2.5. Top Quark Decay
Once top quarks are produced, they decay rapidly via the weak force. The decay of the top quark within the SM, is via a W± boson to either one of the down, strange, or bottom quarks. The probability for a given quark from the top decay is described by the CKM matrix. The CKM matrix is theorized to contain a Vtb, which when squared, gives the probability of a top decaying to a bottom through the W boson. The value of |Vtb|2 is found to be almost 1; the exact value is shown in Eq. 2.32. This means that almost all of the top decays are to a bottom quark.
Using the two properties of the top quark: that the mass is large and that the Vtb
entry of the CKM matrix is almost unity, it is possible to calculate the lifetime of the top quark. Using only exclusive t → W b decays (|Vtb|2 = 1), one can calculate the expected top width given a certain top mass, assuming mb = 0 and mt= 170 GeV/c2 and mW = 80.4 GeV/c2 [53, 54]:
Γt= GF m3t 8π√
2 × |Vtb|2
1−m2W m2t
2
1 + 2m2W
m2t 1−2αs
3π 2π2
3 −5 2
≈1.5 GeV/c2. (2.40) In the equation,GF denotes the Fermi coupling constant. The top width of 1.5 GeV/c2 corresponds to a top lifetime of about 5·10−25 s. Since this means:
Γt>ΛQCD ≈200 MeV/c2, (2.41) the top quark decays before hadronizing. The hadronization time scale is of the order of 10−24s: an order of magnitude longer than the lifetime of the top quark. This makes the top quark of special interest to study. It does not hadronize with a second quark and is therefore a “bare” quark.
With top quarks decaying exclusively viat→W b, the classification of atdecay is solely based on the decay of the W boson. TheW boson has the possibility of either decaying hadronically or leptonically: W →qq¯orW →lνl. Also to note, the two quarks to which the W can decay hadronically are not of the same type since the pairs total charge must be equal to the original ±1 of the original W. Taking the t¯tdecay to be:
t¯t→W+W−b¯b, (2.42)
along with the two W bosons, there will always be two bottom quarks in all possible tt¯ decay channels. The probability for a W boson to decay hadronically is 2/3 compared to the possibility of decaying into a charged lepton and neutrino, which is only 1/3. In the first scenario, there are six possible outcomes compared to only three in the leptonic decay. From the decay of the two W bosons, the decay can be classified as:
alljets : both W bosons decay into two quarks each, leaving 6 jets in the final t¯t decay, two of which are bjets,
lepton + jets : oneW boson decays into two quarks and the other into a charged lepton and neutrino, resulting in two b quarks, two light quarks and a lepton and neutrino.
In this case, theW decay to tau is only partially considered since the tau will decay furthermore. Only the tau final states containing an electron or muon are considered, or
2. Physics
dilepton : both W bosons decay into a charged lepton and neutrino separately resulting in two b quarks, two charged leptons and two neutrinos.
The detailed decay possibilities along with the branching ratios are shown in Figure 2.9.
all-hadronic
Figure 2.9.: t¯t decay modes and their branching rations. The t¯t decay only depends on the possible decays of the twoW bosons. The decay is limited to three general categories: alljets, lepton+jets, or dilepton. Figures taken from [55].
It is possible to measure the top mass in all three channels of decay, each having its own advantages and disadvantages. The resulting topology of the events from each channel are slightly different. In the alljets channel, the two b quarks are among a six quark jet final state. This channel has a large branching fraction (≈ 46%) and no missing transverse energy (6ET) from an escaping neutrino. Even though this channel is very susceptible to variations in the Jet Energy Scale (JES), it allows the possibility to measure two W boson masses to obtain a handle on the scale. The alljets channel however has a very large background contribution from QCD multijets, events which are very difficult to model and must be understood from data.
The dilepton channel is the other extreme. In this scenario, two charged leptons with their neutrino pairs are created alongside the twobquarks. There is a very small branching fraction of t¯tdecays in this channel, only about 9%. There is also a large 6ET component and limited kinematic knowledge as the system is under-constrained. The dilepton channel however has a very clean signature. As a negative, the channel has no handle on the JES as both W bosons decay to leptons only.
The last channel, lepton + jets or single lepton, is a mixture of the two extremes. In the lepton + jets channel one W decays leptonically and the other hadronically, resulting in two light quarks, one charged lepton and one neutrino alongside the two bquarks. The branching fraction is still quite large, even when only the τ + jets decays where the tau decays leptonically are considered. The signature is also clean, comprising of two light jets, two b jets, a charged lepton and some 6ET. The channel suffers from effects due to variations in the JES, but still contains a hadronically decaying W boson in order to
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2.5. Top Quark Decay
measure the scale. The JES, however, is still one of the largest challenges to properly determine the top mass in this channel. The lepton + jets decay channel is shown in Figure 2.10.
Figure 2.10.: Diagram of the t¯t decay into the lepton + jets channel. In this decay scenario, oneW decays into two light quarks whereas the secondW decays into a charged lepton and a neutrino. The original twob quarks from the t→W b highlight the signature. This Figure is taken from [55].
A candidate t¯t event at ATLAS, decaying into the lepton + jets channel where the reconstructed lepton is an electron, is found in Figure 2.11. The decay contains four jets, one electron and a significant amount of missing energy from the neutrino.
Figure 2.11.: Candidate t¯t decay into the lepton + jets channel at ATLAS. Four jets are reconstructed along with the electron, which contains a single track.
The dashed line shows the direction of the missing energy in the transverse direction, representing the neutrino. Figure is taken from [56].
2. Physics