Model Independent Search for Deviations from the Standard Model ...

56 Monte Carlo Samples
5.3 Energy Scale and Smearing
A detector measures a signal of a certain height if a particle traverses. This signal must
be transformed into an energy value. If a jet showers in the calorimeter, only a certain
amount of the total energy can be measured because inert absorbing material which is
not instrumented exists. The calorimeter, therefore, must be calibrated, which means that
the measured hardware signal is multiplied by a certain factor, the Jet Energy Scale (see
Section 4.3.4). This energy value then reects the true physical value of the jet. Similar
energy scales must be applied to all particles, even though the JES is the largest and
has a signicant uncertainty. A detector simulation must mimic all these energy scales.
Besides this, every subsystem of the detector responsible for measuring a certain particle,
e.g. the tracker or the calorimeter, has a certain intrinsic momentum or energy resolution.
A detector simulation must describe these resolutions properly.
The detector simulation is often insucient to reproduce the exact data distributions, so
one must often ne-tune the MC. The analysis package Top Analyze [23] provided by the
Top Group implements all smearing factors and energy scales, each of them determined
in a separate analysis. Only the MET-smearing is performed self-contained within the
analysis code. The following parameterizations can be found in [12], combined with the
values used in the program version Top Analyze-Stradivarius.
Electrons
TheelectronenergyissmearedwitharandomGaussianwithmeanzerousingthefollowing
formula:
E ′ = E · α + E · Gauss(0, σ) . (5.2)
The energy scale is the corretion factor α = 1.007 ± 0.001, and the smearing factor is
σ = 0.042 ± 0.004 for ducial electrons (i.e. energy deposition ouside the calorimeter
cracks, see Section 4.3.1). For non-ducial electrons, one obtains α = 0.971 ± 0.012 and
σ = 0.083 ± 0.006. The parameters are determined by comparing the Z-peak position and
width in data and MC. The relative errors can be found in [51], bearing in mind that the
mean parameters in this analysis have changed slightly compared to the ones stated in [51]
as a new version of the analysis program Top Analyze is used.
Muons
Muon p T ismeasuredbydeterminingthesagitta,whichis ∝ 1/p T . Thisleadstoasmearing
function:
1
p ′ T
= 1
α p T
+ Gauss(0, σ) . (5.3)
Here α = 0.991 ± 0.003 and σ = 0.0025 ± 0.0002 [ GeV −1 ]. Again the Z-peak serves as a
calibration tool, and the errors can be found in [52].