=0.5.
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Fig. 33:
Difference between data and MC imbalances in
photon+1jet events, for 0.8<|eta(jet)|<1.2 and Rcone=0.5.
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Fig. 34:
Difference between data and MC imbalances in
photon+1jet events, for 1.2<|eta(jet)|<1.6 and Rcone=0.5.
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Fig. 35:
Difference between data and MC imbalances in
photon+1jet events, for 1.6<|eta(jet)|<2.0 and Rcone=0.5.
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Fig. 36:
Difference between data and MC imbalances in
photon+1jet events, for 2.0<|eta(jet)|<2.4 and Rcone=0.5.
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