Top Quark Decay

After the description of possible production mechanisms of top quarks, the decay of the heaviest SM elementary particle, which is less diverse than top quark production, is outlined in this section.

In the SM, top quarks decay via the weak interaction into aW boson and a down-type quark. The probability of how often which down-type quark acts as decay product is expressed by the CKM matrix elements that contain top quarks, namely|V_{t d}|,|V_ts|and|V_{t b}|. According to the measured value of|V_{t b}|=0.99915±0.00005[28], extracted on the assumption of CKM unitarity (see also Sec. 2.3), top quarks decay almost exclusively into a W⁺ boson and a bottom quark, the antitop quark correspondingly into a W⁻ boson and an antibottom quark. This relationship can also be written in terms of branching ratiosBwhich are defined asBi=Γi/Γ with the total decay width Γ and the partial decay widthΓi that is associated with a certain decay modei. Thus,Bi describes the fraction of particles which decay via the modeiwith respect to the total number of decaying particles. Considering again the unitarity of the CKM matrix, the following ratio of branching ratios can be defined for top quark decays with the three quark generations whereqrefers to all three possible down-type quarksd,sandb:

B(t→W b)

B(t→W q) = |V_{t b}|²

|V_{t d}|²+|V_ts|²+|V_{t b}|² =|V_{t b}|²≈1 .

Compliant with this definition of the ratio of branching fractions, such a ratio can also be written in terms of decay widths and partial decay widths. Direct measurements of this quantity were performed in the past resulting inΓW b/ΓW q=0.957±0.034[28]whereqcontains the sum of three down-type quark contributions. This value, obtained assuming the unitarity of the CKM matrix, is close to the above stated values and underlines once more the rarity of top quark decays into the lighter quarksd ands.

The fact that top quarks decay to bottom quarks in almost all cases can be exploited for the iden-tification of top quark decays in collider experiments. The b quarks from the top quark decays hadronise to form jets which include Bhadrons. These hadrons, like theBmesons, can possess a relatively long lifetime of about 1.5 ps leading to a flight length path exceeding 1 mm. This may result in a decay vertex of bjets that is displaced from the primary vertex as the initial interaction point where the top quark decayed. Such a secondary vertex allows for the differentiation between

bjets and jets originating from lighter quarks.

TheWboson as the second decay product of the top quark decays either into two light quarksq₁and q₂which then hadronise to light jets, called hadronic decay, or, alternatively, into a charged lepton

` and the corresponding antineutrino where `comprises electrons e, muonsµ and tau leptons τ, called leptonic decay. Approximate branching fractions B in the different decay channels of W bosons are presented in Table 2.6. There,n_C denotes a colour factor, as already introduced in Sec. 2.1.2, which is essential for a correct estimate and set ton^lep_C =1 andn^had_C =3.

2 . 2 T H E T O P Q U A R K

Final states eν_e µν_µ τν_τ ud/d¯ u¯ c¯s/s¯c

n_C 1 1 1 3 3

B ¹9

1 9

1 9

1 3

1 3

Table 2.6:Final states ofWboson decays and their roughly estimated branching ratios. The most probable final states according to the CKM matrix are given for the hadronic decays. Possible combinations are specified in the latter case, depending on the charge of the related initial Wboson.

Decay Channels of Top Quark Pairs

The twoW bosons from a t¯t pair decay independently, leading to three different combinations of the two W boson decays for the t¯t pair: all-jets, dileptonic andlepton+jets, where the latter specifies a channel with oneW boson decaying leptonically while the other decays into two jets.

The following description of these threet¯tdecay channels ignores the contribution from tau leptons as those are difficult to identify because of the different decays of tau leptons in either two lighter leptons or quarks. Thus, the decay probabilities ofW bosons decaying leptonically or hadronically are P_lep=2/9 andP_had=2/3, based on the numbers in Table 2.6. These probabilities allow for an estimate of the branching ratios oft¯t pair decays.

Theall-jets decay channelwith bothW bosons decaying hadronically has a large branching ratio ofB '2/3·2/3=4/9. But the six jet signature with two bjets resembles that of QCD multijet background impeding the clean separation of signal and background. Furthermore, the event re-construction is difficult in this channel. The correct assignment of all jets is hard to achieve, leading to larger combinatorial background, apart from the fact that the energy and angular resolution of leptons is better than the one of jets. In contrast to the other channels, however, no missing transverse momentum needs to be taken into account.

Thedileptonic decay channel, where both participatingW bosons decay leptonically into either elec-trons or muons, has a low branching ratio ofB '2/9·2/9=4/81. The signature is composed of two oppositely charged leptons having high transverse momenta, two bjets and missing transverse momentumE_T^miss. Energy and momentum conservation enable the reconstruction of the momen-tum sum of the involved neutrinos based on the contribution of missing transverse momenmomen-tum, delineated in Chapter 4.6. The signature is the cleanest of all possible t¯t decays as the multijet background is negligible. But, at the same time, the full event reconstruction is challenging because of the two undetectable neutrinos. In latest analyses atp

s=13 TeV, however, the dilepton channel yields most precise results despite these challenges.

The lepton+jets decay channelwith one hadronically and one leptonically decaying W boson is characterised by the following signature: four jets, out of which two arebjets, one isolated lepton

`=e,µand, due to the neutrino emerging from theW decay, missing transverse momentum. The resulting branching ratio amounts toB '2·2/9·2/3=8/27.

Figure 2.6: Feynman diagram for the decay of a t¯t pair in the lep-ton+jets decay channel.

This channel constitutes a compromise between the other chan-nels; it has an adequate branching ratio and a reduced amount of background events. It benefits from a sufficient rejection of multijet background and from the possibility to fully recon-struct these events since only one neutrino contributes so that no quantity remains underconstrained[74, 109]. This is why this final state, visualised in Fig. 2.6, is chosen for the mea-surement of the top quark decay width in this thesis.

The discussion of the three t¯t decay channels is facilitated by explicitly not considering tau leptons. In fact, they contribute to the measured signal as lepton+jets events may contain a tau lepton subsequently decaying leptonically. Further poten-tial migration effects are caused by dileptonic t¯t events with one top quark decaying into a tau lepton which decays into hadrons (migration to the lepton+jets channel) or caused by lepton+jets events where the lepton is a hadronically decaying tau lepton (migration to the all-jets channel).

Background Contributions

Several backgrounds contribute to the lepton+jets decay channel. One contribution arises from W+jets events caused by light jets misidentified as bjets or byW production in association with heavy flavour jets. Two LO Feynman diagrams for the W+jets production with one jet in the final state are shown by way of example in Fig. 2.7. Single top events constitute another relevant background. Those events including Feynman diagrams are discussed thoroughly in Sec. 2.2.1.

Diboson (W W,W Z,Z Z) andZ+jets events are smaller background sources which are taken into consideration as well. Details are given in Ch. 5.3.

Generic QCD multijet production is an important instrumental background originating from a high-p_T lepton within a jet emerging from the decay of a heavy flavour hadron in a jet or from a jet misidentified as a lepton.

Figure 2.7:W+1 jet production: QCD Compton process (left) andq¯qannihilation (right).

2 . 2 T H E T O P Q U A R K