8.5.1 Impact Parameter
The uncertainty on the expected collision point distribution has an impact on the signal reconstruction efficiency. In current Monte Carlo simulations it is assumed that the collision points are Gaussian distributed, centered at 0 with a width of 50mm. Muon tracks are required to have an absolute η-value below 2.5. Muons which are produced in reality with larger distances in z-direction than in the Monte Carlo simulation, might have an η-value below 2.5 but are not reconstructed. This effect is illustrated in Figure 8.44 and discussed in this section. Muon Spectrometer Inner Detector (η=2.5) Muons Point 1 Collision Point 2 Collision
Figure 8.44: Illustration of the impact of the collision point on the signal reconstruction efficiency
To study this effect, the generated collision point inz-direction was modeled with a Gaussian with a width σZ0 (Figure 8.45). In a second step, it is simulated if the muon could be
reconstructed and fulfills the |η <2.5| requirement. The impact of the additional Gaussian smearing widthσZ0 on the reconstruction efficiency is shown in Figure 8.46. An uncorrected
net shift of the average collision point by1mminy- andz-direction has also been studied. It turned out for both cases that the relative change of the selection-efficiency is smaller than
0.0005. Hence it seems reasonable to neglect the systematic uncertainty due to these effects, since even a rough description of the collision point distribution, is sufficient for this study.
[mm] 0 Z -800-600-400-200 0 200 400 600 800 Number of Events 0 2000 4000 6000 8000 10000 12000 14000 σ (Z0)=50mm )=500mm 0 (Z σ
Figure 8.45: Collision point distribution for two values ofZ0. [mm] 0 Z σ 0 500 1000 1500 2000 2500 Efficiency 0.738 0.74 0.742 0.744 0.746 0.748 0.75 0.752 0.754 0.756 0.758 1 c 8.078 ± 7.048e-05 2 c 64.49 ± 0.001393 m 0.0006962 ± 2.394e-05 1 c 8.078 ± 7.048e-05 2 c 64.49 ± 0.001393 m 0.0006962 ± 2.394e-05
Figure 8.46: Width of collision point distribu- tionZ0 vs. impact on accpentance
8.5. FURTHER STUDIES OF SYSTEMATIC UNCERTAINTIES 97
8.5.2 Impacts of Misalignment
Misalignment of the ATLAS Muon Spectrometer is expected to have a significant impact on the pT-resolution but only a small impact on the reconstruction efficiency [7]. These
impacts can be determined with the methods, presented in section 8.3 and 8.4. Impacts of misalignments in the large |η|-region need special attention, since they may affect the η-determination and hence the acceptance-cut at|η|=2.5.
For a first estimation, a single 50GeV single muon sample has been reconstructed with an ideal and a misaligned Muon Spectrometer layout. The ratio of reconstructed muons with |η| < 2.5 over the overall number of reconstructed muons has been calculated for both reconstructed samples. The difference of this ratio was found to be 0.0023±0.003, which is compatible with 0.0 within the statistic uncertainty as expected. It should be noted, that deviation of0.0023±0.003is due to the limited statistics of the available Monte Carlo sample. To estimate the effect in more detail, it can be assumed, that the η-measurement is driven by the inner and outer MDT-chamber of the Muon Spectrometer Endcap only and no in- formation of the Inner Detector or a vertex constrained is used. Moreover, it is assumed that all muon tracks can be considered as straight lines in a first approximation. Figure 8.47 illustrates the idea of this simplified η-measurement. A 2mm shift of the y-position of the outer MDT-chamber with respect to the inner MDT-chamber is a conservative assumption of an uncorrected misalignment [70]. This leads to a measuredη-variation of∆η ≈0.0004and induces an uncertainty on the number of selected events of∆Nη−mis/N ≈1×10−5. This esti-
mation is conservative, since the assumed2mmmisaligned chamber position must be applied randomly to all 16 sectors in the φ-plane on both sides of the Muon Spectrometer. Hence, in the case of uncorrelated misalignments, these uncertainties are expected to cancel out to a certain extend.
A more serious impact is expected if a correlated shift is introduced, i.e. the Muon Spec- trometer is shifted globally in one direction. To estimate this effect, it is assumed, that the η-measurement is driven only by the innermost MDT station by requiring that the muon comes from the interaction point. A shift of 2mm of the innermost MDT cham- ber leads to ∆η ≈ 0.002 and induces an uncertainty on the number of selected events of ∆Nη−mis/N ≈ 5×10−4. Hence, it seems to be justified to neglect a systematic contribution
due to this effect.
~ ~ z 12m ∆ 14m 22m 8m ~ ~ ∆y 2m Muon Track =2.5 η Middle Chamber Inner Chamber Outer Chamber
Figure 8.47: Illustration of assumedη-measurement of a muon track in the
|η| ≈2.5-region.
8.5.3 PDF Contributions
The theoretical uncertainties on the parton distribution functions (PDFs) lead to an impact on the rapidity and kinematic properties of the Z boson, and hence on the acceptance of the
98 CHAPTER 8. CROSS-SECTIONσ(PP→Z/γ∗ →µ+µ−) MEASUREMENT η- and pT-cuts. These effects have been studied on the Pythiagenerator level.
The CTEQ6.1M description of the PDFs was chosen [24]. The core of the PDF description are the probability density functions for each parton, i.e. one function for the u-quark, one function ford-quark and so on. These functions are determined by experiment and evolved to smaller values ofx. Each of PDFs can be varied within the uncertainty of the measurements. It was chosen by the CTEQ collaboration to describe all possible variations of the complete set of functions by 20 orthogonal vectors. The PDF uncertainties are therefore estimated from 40 different PDF sets, each containing the average density functions varied by one error vector in either direction.
To estimate the overall effect on the selection efficiency,300,000Z →µµ events were gener- ated for each of the 40 different PDF sets. The invserse transverse momentum of all generated muons have been smeared by a Gaussian function to account for the pT-resolution of the com-
bined tracking of the ATLAS Detector (see Appendix D.3), as well as a cut on the η of the muons has been applied (|η|<2.5). In a last step kinematic cuts have been applied on the simulated muons and their invariant di-muon mass.
The detector acceptanceα is defined as the fraction of events, which pass the kinematic cuts and the |η|<2.5 requirement. The overall acceptances αi have been calculated for each of
the 40 PDF sets, where the index istands for the PDF set chosen. Also, the acceptance αs
of the average PDF-set has been determined with a higher statistics of two million events in an analogue way.
The quadratic sum of all differencesαs−αi with the same sign leads to an estimation of the
PDF uncertainty impact on the selection efficiency
∆εPDF =+−00..012006±±00..003003((statstat)),
which is in agreement with [71].