The top quark is the heaviest known elementary particle, even heavier than the Higgs boson. Its large mass is the reason for its very short lifetime. In the SM the top quark has the same quantum numbers and interactions as all other up-type quarks. It is the weak isospin partner of the b quark with spin 1/2 and electric charge Qt= +2/3. The left-handed top quark is the upper component of the weak isospin doublet and the right-handed component is a weak isospin singlet. It is a colour triplet with respect to the SU(3)Cgauge group. From the theory side, the top quark is absolutely needed to ensure cancellation of the chiral anomaly in the SM and therefore to ensure its consistency as a quantum field theory. An accurate knowledge of its properties (mass, couplings, production cross section, decay branching ratios, etc.) can bring key information on fundamental interactions at the electroweak breaking scale and beyond.
Top quark mass and lifetime
Measurements of the top quark mass, mt, using kinematic properties of the decay
products of the top quark, i.e., using direct approaches, have been performed by the ATLAS, CDF, CMS, and D∅ Collaborations using a variety of experimental techniques.
The first world combination of mt measurements was performed in 2014 [10] and
taking into account the correlations between the colliders, experiments, and analysis channels for all sources of systematic uncertainty considered. The combined value is mt= 173.34±0.27(stat)±0.71(syst) GeV, which corresponds to a relative uncertainty of 0.44%. The latest results from averaged 7-8 TeV data at CMS get even a more precise measurement ∼0.5 GeV [13]. Expectations range from a pessimistic 500 MeV after the complete LHC program to 200 MeV. These prospects do not include the uncertainty in the interpretation of the direct mass measurement as the pole mass [14]. On the other hand the most precise measurement of the top quark pole mass to date, with data collected by ATLAS at 7 TeV and luminosity of 4.6 fb−1, is found in Reference [15]. They show that the normalized differential cross section of the t¯t+ 1jet system as a function of its invariant mass can be used for a precise measurement of the top quark mass using the pole-mass scheme at NLO theoretical accuracy in QCD.
The lifetime τ and the related resonance width Γ = 1/τ are primary characteristics of any particle. A small value of the top lifetime τtis expected due to its large mass and the large value of Vtb. The width of the top quark is computed in the SM to be 1.32 GeV with about 1% uncertainty [16] which translates into a top quark lifetime of (τt ≈ 5 × 10−25s) that is much smaller than the typical time for formation of
QCD bound state hadrons (τQCD ≈ 1/ΛQCD ≈ 3 × 10−24s). Therefore hadrons
containing a top quark are not expected to exist. It is impossible to measure such a short lifetime directly by measuring the distance between creation and decay. An alternative approach used for strongly interacting decays is the measurement of the
1.3. The Top Quark 24 width. The most precise measurement of the top quark width was obtained by CMS [17] using the indirect method proposed by D∅ experiment [18], Γt = 1.36± 0.02 (stat) +0.14
−0.11 (syst) GeV, in good agreement with the SM prediction.
Vtb element of CKM matrix and top quark decay
The matrix element Vtbis close to unity while the elements Vtdand Vtsare very small ( |Vtd| = (8.4 ± 0.6) × 10−3,|Vts| = (40.0 ± 2.7) × 10−3 [3]). A global fit in the SM gives |Vtb| = 0.999146 +0.000021−0.000046 [3]. Any experimental deviation from this value will be evidence for new BSM physics. The large mass and the small mixing of the top quark cause the top quark to decay to a W boson and b quark with a probability close to 100%. Feynman diagrams of the top and anti top quark decays are shown in Figure
1.12.
(a) t → W+b (b) t → W+b
Figure 1.12: Top and anti-top quark decay.
Since the top quark decays to a W boson and a b quark, the final state is determined by the way that the W boson decays. The W boson can decay into a lepton plus its associated neutrino or in a light quark pair. Hence t¯t pair decays can be classified according to the decays of the two W coming from these tops. If both W bosons decay to a lepton plus a neutrino, the final state has two leptons, two b-jets and missing transverse energy (ET) carried by the two neutrinos (dileptonic channel). If one W decays to a lepton and the other to quark pairs (semi-leptonic channel or “lepton+jets”), the final state is one lepton, four quarks (of which two are b-quarks) and a neutrino. If both W bosons decay to quarks (fully-hadronic channel), the final state has six quark jets. The three final states correspond to 10.5%, 43.8% and 45.7% of t¯t events, respectively.
Top quark electroweak couplings
At the LHC, significant progress has been achieved in the study of the processes p¯p→ t¯tγ, t¯tZ, and t¯tW , which together with t¯tH associated production, will provide
1.3. The Top Quark 25
Figure 1.13: t¯t pair branching fractions.
further information on the top-quark electroweak couplings. The prospects study presented by [19] is an analysis at leading order QCD. The analysis carried out in [20] suggests that higher-order effects in the theory may allow for an improvement of the LHC precision by up to 40% the precision. Electroweak couplings are measured also in single t quark production. In the effective field theory approach, assuming SU (2)L× U(1)Y gauge symmetry for the operators, the relation
δgLtbW gtbW L ≈ 0.35δg Z L gZ L (1.19) can be established. Here gtbW
L is the charged current coupling of the decay t → W b.
The CMS Collaboration [21] reports a precision for the t-b transition probability Vtb of about 4%. In the Standard Model Vtb is identical to gLtbW. Hence, by means
of Eq. 1.19 the coupling of left-handed t quarks to the Z boson can be derived to
a precision of order 11%. Noting that σ(pp → ¯ttZ) ∝ (gZ
L)2+ (gZR)2 this allows in principle also for deriving (gZ
R)2, albeit with a poor precision given that (gLZ)2 (gRZ)2. Loop corrections in heavy flavour physics as e.g. in the processes b → sγ, B → µ+µ− or K → µ+µ−, respectively, may also lead to competitive determinations of δgZ
L [22]. However, again gZ
R can only be constrained rather poorly. In e+e−colliders with√s > 2m
ttop quark pairs are produced in e+e−→ Zγ → t¯t, giving direct access to the EW couplings. Note at this point that the interference between the γ and the Z in case of e+e−→ t¯t will allow for measuring the sign of the form factors that will be unnoticed in associated ¯ttZ at the LHC.
In Chapter 6 the potential measurements of the top quark couplings to the elec-
troweak gauge bosons Z and γ at e+e− colliders, as a probe for BSM physics, are
1.3. The Top Quark 26