4.4 Selection Cuts
4.4.4 Further Rejection: Signal vs Background Optimisation
The previous cuts were introduced to reduce specific background processes. However, the back-ground contribution in general can be further reduced using the fact that squarks and gluinos produce large E/ and have large masses. It is expected that the mSUGRA signal events be char-T acterised by isotropic (spherical) final-state topologies with large amounts of transverse energy measured in the calorimeter. The variables that help on discriminating signal from background at
2] [Gev/c MInv
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+jets) ν µ Z invariant mass (W->µν+jets) Z invariant mass (W->
Fig. 4.10:Invariant mass distribution of the two highest isolated tracks in the event. The plot on the left corresponds to Z/γ∗→ µµ, while the plot on the right corresponds to W → µν. This cut does little to reduce the W→ µνbackground since not many of the events have two or more isolated tracks. However, it rejects most of the Z/γ∗→ µµ background.
The arrows show were the invariant mass window cut is placed.
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Expected events
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+ jets) ν µ ,iso.track) (W->
ET
φ(
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Fig. 4.11: ∆φ(track, E/ ) distribution for Z/γT ∗→ µµ events (left) and W → µνevents (right). This cut rejects events in which the direction of the E/ is aligned with that of an isolated track. A significant fraction of the backgrounds isT rejected by the cut placed where the arrow indicates.
this point are the following:
• ETjet 1: transverse energy of the leading jet.
• ETjet 2: transverse energy of the second leading jet.
• ETjet 3: transverse energy of the third leading jet.
• HT: total transverse energy defined as the sum of the transverse energies of the three leading jets (HT=∑3jetsETjet).
• E/ : missing transverse energy corrected as explained in Section 4.1.2.T
A careful MC study was performed to set the optimal values for these variables and maximise their ability to separate the mSUGRA signal from the background. This ability is quantified by S/√
B, where S denotes the expected number of signal events and√
B is the statistical uncertainty on the Standard Model background. Due to the complexity of optimising 103 points of signal with five variables that are correlated, a step-by-step procedure was considered:
• First, the number of points in Fig. 4.3 was reduced and only the points with similar squark mass and increasing gluino mass (row points 31-91) together with a set of points with M˜q ≈ M˜g (diagonal points 23-91) were selected in this study. It is noticeable that the difference between points belonging to the same column, or same gluino mass, is less significant. At the bottom of a column, squarks and gluinos have similar masses, and therefore they tend to be produced with similar probability. As the mass of the squark increases (moving up in the column), the squark cross section becomes smaller. Thus, at the top of the column most of the events tend to come from gluinos, whose mass has not changed.
All optimisation plots were done with these limited set of mSUGRA points, with the aim to determine the different cuts defining the minimum number of zones into which the mSUGRA mass plane can be divided.
• Fig. 4.12 and Fig. 4.13 show the S/√
B distributions for the points with M˜q≈ M˜g(diagonal), and the points with similar squark masses (row), respectively. Each triangle in each of the plots corresponds to a different cut on HT. From these plots, three different regions are defined. In region A, the HT cut is set to 255 GeV. Region B has a HT cut of 330 GeV.
Finally, region C has a cut of 355 GeV. All of these cuts are directly extracted from the maximum of the S/√
B distributions.
Fig. 4.14 and Fig. 4.15 show the HT distributions for the points with M˜q≈ M˜g(diagonal), and similar squark mass (row), respectively. When comparing the distributions, the dif-ference between two points with similar gluino mass and different squark masses (points 23-31, 35-42, 46-52, etc) is negligible compared to the difference between two points with similar squark masses and different gluino masses.
• The HTcut is applied and now a similar study is performed with the E/ variable. Fig. 4.16T
and Fig. 4.17 show the S/√
B distribution for the points along the diagonal and the row.
From these plots, a E/ cut of 75 GeV for region A is assigned. The cuts for regions B andT C are chosen to be 100 GeV and 130 GeV, respectively. Fig. 4.18 shows the E/ distributionT
for the points along the diagonal. Similarly, Fig. 4.19 shows the E/ distribution for theT points along the row.
• After applying the HT and E/ cuts, the ET T of the jets have less discriminating power. As an example, Fig. 4.20 shows the S/√
B distribution of the leading jet for points along the
diagonal. The distribution is flat until it starts to drop, which implies that signal and back-ground have the same shape. Therefore, the cut on this variables is chosen so that the signal acceptance remains high and the low-end tails of the jet’s ET distributions are removed.
This can be seen in Fig. 4.21 through Fig. 4.23, where the arrows show the placement of the cut for the different regions. The only cut applied to the third jet transverse energy is the one from the pre-selection (25 GeV).
Fig. 4.12:S/√
B distribution for HTof the mSUGRA points along the diagonal.
Different ordering for the applied cuts was also studied and the one which maximised the S/√ B was chosen.
In conclusion, the entire generated mSUGRA plane was finally divided into three distinct regions as a function of the gluino mass, as seen in Fig. 4.3. The value of the different thresh-olds which defined the three different signal regions is shown in Tab. 4.3 and the efficiencies for each of the cuts applied in the analysis (pre-selection and optimised cuts) for three representative mSUGRA points, together with the number of expected events after all cuts, are given in Tab. 4.4.
Only statistical uncertainties are considered at this point.
Fig. 4.13:S/√
B distributions for HTof the mSUGRA points along the row.
E/ (GeV)T HT(GeV) ETjet 1(GeV) ETjet 2 (GeV) ETjet 3(GeV)
Region A 75 230 95 55 25
Region B 90 280 120 70 25
Region C 120 330 140 100 25
Tab. 4.3:Cut thresholds for the three different regions in which the signal plane is divided.