All processes containing a leptonically decaying W boson can be reduced effectively by reconstructing the transverse mass of the common parent particle of the lepton and the ETmiss, if a cut is put above the W boson mass. The transverse massmT is defined as follows:
mT = q
2·p`T·ETmiss 1−cos ∆Φ(~`, ~ETmiss)
. (8.1)
Here, p`T is the lepton pT, and ∆φ(~`, ~ETmiss) is the azimuthal angle between the lepton and the E~Tmiss direction. It is assumed that the lepton mass is negligible.
By this mean, single-leptonict¯tandW+jets processes are suppressed by about 90%. Events originating fromt¯t andW+jets can escape such a cut either due to the limited resolution of the reconstructedmT or if an additional source of ETmiss is present in the event. The latter is
Chapter 8. Search for New Physics in Events with Missing Energy and Top Quarks 191
5.2 Additional variables 29
the y-component are known. Therefore only these two components for the leptonically decaying top quark are used as well. With this, the length of the perpendicular component of the E /
Tto the leptonically decaying top quark can be calculated. This is illustrated in figure 5.11. The corresponding distribution is shown in figure 5.12.
(a) Standard Model tt decay (b) ˜tt˜ú decay
Figure 5.11: Illustration of the perpendicular E /
Tcomponent to the leptonically decaying top quark. In the Standard Model decay, the neutrino is orientated in the same direction as the leptonically decaying top quark, therefore the component is small (a). In the ˜ t ˜ t
údecay, the neutralinos contribute to the missing transverse energy and they are not collinear to the leptonically decaying top quark. Therefore the component is larger (b) than in the Standard Model decay.
[GeV]
Figure 5.12: The perpendicular E /
Tcomponent to the leptonically decaying top quark for the Standard Model decays and the ˜ t ˜ t
údecay is shown for the electron channel. The distributions are normalised to unit area in order to show the shapes.
For the SM t ¯ t decay, small values are observed, because the neutrino is mostly collinear to the leptonically decaying top quark. In the ˜ t ˜ t
údecay, the neutralinos contribute to the missing transverse energy. Therefore the missing transverse energy is no longer collinear
_
Figure 8.7: Sketch of the definition of the perpendicular ETmiss variable.
true for signal events, but also for dileptonict¯tevents where one lepton is not identified or out of acceptance. Alsot¯tevents in which oneW decays leptonically and one into a hadronic tau often have a larger mT. Hence, most of the analysis-specific variables, described in further detail in Ref. [238], aim at rejecting these background components.
A first strategy is to try to reconstruct the hadronic top candidate. Via a χ2-minimisation, the three jets that are best compatible with originating from a top quark are selected, according to their momenta and considering their momentum resolution. Their invariant mass is defined to be mχtop. In the case of dileptonic t¯t this variable will not be close to the top mass by any means, whereas this is the case for signal and background events containing a true hadronic top decay. This approach is extended to the case of dileptonic tt¯with a lost lepton by the so-called topness variable [239]. Furthermore, the ETmiss perpendicular to the reconstructed leptonic top candidate can be used to distinguish between signal and background. After the hadronic top candidate is reconstructed as described above, the additional b-jet is combined with the identified lepton to form the leptonic top. While this ET,⊥miss is expected to be small for background events, where the ETmiss from the neutrino is aligned with the leptonic top, this variable is likely large for signal events (see Fig. 8.7).
A second strategy, based on the mT approach, is to reconstruct the different decay chains and give an upper bound on the hypothetical parent mass. First, the so-called stransverse mass, mT2 [240] can be defined. It extends the transverse massmT to decay topologies with two branches, a and b, originating from the same, pair-produced parentA. In each branch, it is assumed that there are some particles with measured momenta and some unmeasured particles. The sum of the measured momenta in branchi∈ {a, b}is denotedpi = (Ei, ~pTi, pzi)
192 Chapter 8. Search for New Physics in Events with Missing Energy and Top Quarks
Figure 8.8: Schematic view on the variablesamT2 (left) andmτT2 (right).
and the sum of the unmeasured momenta is denotedqi = (Fi, ~qTi, qzi). Then, m2pi =Ei2−~pi2 and m2qi =Fi2−~qi2. The mT of the particles in branch i is given by:
m2Ti =q
p2Ti+m2pi +q
qTi2 +m2qi2
−(~pTi+~qTi)2 (8.2) which, in the case of mqi =mpi = 0, is the same as the expression for mT given above. It has an end point at the parent mass mA. Now, mT2, is defined as a minimisation over the allocation of~pmissT between~qTa and ~qTb of the maximum of the corresponding mTa or mTb:
mT2 ≡ min
~
qTa+~qTb=~pmissT {max(mTa, mTb)}. (8.3) An assumption of mqa and mqb must be made in the computation of mT a and mT b. The result of the above minimisation is the minimum parent massmAconsistent with the observed kinematic distributions under the inputsmqa and mqb. The variants of mT2 described below only differ in the considered measured particles, assumed unmeasured particles, and choices for the input masses,mqa and mqb.
ThemT2 is adapted to target dileptonictt¯by accounting for missed leptons in the so-called asymmetric mT2 (amT2) [241–244] (see Fig. 8.8). Here, decay branch a assumes a b-jet as visible object and takes the lepton originating from the leptonically-decayingW boson as lost, and so the lepton and the neutrino as unmeasured. Hence, mqa equals the W mass. Decay branch b takes ab-jet6 and the lepton as visible objects, the neutrino from the leptonically-decaying W boson is the invisible part. Both possible assignments of the b-jets are tested
6In case there is only one or more than two b-jets found in the event, the ones with the highest b-tagging weights are considered.
Chapter 8. Search for New Physics in Events with Missing Energy and Top Quarks 193 Selection Comments
HLT_xe80_tc_lcw_L1XE50 trigger
jet cleaning veto events that contain a jet that fails the loose jet cleaning criteria
exactly one signal lepton and no additional baseline leptons
≥4 signal jets reduce low-jet multiplicity backgrounds (diboson, W/Z)
ETmiss >200 GeV start of the XE trigger plateau mT >30GeV control of QCD/multijets
|∆φ(j1,2, ~pmissT )|>0.4 control of QCD multijet backgrounds mτT2 based τ-veto (mτT2 >80 GeV) remove events with hadronic tau candidates
Table 8.2: Common preselection for the optimisation of the signal regions.
and the one resulting in the smalleramT2 is taken. In such a dileptonict¯tscenario, theamT2
is bounded from above by the top quark mass, while signals typically exceed this bound.
Similarly, themτT2 variable is optimised for the case of aW boson that decays into a hadronic tau (see Fig. 8.8). Decay branchaconsiders a reconstructed hadronic tau candidate as visible object, the two neutrinos resulting from the W and the tau decay present the unmeasured components. Decay branch b takes the lepton as visible and its neutrino as invisible object.
Bothmqa andmqb are taken to be zero. This variable can be used as a tau veto fort¯t decays into one lepton (electron or muon) and one hadronically-decaying tau lepton by removing events in which the mτT2 does not exceed 80 GeV, i.e. the W mass bound.
It proved useful to define HT,sigmiss, the significance of a purely object-based missing transverse jet energy, as:
HT,sigmiss = |H~Tmiss| −M σ|H~Tmiss|
, (8.4)
whereH~Tmiss is the negative sum of the jet and lepton momentum vectors. The denominator gives the resolution of H~Tmiss and considers the the per-event energy resolution of the jets determined from the per-event jet energy uncertainties. The lepton energy is assumed to be measured significantly better and hence its resolution is neglected. The parameter M denotes a “characteristic scale” of the background [245]. Based on optimisation studies it is fixed at 100 GeV in this analysis.
194 Chapter 8. Search for New Physics in Events with Missing Energy and Top Quarks