4 | Signal and background processes
4.2 Signal processes considered in the analysis
The analysis described in chapter 5 is restricted to R-parity conserving models, where stops are produced in pairs and the LSP is stable. We only consider the direct production of stop pairs through the strong force, in contrast to models where gluinos are produced and decay to stops, for example. We assume the lightest neutralino, χ˜01, to be the LSP, in order to have an electrically neutral, spin-1/2 dark matter candidate.
4.2.1 Stop decay modes
The analysis is developed around two major decay modes, where the stop either decays into a top quark and the LSP (figure 4.3a) or into a bottom quark and a light charginoχ˜˘1, which subsequently decays into aW boson and the LSP (figure 4.3b). All sparticles not appearing in the Feynman diagrams of figure 4.3 are assumed to be sufficiently massive to be of no relevance. In both decay modes, twoW bosons are generated, which can then decay leptonically or hadronically. As illustrated, we are interested in the semi-leptonic case with exactly one electron or muon in the final state.
There are a few special cases to be aware of, for example when the stop mass is very near the top quark mass (stealth stop), or when some of the mass differences are
Figure 4.3: Tree-level Feynman diagrams of direct stop pair production with subsequent decays to a) t`χ˜01 or b) b`χ˜˘1 followed byχ˜˘1 Ñ W `χ˜01. Both diagrams show the semi-leptonic case, where oneW decays leptonically and the other hadronically. The big circle represents various strong production modes; at the LHC, the largest contributions are from gluon-gluon processes.
insufficient to produce on-shell particles. The first case can be searched for in precision measurements of thet¯tproduction cross-section  or the t¯tspin correlation .
Figure 4.4a shows an example of the second case: if the mass difference∆mbetween
˜t1 and χ˜01 is less than the top mass, and no other stop decay mode is available, the top quark will necessarily be produced off-shell. In the Feynman diagram, this is represented by collapsing the top propagator line and having the stop decay directly into ab-quark, aW boson and a χ˜01. For this reason, this decay mode is also referred to as a three-body decay. If the mass difference is reduced further, ∆m ă mW `mb, also the W boson cannot be produced on-shell, further collapsing the diagram to yield a four-body stop decay. In both cases, the same final state objects as for larger∆m are present, but with different kinematic properties. In particular, it is no longer possible to identify a top quark using the invariant mass of its decay products in a three-body stop decay.
While the decay modes shown in figure 4.3 can be studied separately, assuming a 100% branching ratio for one or the other, it is also possible to study both decay modes together, resulting in the additional type of diagram shown in figure 4.4b, referred to as an asymmetric stop decay. We refer to signal models where both ˜t1 Ñ t`χ˜01 and
˜t1 Ñ b`χ˜˘1 decays are allowed and consequently all three diagrams (4.3a, 4.3b, 4.4b) can occur asmixed stop models.
4.2.2 Model parameters
The masses of˜t1,χ˜˘1, andχ˜01 are free parameters. To reduce the number of parameters, we always assumempχ˜˘1q “2ˆmpχ˜01q. While other choices are possible, this is justified from SUSY GUT models with gaugino universality  (orgaugino unification; see for
Figure 4.4: Tree-level Feynman diagrams of stop pair production with the particular decay patterns that are the focus of this thesis: a) three-body decay (off-shell top) and b) asymmetric decays (the opposite assignment of leptonic and hadronic W decays is also possible).
example ref. , sec. 4.3), and it assures that the χ˜˘1 Ñ W `χ˜01 decay products are produced on-shell and with significant transverse momentum, except near the edge of the experimental constraintmpχ˜˘1q Á100GeV established by the LEP experiments .
The lightest neutralino,χ˜01, which is in general a mixture of the uncharged gauginos and higgsinos (B,˜ W˜3,H˜10,H˜20), is assumed to be mostly bino. This means the effects of EWSB are assumed to result only in a small perturbation on the neutralino mass matrix.
In thet˜1 Ñt`χ˜01 models,˜t1 is mostlyt˜R, while the˜t1 Ñb`χ˜˘1 models assume˜t1 to be fullyt˜L. For the asymmetric decays, equal contributions of˜tLand˜tRare assumed. As outlined in section 2.4, an increasing contribution from ˜tR is expected as the branching ratio for the˜t1 Ñt`χ˜01 decay mode increases. Models with˜t1 “˜tLhave been evaluated for comparison, and have been found to have lower lepton transverse momentum, reducing the exclusion limits on the stop mass by typically 50–100GeV (figure 4.5).
4.2.3 Mixed stop decays at arbitrary branching ratios
Since the asymmetric events on their own do not represent a physical sample, one needs to mix them with t+χ˜01 and b+χ˜˘1 samples according to the assumed branching ra-tio. Since we do not consider other stop decay modes beyond these, we always have BR` we can express mixed quantities in the following way, using the expected yield as an ex-ample:
1,b˜χ˘1 `2xp1´xq ¨Nt˜χ0
350 400 450 500 550 600 650 700
All limits at 95% CL
1-lepton + jets + Emiss
pair prod. cross section t1
Figure 4.5: Impact of different stop mixing assumptions on the exclusion reach for˜t1Ñ t`χ˜01 models with a χ˜01 mass of 50 GeV from . The ˜t1 is either pure ˜tL (yellow lines) or mostly˜tR(red lines). The upper and lower blue lines correspond to the nominal signal cross-section scaled up and down by the theoretical uncertainty.
The expressions on the right-hand-side should be normalised separately according to the theoretical stop production cross-section, and should use the same SUSY masses and mixing assumptions. The mixed decays use the same χ˜˘1 mass assumption m`
˜ mixing between the two stop decay modes (i.e. x “0.5), as this results in the highest contribution of asymmetric decays, but the results for mixing withx“0.25 or x“0.75 are evaluated as well.