1

61. Top Quark

61. Top Quark
Revised September 2023 by T.M. Liss (City Coll. of New York), F. Maltoni (CP3 U. catholique deLouvain; Bologna U.) and A. Quadt (Göttingen U.).

61.1 Introduction and SM theory overview
In the Standard Model (SM), the left-handed top quark is the Q = 2/3, T3 = +1/2 memberof the weak-isospin doublet containing the bottom quark, while the right-handed top is an SU (2)Lsinglet (see, e.g., the review “Electroweak Model and Constraints on New Physics” here). Its
phenomenology is driven by its large mass, mt ' √v2 , where v = 246 GeV is the vacuum expectation
value of the Higgs field, i.e., it is the only quark whose Yukawa coupling to the Higgs boson is oforder unity. As it is heavier than the W boson, it is the only quark that decays semi-weakly into areal W boson and a b quark. This results in a lifetime that is shorter than the time that is needed
for strong interactions to modify its properties or to bind it into a hadron. In this respect, the top
is the only quark that, in its brief life, behaves as a free one. Because of its large mass and Yukawa
coupling to the Higgs boson, it also gives important contributions (via loops) to Standard Model
precision observables measured at lower scales.
For these reasons, the top quark provides a unique laboratory to test our understanding of matter and fundamental interactions at the ElectroWeak (EW) symmetry-breaking scale and beyond.
In addition, since it is abundantly produced at the Large Hadron Collider (LHC), a precise knowledge of its properties (mass, couplings, production cross sections, decay branching ratios, etc.) canbe achieved. This review provides a concise discussion of the experimental and theoretical issues
involved in the determination of the top-quark properties.
61.1.1 Properties
61.1.1.1 Mass
The top quark mass determines to a large extent the unique phenomenology of this quark. In the
SM quark masses are derived parameters from the Yukawa coupling and the vacuum expectation
value. At the loop level, with the Higgs boson discovery and per mil measurement of its mass,
the values of the W -boson and top quark mass are correlated, so that their precise determinations
provides a strong test of the SM (see Section 10 "Electroweak Model and constraints on new physics"of this Review). At present there is some tension at the 1.7 σ level, between the indirect top quark(pole) mass determination from electroweak precision data (176.12 ± 1.9 GeV) and the combinationof direct measurements at the LHC that yields 172.52 ± 0.14(stat.) ± 0.30(syst.) GeV [1].
The top mass value is also critical in the issue of vacuum stability in the SM [2–4]. At highscales, the Higgs quartic coupling λ evolves to increasingly small values as mt grows. Abovemt = 171 GeV, i.e., very close to the most precise measurements, λ becomes negative at the Planckscale leading to a meta-stable electroweak vacuum, while for slightly larger values, mt > 176 GeV
the electroweak vacuum would become unstable. Current top-quark measurements therefore point
to a Higgs quartic coupling which is nearly vanishing at the Planck scale. While being quite
suggestive, in absence of a clear UV picture this argument allows only to conclude that comparison
between our best SM predictions and the data does not imply new physics below the Planck scale(see Section 11.2.3 of "Status of Higgs Boson Physics" in this Review).
Given its importance and the large samples of top quarks produced at the LHC, the top mass
determination has been one of the most important goals in the precision measurement campaignof the ATLAS and CMS collaborations. The basic methodology rests on the idea of fitting mt dependent kinematic distributions to fully-exclusive (Monte Carlo) predictions, via the full or partial
reconstruction of the system of the t and t̄ decay products. These are called “direct measurements”
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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61. Top Quark2

and aim at a target accuracy in the permil range. With an absolute uncertainty of order or better
than ΛQCD , however, a clear relation between the extracted mass and a well defined quantum field
theory parameter of the underlying theory has become necessary.
Several mass parameter definitions exist with a precise field-theoretical meaning, that can beorganised in two broad classes, the long-distance ones, such as the “pole mass”, and short-distancemasses, such as MS mass. A mass definition, the MSR mass [5], exists that interpolates between
the two. The one measured through direct measurements is sometimes referred to as “Monte
Carlo” mass. Several other observables have been put forward that could be expressed in terms ofwell-defined masses and then overcome the problems of the direct measurements, yet with a target
accuracy not quite competitive with the direct determination.
A top mass cannot be defined solely in terms of the mass of the system of its decay products:
the top quark is a colored object, therefore it cannot be an asymptotic state of the theory andno final-state hadronic system can be unambiguously associated with it. On the other hand, final
state observables such as those arising from its decay, can be related to the top mass throughcomputations, which have perturbative as well as non-perturbative components, as Monte Carlogenerators.
From a purely theoretical (calculational) point of view, the top mass parameter is defined withina given renormalization scheme, since divergent perturbative corrections arise order by order in
perturbation theory, and need to be subtracted. The pole mass scheme prescribes to subtract thedivergent mass corrections so that the pole in the quark propagator remains fixed order by order in
perturbation theory. The MS scheme prescribes to employ dimensional regularization and subtract
the pure 1/ pole in the divergent mass correction. In doing so, the corresponding mass becomes
scale dependent. In this scheme the pole in the top propagator receives corrections at all orders in
perturbation theory. This scheme has the advantage that it makes the relation between the massand the Yukawa coupling straightforward in the SM and is independent from non-perturbative
corrections.
The relation between the top pole mass mpoleand mMS
up to four loops reads [6]
t
t

2
3
4
mpole
= mMS
t (mt )[1 + 0.4244 αs + 0.8345 αs + 2.375 αs + (8.49 ± 0.25) αs ] ,t(61.1)(6)

which for αs = αs (m) = 0.1088 and mpole= 172.5 GeV gives mMSt (mt ) = 162.69 ± 0.006 GeV.
t
The two definitions lead to perturbatively equivalent theories: a perturbative expression of thepole mass in terms of the mMS mass can be translated to a physical result in the pole mass scheme
into the corresponding physical result in the MS scheme. However, the relation above has only
a perturbative meaning, as the two masses differ by non-perturbative, long-distance effects. The
difference between the top pole mass and the mass extracted in direct measurements, ∆mMC , arises
due to non-perturbative effects, that are currently modelled by shower Monte Carlo programs. It is
expected to be of order Q0 · αs (Q0 ) with Q0 ∼ 1 GeV and estimated of order 0.5 GeV. An overview
on the on-going efforts to precisely define and to estimate the uncertainties of the top mass can befound in Refs. [7, 8].
61.1.1.2 Couplings
The SM couplings involving top quarks are of two types: gauge couplings, which are universal,
and Yukawa couplings, which instead depend on the generation. Following the notation of Sections
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61. Top Quark

3

9 and 10 of this Review, after EWSB and in the mass eigenstate basis, top quark interactions readµLSM
= ψ̄t i∂/ − mt ψt − gs ψ̄t γ µ tC ψt AC(61.2)tµ − eQt ψ̄t γ ψt Aµ


g
g
t 5
γ ψ t Zµ− √ Ψ̄ γ µ (1 − γ 5 )(T + Wµ+ + T − Wµ− )Ψ −
ψ̄t γ µ gVt − gA
2 cos θW
2 2mt−
H ψ̄t ψt ,v
where in the first line we include the coupling to the SU (3) field Aµ , and Ψ = (t, b0 ) with b0 =Vtb b + Vts s + Vtd d. There are no neutral flavor changing interactions in the SM at tree level.



Table 61.1: List of SMEFT operators at dimension six, assuming U (2)q × U (2)u × U (2)d flavor
symmetry. For more details on notation and conventions, see reference in the text.
Operator
1(ijkl)Oqq

3(ijkl)Field content
Four-quark(q̄i γ µ qj )(q̄k γµ ql )Oqq(q̄i γ µ τ I qj )(q̄k γµ τ I ql )1(ijkl)Oqu8(ijkl)Oqu1(ijkl)Oqd
8(ijkl)Oqd(ijkl)Ouu
1(ijkl)Oud
8(ijkl)Oud‡ O 1(ijkl)
quqd‡ O 8(ijkl)
quqd(q̄i γ µ qj )(ūk γµ ul )(q̄i γ µ T A qj )(ūk γµ T A ul )(q̄i γ µ qj )(d¯k γµ dl )(q̄i γ µ T A qj )(d¯k γµ T A dl )(ūi γ µ uj )(ūk γµ ul )(ūi γ µ uj )(d¯k γµ dl )(ūi γ µ T A uj )(d¯k γµ T A dl )lq
(ijkl)
Olu(ijkl)
Oeq(ijkl)Oeu‡ O 1(ijkl)
lequ‡ O 3(ijkl)
lequ‡ O (ijkl)
ledq(¯li γ µ lj )(ūk γ µ ul )(ēi γ µ ej )(q̄k γ µ ql )(ēi γ µ ej )(ūk γ µ ul )(¯li ej ) ε (q̄k ul )(¯li σ µν ej ) ε (q̄k σµν ul )(¯li ej )(d¯k ql )(q̄i uj ) ε (q̄k dl )(q̄i T A uj ) ε (q̄k T A dl )Two-quark operators‡ O (ij)q̄i uj ϕ̃ (ϕ† ϕ)
uϕ
←
→
1(ij)
Oϕq
(ϕ† iD µ ϕ)(q̄i γ µ qj )
←
→
3(ij)
Oϕq
(ϕ† iD Iµ ϕ)(q̄i γ µ τ I qj )
←
→
(ij)
Oϕu
(ϕ† iD µ ϕ)(ūi γ µ uj )‡ O (ij)(ϕ̃† iDµ ϕ)(ūi γ µ dj )ϕud
‡ O (ij)uW‡ O (ij)dW‡ O (ij)uB‡ O (ij)uG

Operator Field content
Two-quark-two-lepton
1(ijkl)Olq(¯li γ µ lj )(q̄k γ µ ql )3(ijkl)O(¯li γ µ τ I lj )(q̄k γ µ τ I ql )Baryon- and lepton-number-violating(q c iα εqjβ )(uc kγ el ) αβγ
(q c iα εqjβ )(q c kγ εll ) αβγ
(q c iα τ I εqjβ )(q c kγ τ I εll ) αβγ
(dc iα ujβ )(uc kγ el ) αβγ

‡ O (ijkl)
qqu‡ O 1(ijkl)
qqq‡ O 3(ijkl)
qqq‡ O (ijkl)
duuI(q̄i σ µν τ I uj ) ϕ̃WµνI(q̄i σ µν τ I dj ) ϕWµν(q̄i σ µν uj ) ϕ̃Bµν(q̄i σ µν T A uj ) ϕ̃GAµν

In absence of evidence for physics beyond the SM at the weak scale or below, the Standard
Model Effective Field Theory (SMEFT) [9–11] provides a simple and consistent framework tosystematically parameterise possible deviations from the SM predictions in the interactions among
the known particles, using minimal theoretical assumptions. It amounts to extend the Lagrangianof the SM, by all higher-dimensional operators that respect the gauge symmetry
LSMEFT = LSM +ND(D) (D)
XX
C O
i

D>4 i
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i

ΛD−4

,

(61.3)

61. Top Quark

4(D)

where D is the dimension of the operator Oi and Λ provides an upper bound for the scale of new
physics. An EFT model is generally characterised by power counting rules that identify a hierarchy
among operators. In the case of the SMEFT, a minimal approach is considered where the large
scale Λ provides a universal suppression factor for the higher dimensional operators.
The currently adopted parametrization for SMEFT interpretations of top quark measurements
relies on the Warsaw basis of gauge-invariant dimension-six operators [11] and it is presented in
Tab. 61.1 as detailed in Ref. [12] (see [13, 14] for early discussions of top-quark related operators).
For convenience, often specific degrees of freedom are identified from combinations of Warsawbasis operator coefficients aligned with the directions of the EFT parameter space which appear
in given processes, in interferences with SM amplitudes, and in top-quark interactions with someof the gauge boson mass eigenstates. Model implementations are available for tree-level and evenone-loop Monte Carlo simulations.
The definitions of the SMEFT operators can be organised in four categories: Four-quark, twoquark, two-quark-two-lepton, and baryon-lepton-number violating operators. The overwhelming
number of four-fermion operators is tamed by adopting simplifying assumptions about beyond-thestandard-model flavor structures. A baseline flavor scenario in the quark sector and motivated by
the minimal flavor violation (MFV) ansatz [15–17] corresponds to imposing a U (2)q ×U (2)u ×U (2)dsymmetry among the first two generations. In this case the following numbers of degrees of freedom
are produced for the operators of each category of field content:
four heavy quarks
two light and two heavy quarks
two heavy quarks and bosons
two heavy quarks and two leptons

11 + 2 CPV
14
9 + 6 CPV
(8 + 3 CPV) × 3 lepton flavors

where we counted separately CP-conserving and CP-violating (CPV) parameters. They are collected in Table 61.1. Other less restricted scenarios, such as that obtained by imposing U (2)q+u+dsymmetry featuring additional 10 + 10 CPV degrees of freedom, or more restricted ones, such as
top-philic scenario where it is assumed that new physics couples dominantly to the left-handed
doublet and right-handed up-type quark singlet of the third generation as well as to bosons, featuring only 19+6 (CPV) degrees of freedom, are often considered. It is also customary to analyse
top-quark flavor-changing neutral currents (FCNCs) separately as, at the tree level, they enter only
quadratically. More details can be found in Ref. [12].
61.1.2 Decay
As other unstable elementary particles, the lifetime of the top quark, and therefore its width, isperturbatively calculable within the SM. With a mass above the W b threshold, and |Vtb |  |Vtd |,|Vts |, the decay width of the top quark is expected to be dominated by the two-body channel
2 /m2 , the width predicted in the
t → W b. Neglecting terms of order m2b /m2t , αs2 , and (αs /π)MWt
SM at NLO is [18]:GF m3
Γt = √ t
8π 2

M2
1− W
m2t

!2

M2
1+2 W
m2t

!"

2αs
1−
3π

2π 2 5
−
3
2

!#

,

(61.4)

where mt refers to the top-quark pole mass. The order αs2 QCD corrections to Γt as well as the EW
NLO corrections are known [19, 20], thereby improving the overall theoretical accuracy to better
than 1%. As a result, between mt = 170 GeV and 175 GeV the width changes from 1.258 GeV to
1.394 GeV, with a linear dependence (αs (MZ ) = 0.1179 and mW = 80.377 GeV). At the reference
value of mt = 172.5 GeV, Γt = 1.326 GeV.
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61. Top Quark

With its correspondingly short lifetime of about 0.5×10−24 s, the top quark is expected to decay
before top-flavored hadrons or tt-quarkonium-bound states can form [21]. In fact, since the decay
time is close to the would-be-resonance binding time, a peak will be visible in e+ e− scattering at
the tt threshold [22] and it is in principle present (yet very difficult to measure) in hadron collisions
too [23, 24].
As mentioned above, flavor changing neutral interactions are allowed starting at one loop. The
branching ratios to charm final state are estimated to be [25, 26]:
BrSM (t → gc) = 5 · 10−12 , BrSM (t → gu) = 4 · 10−14 ,BrSM (t → γc) = 5 · 10−14 , BrSM (t → γu) = 4 · 10−16 ,BrSM (t → Zc) = 1 · 10−14 , BrSM (t → Zu) = 7 · 10−17 ,BrSM (t → Hc) = 3 · 10−15 , BrSM (t → Hu) = 2 · 10−17 .
61.1.3 Production
61.1.3.1 Pair production
In hadron collisions, top quarks are produced dominantly in pairs through the processes qq → tt
and gg → tt, at leading order in QCD. At the Tevatron (pp̄ at 1.96 TeV) approximately 85% of
the production cross section is from qq annihilation, with the remainder from gluon-gluon fusion.
√
Conversely, at the LHC about 90% (80%) of tt̄ production is from gluon-gluon fusion at s = 13 TeV√( s = 7 TeV).
Predictions for the top-quark production total cross sections are available at next-to-next-to
leading order (NNLO) [27, 28], also including next-to-next-to-leading-log (NNLL) soft gluon resummation. Assuming a top-quark mass of 173.3 GeV, close to the Tevatron + LHC combination [29], the resulting theoretical prediction of the top-quark pair cross-section at NNLO+NNLL√+0.17
accuracy at the Tevatron at s = 1.96 TeV is σtt̄ = 7.16+0.11−0.20 −0.12 pb where the first uncertainty is from scale dependence and the second from parton distribution functions. At the+4.8 +6.1
LHC, assuming a top-quark mass of 172.5 GeV the cross sections are: σtt̄ = 179.6−6.2−6.1 pb at
√
√
√
+8.0
+20.5 +21.0
s = 7 TeV, σtt̄ = 256.0+6.7
pb
at
s
=
8
TeV,
σ
=
833.9
pb
at
s
=
13 TeV,tt̄−8.9−30.0 −21.0√ −8.0√+22.8+24.1 +24.1
σtt̄ = 923.6+22.6
pb
at
s
=
13.6
TeV,
and
σ
=
985.7
pb
at
s
=
14
TeV
[27],
where
tt̄
−33.4 −22.8−35.7 −24.1
the first uncertainty is from scale dependence and the second from parton distribution functionsand αs .
The identification of tt̄ events at a collider has to take into account that top quarks decay at
microscopic scales and only their decay products can be detected. The final states for the leading
pair-production process can be divided into three classes:
A. tt → W + b W − b → qq 0 bq 00 q 000 b,
B. tt → W + b W − b → qq 0 b`− ν ` b + `+ ν` b q 00 q 000 b,
C. tt → W + b W − b → `+ ν` b `0− ν `0 b.

(45.7%)(43.8%)(10.5%)The quarks in the final state evolve into jets of hadrons. A, B, and C are referred to as the
all-hadronic, lepton+jets (`+jets), and dilepton (``) channels, respectively. Their relative contributions, including hadronic corrections, are given in parentheses assuming lepton universality. While` in the above processes refers to e, µ, or τ , most of the analyses distinguish the e and µ from theτ channel, which is more difficult to reconstruct. Therefore, in what follows, we will use ` to referto e or µ, unless otherwise noted. Here, typically leptonic decays of τ are included. In addition
to the quarks resulting from the top-quark decays, extra QCD radiation (quarks and gluons) fromthe colored particles in the event can lead to extra jets.
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61. Top Quark

The number of jets reconstructed in the detectors depends on the decay kinematics, as wellas on the algorithm for reconstructing jets used by the analysis. Information on the transverse
momenta, pT of the neutrinos is obtained from the imbalance in transverse momentum measured
in each event, the missing pT , whose magnitude is also called missing transverse energy, ET .
61.1.3.2 Single top production
Electroweak single top-quark production mechanisms, namely from qq 0 → tb [30], qb → q 0 t [31],mediated by virtual s-channel and t-channel W -bosons, and W t-associated production, throughbg → W − t, lead to somewhat smaller cross sections. For example, t-channel production, while suppressed by the weak coupling with respect to the strong pair production, is kinematically enhanced,
resulting in a sizeable cross section both at Tevatron and LHC energies. At the Tevatron, the tand s-channel cross sections for top quarks are identical to those for antitop quarks, while at the
LHC they are not, due to the charge-asymmetric initial state. NNLO cross sections for t-channel
single top-quark production (t + t̄) are calculated for mt = 173.2 GeV to be 2.08+0.04+0.08−0.03−0.10 pb in pp√
collisions at s = 1.96 TeV, where the first uncertainty is from scale dependence and the second
from parton distribution functions. [32]. A calculation at NNLO accuracy for the t-channel crosssection at the LHC has first appeared in [33], superseded by more recent calculations [32,34] which√+0.9 +1.1+0.6
predict (mt = 172.5 GeV): σt+t̄ = 30.3+0.4
pb at
pb at s = 5.02 TeV, σt+t̄ = 63.7−0.5
−0.3
−0.4
√
√
√ −0.7+1.1 +1.4+2.4 +3.3
s = 7 TeV, σt+t̄ = 84.3−0.7 −0.9 pb at s = 8 TeV, σt+t̄ = 214.2−1.7 −2.0 pb at s = 13 TeV,√√
+3.4
+2.7 +3.5
σt+t̄ = 232.2+2.6
s = 13.6 TeV, and σt+t̄ = 244.5−2.0
s = 14 TeV, where−1.7 −2.2 pb at−2.5 pb at
the first uncertainty is from scale dependence and the second from parton distribution functionsand αs . The corresponding fraction of top quarks are 67%, 65%, 65%, 63%, 62%, and 62%.
For the s-channel, NNLO approximated calculations yield 1.03+0.05−0.05 pb for the Tevatron [35]. An
+0.03
+0.06
+0.06
NNLO calculation gives (t + t̄), 3.00−0.03
pb, 3.61+0.03
pb,
6.84
−0.03
−0.03 pb, and 7.25−0.04 pb, for√s = 7, 8, 13, 13.6 TeV at the LHC, respectively, where the uncertainty is from scale dependence
only. While negligible at the Tevatron, at LHC energies W t-associated production becomes rel√
+0.7
evant. At s = 7, 8, 13, 13.6, 14 TeV, an NLO+NLL calculation gives (t + t̄), 17.1+0.4−0.3 −0.7 pb,+0.6 +0.9+1.9 +2.2+2.0 +2.3+2.2 +2.5
24.4−0.5−0.9 pb, 79.3−1.8 −2.2 pb, 87.9−1.9 −2.4 pb, and 93.8−2.1 −2.5 pb, respectively, where the first
uncertainty is from scale dependence and the second from parton distribution functions and αs . In
this process, an equal proportion of top and anti-top quarks is foreseen. [36].
Assuming |Vtb |  |Vtd |, |Vts | (see the Section “The CKM Quark-Mixing Matrix” in this Review
for more information), the cross sections for single top production are proportional to |Vtb |2 , and no
extra hypothesis is needed on the number of quark families or on the unitarity of the CKM matrix
in extracting |Vtb |. Separate measurements of the s- and t-channel processes provide sensitivity tophysics beyond the Standard Model [37].
The identification of top quarks in the electroweak single top channel is much more difficult
than in the QCD tt channel, due to a less distinctive signature and significantly larger backgrounds,
mostly due to tt and W +jets production.
61.1.3.3 Monte Carlo predictions
Fully exclusive predictions via Monte Carlo generators for the tt̄ and single top production
processes at NLO accuracy in QCD, including top-quark decays and possibly off-shell effects areavailable [38,39] through the MC@NLO [40] and POWHEG [41] methods. Recently, the first Monte
Carlo implementation of the NNLO QCD computation has become available [42].
61.1.3.4 Associated production
Besides fully inclusive QCD or EW top-quark production, more exclusive final states can beaccessed at hadron colliders, whose cross sections are typically much smaller, yet can provide key
information on the properties of the top quark. For all relevant final states (e.g., tt̄V, tt̄V V with
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61. Top Quark

V = γ, W, Z, tt̄H, tt̄+jets, tt̄bb̄, tt̄tt̄) automatic or semi-automatic predictions at NLO accuracy
both in QCD and EW expansions, also in the form of event generators are available (see thereview “Monte Carlo event generators” for more information). Results for total cross sections at
NLO+NLL in QCD and NLO EW, are available for tt̄Z, tt̄W , tt̄H [43] and for tt̄tt̄ [44]. Recently,
approximate NNLO QCD predictions for and tt̄H and tt̄W have become available [45, 46].

61.2 Top-quark and precision SM tests
Since the discovery of the top quark, direct measurements of tt production have been madeat seven center-of-mass energies in pp or pp̄ and in pP b or P bP b collisions, providing stringent
tests of QCD and electroweak theory including parton distribution functions, the strong coupling
αs and the dependence on the top-quark mass mtop . The first measurements were made in Run I√
at the Tevatron at s = 1.8 TeV. In Run II at the Tevatron relatively precise measurements√
were made at s = 1.96 TeV. Finally, beginning in 2010, measurements have been made at the√√√
LHC at s = 7 TeV, s = 8 TeV, and s = 13 TeV, later also in dedicated low energy runs at√√
s = 5.02 TeV in pp and at s = 5.02 TeV in P bP b collisions and at 8.16 TeV in pP b collisions and√recently at s = 13.6 TeV in pp. With the enormous number of over 120 million top quark pairs
produced at the LHC, we are entering the era of high precision measurements in the top quark
sector.
Production of single top quarks through electroweak interactions has now been measured with√√√good precision at the Tevatron at s = 1.96 TeV, and at the LHC at s = 5 TeV, s = 7 TeV,√√
s = 8 TeV, and also at s = 13 TeV. Measurements at the Tevatron have managed to separate
the s- and t-channel production cross sections, and at the LHC, the tW mechanism as well, though
the t-channel is measured with best precision to date. The measurements allow an extraction of the
CKM matrix element Vtb . Also more exclusive production modes and top-quark properties havebeen measured in single-top production.
With approximately 10 fb−1 of Tevatron data, and 255 pb−1 at 5 TeV, almost 5 fb−1 at 7 TeV,
20 fb−1 at 8 TeV, 139 fb−1 at 13 TeV and 29 fb−1 at 13.6 TeV at the LHC, many properties of
the top quark have been measured with high precision. These include properties related to the
production mechanism, such as tt spin correlations, forward-backward or charge asymmetries, anddifferential production cross sections, as well as properties related to the tW b decay vertex, suchas the helicity of the W -bosons from the top-quark decay. Also studies of the tt̄bb̄, tt̄tt̄, tt̄γ, tt̄Z,
tt̄h, th, tZq, tγq or tW Z processes and the corresponding vertices as well as contact interactions
have been made, most yielding observations, while first evidence for tW Z has been found and this still far from evidence. Those processes probe genuinely new aspects of the top-quark such as
electroweak couplings to neutral gauge bosons or possibly four-top-quark production via contact
interactions. Recently, also first studies for the very fundamental concept of quantum entanglement
in top-quark production were pursued. In addition, many searches for physics beyond the Standard
Model are being performed with increasing reach in both production and decay channels.
In the following sections we review the current status of measurements of the characteristics ofthe top quark.
61.2.1 Top-quark production
61.2.1.1 tt production
Fig. 61.1 summarizes the tt production cross-section measurements from both, the Tevatronand LHC. Please note that some cross section measurements at the LHC have luminosity-related
uncertainties which have improved in the meantime [47]. The latest measurement from DØ [48]√(pp̄ at s = 1.96 TeV), combining the measurements from the dilepton and lepton plus jets final+0.57
states in 9.7 fb−1 , is 7.26 ± 0.13 (stat.)−0.50(syst.) pb (7.5%). From CDF the most precise
measurement made [49] is in 8.8 fb−1 in the dilepton channel requiring at least one b-tag, yielding
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61. Top Quark

7.09 ± 0.84 pb. Both of these measurements assume a top-quark mass of 172.5 GeV/c2 . The
dependence of the cross-section measurements on the value chosen for the mass is less than thatof the theory calculations because it only affects the determination of the acceptance. In someanalyses also the shape of topological variables might be modified.
Combining the recent cross section measurements with older ones in other channels yields
σtt̄ = 7.63 ± 0.50 pb (6.6%) for CDF, σtt̄ = 7.56 ± 0.59 pb (7.8%) for DØ and σtt̄ = 7.60 ± 0.41 pb(5.4%) for the Tevatron combination [50]. The contributions to the uncertainty are 0.20 pb fromstatistical sources, 0.29 pb from systematic sources, and 0.21 pb from the uncertainty on the
integrated luminosity. The combined result is in good agreement with the SM expectation of+0.28
7.35−0.33
pb at NNLO+NNLL in perturbative QCD [27] for a top mass of 172.5 GeV/c2 .
CDF has measured the tt̄ production cross section in the dilepton channel with one hadronicallydecaying tau in 9.0 fb−1 , yielding σtt̄ = 8.1 ± 2.1 pb. By separately identifying the single-tau andthe ditau components, they measure the branching fraction of the top quark into the tau lepton,
tau neutrino, and bottom quark to be (9.6 ± 2.8)% [51]. CDF has also performed measurements ofthe tt̄ production cross section normalized to the Z production cross section in order to reduce theimpact of the luminosity uncertainty [52].
DØ has performed a measurement of differential tt cross sections in 9.7 fb−1 of lepton+jets data
as a function of the transverse momentum, and absolute value of the rapidity of the top quarks aswell as of the invariant mass of the tt pair [53]. Observed differential cross sections are consistent
with SM predictions.
The LHC experiments ATLAS and CMS use similar techniques to measure the tt̄ cross sectionin pp collisions. The most precise measurements typically come from the dilepton channel, and inparticular the eµ channel. In order to test consistency of the cross-section measurements with somesystematic uncertainties cancelling out while testing pQCD and PDFs, cross-section ratios between
measurements at 7 TeV and at 8 TeV are performed and quoted in several cases. In other cases, thecross-section ratio between tt̄- and Z-production is determined as that is independent of luminosity
uncertainties, but keeps its sensitivity to the ratio of gluon versus quark PDFs. These experimental+0.20
results should be compared to the theoretical calculations at NNLO+NNLL that yield 7.16−0.23
pb√
2
for top-quark mass of 173.3 GeV/c at s = 1.96 TeV‘ [27], for top-quark mass of 172.5 GeV/c2√√
σtt̄ = 68.2+5.2
s = 5 TeV [54], σtt̄ = 158+23
s = 7 TeV [55, 56], σtt̄ = 253+13−15.4 pb at−24√pb at−15 pb√+46
at s = 8 TeV [27, 54, 57–60], σtt̄ = 832.0−51 pb at s = 13 TeV [27, 54, 58–60], σtt̄ = 924+32−40 pb√at s = 13.6 TeV [27, 57–61]. Unless noted otherwise, the theoretical prediction is in agreementwith the measurements. Both are aiming for further improvements in precision. The exact detailsof the measurements such as the top-quark mass assumption at which the cross section values arequoted can be found in the original publications.
√s = 5.02 TeV measurements: In a special run, ATLAS recorded 257 pb−1 . The tt̄ crosssection is measured in both the dilepton and single-lepton final states of the tt̄ system and then
combined. The combination of the two measurements yields σtt̄ = 67.5 ± 0.9(stat.) ± 2.3(syst.) ±1.1(lumi.) ± 0.2(beam) pb [62], giving a total uncertainty of 3.9%. The result is in agreement withtheoretical QCD calculations at NLO in the strong coupling constant, including the resummationof NNLL soft-gluon terms, and constrains the parton distribution functions of the proton at large
Bjorken-x. CMS has measured the tt̄ production cross section, accumulating 27.4 pb−1 of data. The
measurement is performed by analyzing events with at least one charged lepton. The measured
cross section is σtt̄ = 69.5 ± 8.4 pb [63], with a relative precision of 12%, in agreement withthe expectation from the Standard Model. The impact of the presented measurement on thedetermination of the gluon distribution function is also investigated. In addition, they performed
a measurement in opposite-sign eµ-dilepton events with at least two jets using 302 pb−1 . Theyobtain a Drell-Yan scale factor under the Z-boson mass to estimate the background and extract
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961. Top Quarka cross section using a counting technique of σtt̄ = 60.7 ± 5.0(stat) ± 2.8(syst) ± 1.1(lumi) pb.
A combination with the result in the single lepton + jets channel is performed, yielding σtt̄ =63.0 ± 4.1(stat) ± 3.0(syst + lumi) pb [64].
√√s = 7 TeV measurements: At s = 7 TeV, ATLAS uses the full dataset of 4.6 fb−1 of eµ
events, yielding σtt̄ = 182.9 ± 7.1 pb, corresponding to 3.9% precision [65]. Other measurements by
ATLAS include a measurement in 0.7 fb−1 in the lepton+jets channel [66], in the dilepton channel[67], and in 1.02 fb−1 in the all-hadronic channel [68], which together yield a combined value of σtt̄ =177±3(stat.)+8−7 (syst.)±7(lumi.) pb (6.2%) [69]. Further analyses in the hadronic τ plus jets channel−1
in 1.67 fb [70] and the hadronic τ + lepton channel in 2.05 fb−1 [71], and the all-hadronic channel
in 4.7 fb−1 [72] yield consistent albeit less precise results. Recently, ATLAS performed a crosssection measurement in the lepton+jets channel using 4.6 fb−1 using a three-class, multidimensional
event classifier based on support vector machines to differentiate tt̄ events from W/Z + bb̄ and other+3.4
background processes, yielding σtt̄ = 168.5 ± 0.7(stat.)+6.2−5.9 (syst.)−3.2 (lumi.) pb [73].
CMS measures the tt̄ cross section in the dilepton channel using 2.3 fb−1 to σtt̄ = 161.9 ±
2.5(stat.)+5.1−5.0 (syst.) ± 3.6(lumi.) pb, corresponding to a 4.2% precision [74]. The most precise
measurement from CMS is also obtained in the dilepton channel using 5 fb−1 , where they measureσtt̄ = 173.6 ± 2.1(stat.)+4.5−4.0 (syst.) ± 3.8(lumi.) pb, corresponding to a 3.6% precision [75]. Other
measurements use 2.3 fb−1 in the e/µ+jets channel [76], with 3.5 fb−1 in the all-hadronic channel[77], with 2.2 fb−1 in the lepton+τ channel [78], and with 3.9 fb−1 in the τ +jets channel [79].
ATLAS and CMS also provide a legacy combined cross section of σtt̄ = 178.5 ± 4.7 pb using 5 fb−1 ,yielding a precision of 2.6% [80].
√√s = 8 TeV measurements: At s = 8 TeV, ATLAS measures the tt̄ cross section
with 20.3 fb−1 using eµ dilepton events, with a simultaneous measurement of the b−tagging efficiency, yielding σtt̄ = 242.9 ± 1.7(stat.) ± 5.5(syst.) ± 5.1(lumi.) ± 4.2(beam energy) pb [81] (3.6%
precision). In the ` + jets channel, they measure σtt̄ = 260 ± 1(stat.)+20−23 (syst.) ± 8(lumi.) ±4(beam energy) pb [82] in 20.3 fb−1 using a likelihood discriminant fit and b-jet identification.
Subsequently, ATLAS performed a new analysis in 20.2 fb−1 using ` + jets events. They model
the W +jets background using Z+jets data and employ neural networks in three jet-multiplicity
and b-jet multiplicity regions for the signal and background separation, yielding σtt̄ = 248.3 ±0.7(stat.) ± 13.4(syst.) ± 4.7(lumi.) pb [83]. ATLAS also performed a cross section measurementin the hadronic τ +jets channel yielding consistent, albeit less precise results [84].
CMS performs a template fit to the Mlb mass distribution using 19.6 fb−1 in the lepton+jets
channel yielding σtt̄ = 228.5 ± 3.8(stat.) ± 13.7(syst.) ± 6.0(lumi.) pb [85] (6.7% precision). In theeµ channel, initially using 5.3 fb−1 [86] the cross sections are extracted using a binned likelihood
fit to multi-differential final state distributions related to identified b quark and other jets in theevent, yielding σtt̄ = 239 ± 2(stat.) ± 11(sys.) ± 6(lumi.) pb (5.3% precision). Later, they also
use the full dataset of 19.7 fb−1 , yielding σtt̄ = 244.9 ± 1.4(stat)+6.3−5.5 (syst) ± 6.4(lumi) pb (3.7%
precision) [75]. This most precise CMS measurement at 8 TeV is also used to determine the toppole mass and set SUSY limits. The cross section is also measured in the hadronic τ +jets channel,
yielding σtt̄ = 257 ± 3(stat.) ± 24(syst.) ± 7(lumi.) pb [87] and in the all-hadronic final state giving
σtt̄ = 275.6 ± 6.1(stat.) ± 37.8(syst.) ± 7.2(lumi.) pb [88]. In combination of the most precise
eµ measurements in 5.3 − 20.3 fb−1 , ATLAS and CMS together yield σtt̄ = 241.5 ± 1.4(stat.) ±5.7(syst.) ± 6.2(lumi.) pb [89] (3.5% precision), challenging the precision of the corresponding
theoretical predictions. ATLAS and CMS also provide a legacy combined cross section of σtt̄ =−1 (2.5% precision) [80]. The combinations also provide the ratio between
243.3+6.0−5.9 pb using 20 fb
cross sections at 8 and 7 TeV, the top quark pole mass, and the strong coupling.
The LHCb collaboration presented the first observation of top-quark production in the forward
region in pp-collisions in the e+jets or µ+jets channel. The results are based on data corresponding
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61. Top Quark

to integrated luminosities of 1.0 and 2.0 fb−1 collected at center-of-mass energies of 7 and 8 TeV
by LHCb. The inclusive top quark production cross sections in the fiducial region are σtt̄ =239 ± 53(stat.) ± 38(syst.) pb at 7 TeV, and σtt̄ = 289 ± 43(stat.) ± 46(syst.) pb at 8 TeV [90].
√s = 13 TeV measurements: In 36.1 fb−1 of eµ data with one or two b-tags, ATLAS
measures σtt̄ = 826.4 ± 3.6(stat.) ± 11.5(syst.) ± 15.7(lumi.) ± 1.9(beam) pb (2.4% precision).
This measurement is also used to determine the top quark pole mass and to derive ratios anddouble ratios of tt̄ and Z cross-sections at different energies as well as absolute and normalised
differential cross-sections as functions of single lepton and dilepton kinematic variables [91]. In the` + jets channel, using 85 pb−1 , the cross-section is extracted by counting the number of eventswith exactly one e or µ and at least four jets, at least one of which is identified as originatingfrom a b-quark, yielding σtt̄ = 817 ± 13(stat.) ± 103(syst.) ± 88(lumi.) pb [92]. Later, ATLAS
measures the inclusive tt̄ cross section in 139 fb−1 in the ` + jets through a profile-likelihood fit tobe σtt̄ = 830.4 ± 0.4(stat.) ± 36(syst.) ± 14(lumi) pb (4.6% precision) [93].
Recently, using the complete Run-2 dataset of 140 fb−1 in events containing an oppositely
charged eµ pair and b-tagged jets, ATLAS has presented their legacy measurement of σtt̄ = 829 ±1(stat) ± 13(syst) ± 8(lumi) ± 2(beam) pb [94], corresponding to a precision of 1.8%. They alsomeasure differential and double-differential distributions of kinematic variables of leptons fromdecays of top-quark pairs. The results are compared with predictions from several Monte Carlogenerators. While no prediction is found to be consistent with all distributions, a better agreementwith measurements of the lepton pT distributions is obtained by reweighting the tt̄ sample so as toreproduce the top-quark pT distribution from an NNLO calculation.
Using 35.9 fb−1 of dilepton data, they use a likelihood fit and yield σtt̄ = 803 ± 2(stat.) ±25(syst.) ± 20(lumi.) pb (4.0%). This result is also used to extract the top quark mass in boththe pole and the MS schemes at NNLO and the strong coupling constant [95]. Using the samedataset in the dilepton channel with a hadronically decaying τ , they measure σtt̄ = 781 ± 7(stat.) ±62(syst.) ± 20(lumi.) pb (8.3%) [96]. A first measurement of the total inclusive and the normalized
differential cross section in the ` + jets channel is made in 42 pb−1 yielding σtt̄ = 836 ± 27(stat.) ±88(syst.) ± 100(lumi.) pb [97]. Using 2.2 fb−1 of data, ` + jets events are categorized according
to the accompanying jet multiplicity. From a likelihood fit to the invariant mass distribution of
the isolated lepton and a b-jet, the cross section is measured to be σtt̄ = 888 ± 2(stat.)+26−28 (syst.) ±20(lumi) pb [98]. This result is also used to extract the top-quark mass. Using the full Run-2
dataset of 137 pb−1 , CMS measures the tt̄ cross section in four regions determined by top pT and btag score in the `+jets channel. They employ a combined χ2 fit considering the migration matrices.
Most of the measured differential cross sections are well described by standard model predictions
with the exception of some double-differential distributions. They obtain σtt̄ = 791 ± 1(stat.) ±21(syst.) ± 14(lumi) pb (3.2%) [99]. In the all-hadronic channel, CMS uses 2.53 fb−1 of data,
yielding a cross section of σtt̄ = 834 ± 25(stat.)+118−104 (syst.) ± 23(lumi.) pb [100]. Also differential
cross sections as a function of the leading top quark transverse momentum are measured. Veryrecently, CMS presents a first search for the central exclusive production of tt̄ pairs using protontagged events, using 29.4 fb−1 . The tt̄ decay products are reconstructed using the central CMS
detector, while forward protons are measured in the CMS-TOTEM precision proton spectrometer.
An observed (expected) upper bound on the production cross section of 0.59 (1.14) pb [101] is set
at 95% confidence level, for collisions of protons with fractional momentum losses between 2 and20%.
Using 1.93 fb−1 , LHCb studies forward top quark pair production in pp collisions in the µeb final
state. The cross-section is measured in a fiducial region defined by both leptons transverse momenta
and pseudorapidities as well as their angular separation, the b-jet transverse momentum and its
angular separation from the leptons, yielding σtt̄ = 126 ± 19(stat.) ± 16(syst.) ± 5(lumi) fb [102].
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61. Top Quark11√
s = 13.6 TeV measurements: Being one year into the Run-3 data taking at s = 13.6 TeV
with an expected increase in the tt̄ cross section by approximately 10%, both experiments, ATLAS
and CMS, present the first tt̄ cross section measurements already.
ATLAS uses 29 fb−1 of data in events with an opposite-charge eµ pair and b-tagged jets toobtain σtt̄ = 850 ± 3(stat.) ± 18(syst.) ± 20(lumi.) pb. Simultaneously, the Z-boson cross section
is determined for inclusive e+ e− and µ+ µ− events in a fiducial phase space, taking cancellation ofseveral systematic uncertainties into account yielding for the ratio Rtt̄/Z = 1.145 ± 0.003(stat.) ±0.021(syst.) ± 0.002(lumi.) [103].
CMS presents the first measurement at this energy using 1.21 fb−1 in events with one or two
charged leptons (e or µ) and additional jets. A maximum likelihood fit is performed in event
categories defined by the number and flavors of the leptons, the number of jets, and the numberof jets identified as originating from b quarks. An inclusive tt̄ production cross section of 881 ±23(stat + syst) ± 20(lumi) pb is measured [104].
proton-lead pP b and lead-lead P bP b heavy ion collision measurements: CMS establishes first evidence for the production of top-quark pairs in P bP b collision data at a nucleonnucleon center-of-mass energy of 5.02 TeV using evens with charged leptons (electrons or muons)and bottom quarks. They obtain σtt̄ = 2.54+0.84
performed a measurement of−0.74 µb [105]. CMS also√
top-quark pair production in proton-lead pP b heavy ion collisions at s = 8.16 TeV in 174 nb−1 of
lepton+jets events. They measure a cross section of σtt̄ = 45 ± 8 nb [106]. Recently, also ATLAS√
presents a tt̄ cross section measurement in 165 nb−1 of pP b collisions at s = 8.16 TeV in the
lepton+jets and the dilepton channels, with a significance well over 5 standard deviations in bothchannels separately, yielding a combination of σtt̄ = 57.9 ± 2.0(stat.)+4.9−4.5 (syst.) nb (9%) [107]. Bothmeasurements are consistent with pQCD calculations and with the scaled pp data.
In Fig. 61.1, one sees the importance of pp at Tevatron energies where the valence antiquarks
in the antiprotons contribute to the dominant qq production mechanism. At LHC energies, thedominant production mode is gluon-gluon fusion and the pp-pp difference nearly disappears. The
excellent agreement of these measurements with the theory calculations is a strong validation of
QCD and the soft-gluon resummation techniques employed in the calculations. The measurements
reach high precision and provide stringent tests of pQCD calculations at NNLO+NNLL level including their respective PDF uncertainties.
Most of these measurements assume a t → W b branching ratio of 100%. CDF and DØ havemade direct measurements of the t → W b branching ratio [108, 109]. Comparing the number of
events with 0, 1 and 2 tagged b jets in the lepton+jets channel, and also in the dilepton channel,Pusing the known b-tagging efficiency, the ratio R = B(t → W b)/ q=d,s,b B(t → W q) can beextracted. In 5.4 fb−1 of data, DØ measures R = 0.90 ± 0.04, which is 2.5 standard deviations from√unity. The currently most precise measurement was made by CMS in 19.7 fb−1 at s = 8 TeV.
They find R = 1.014 ± 0.003(stat.) ± 0.032(syst.) and R > 0.955 at 95% C.L. [110]. A significant
deviation of R from unity would imply either non-SM top-quark decay (for example a flavorchanging neutral-current decay), or a fourth generation of quarks. The latter is excluded by othermeasurements.
√

61.2.1.2 Differential tt cross sections
Thanks to the large available event samples, the Tevatron and the LHC experiments also performed single-, double- or recently even triple-differential cross-section measurements in tt̄ production. Such measurements are crucial, as they allow even more stringent tests of perturbative QCD
as description of the production mechanism, and allow along with other data the extraction of
PDFs in PDF fits. In addition, they enhance the sensitivity to possible new physics contributions,especially now that NNLO predictions for the main differential observables in tt̄ prediction have
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61. Top Quark

Inclusive tt cross section [pb]12

Tevatron combined 1.96 TeV (L ≤ 8.8 fb-1)
ATLAS combined dilepton, l+jets* 5.02 TeV (L = 257 pb-1)-1
CMS combined eµ, l+jets 5.02 TeV (L = 27.4-302 pb )LHC combined eµ 7 TeV (L = 5 fb-1)
LHCtop WG-1
LHC combined eµ 8 TeV (L = 20 fb ) LHCtop WG-1
ATLAS eµ 13 TeV (L = 140 fb )CMS eµ 13 TeV (L = 35.9 fb-1)-1
ATLAS l+jets 13 TeV (L = 139 fb )CMS l+jets 13 TeV (L = 137 fb -1)
ATLAS eµ* 13.6 TeV (L = 11 fb-1)
CMS dilepton, l+jets 13.6 TeV (L = 1.2 fb-1)

103

ATLAS+CMS Preliminary
LHCtop WG

June 2023

1000

102

* Preliminary

900
800
13
NNLO+NNLL, PDF4LHC21 (pp)
NNLO+NNLL, NNPDF3.0 (pp)Czakon, Fiedler, Mitov, PRL 110 (2013) 252004
mtop = 172.5 GeV, α s (M ) = 0.118 ± 0.001

10

13.6

Z

2

4

6

8

10

12

14
s [TeV]

Figure 61.1: Measured and predicted tt production cross sections from Tevatron energies in pp
collisions to LHC energies in pp collisions. The plot is kindly provided by the LHCtopWG working group, status as of June 2023, see https://twiki.cern.ch/twiki/bin/view/LHCPhysics/
LHCTopWGSummaryPlots.

become available [111] and later confirmed [28]. Furthermore, such measurements reduce the uncertainty in the description of tt̄ production as background in Higgs physics and searches for rare
processes or beyond Standard Model physics.
Differential cross sections are typically measured by a selection of candidate events, their kinematic reconstruction and subsequent unfolding of the obtained event counts in bins of kinematic
distributions in order to correct for detector resolution effects, acceptance and migration effects. In
some cases a bin-by-bin unfolding is used, while other analyses use more sophisticated techniques.
Most commonly used unfolding techniques are the iterative Bayesian unfolding (IBU) [112] as implemented in the RooUnfold package [113] and the profile-likelihood unfolding [114] [115], but alsoa singular value composition approach [116] or maximum likelihood fit methods [117] are used. As
general feature across channels, it is found that the measured top quark pT spectrum is significantly
softer than the NLO+PS theory predictions considered in the corresponding publications.
√√s = 7 TeV measurements: At s = 7 TeV, ATLAS and CMS measure single-differential
tt̄ cross sections with respect to jet multiplicity, the top-quark transverse momentum, and of themass, transverse momentum and rapidity of the top quark, the antitop quark as well as the tt̄system or kinematic properties of the final-state charged leptons and jets associated to b-quarks.
While CMS finds in general good agreement with the pQCD calculations [118–120], ATLAS finds
the data to be softer, in particular in the tt̄ mass and the top-quark pT than the Alpgen+Herwig
generator. Also some disagreement in the rapidity spectrum is observed indicating a preference for
the HERAPDF1.5 pdf set over CT10 [121–123].
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61. Top Quark13√
s = 8 TeV measurements: At s = 8 TeV, ATLAS measures single-differential crosssections in the dilepton and lepton+jets channel with respect to the mass, the transverse momentum
and the rapidity of the tt system and event-level kinematic observables [124] [125]. The results are
consistent or in fair agreement with the predictions over a wide kinematic range. Predictions
beyond NLO accuracy improve the agreement with data at high top-quark transverse momenta.
Using the current settings in the Monte Carlo programs and parton distribution functions, improve
the agreement with the rapidity distributions. ATLAS also performs a dedicated differential tt̄
cross-section measurement of highly boosted top quarks in the lepton+jets channel, where thehadronically decaying top quark has a transverse momentum above 300 GeV [126]. Jet substructuretechniques are employed to identify top quarks, which are reconstructed with an anti-kt jet with aradius parameters R = 1.0. The predictions of NLO and LO matrix element plus parton shower
Monte Carlo generators are found to generally overestimate the measured cross sections.
CMS measures normalized differential cross sections for tt production in lepton+jets eventswith respect to four kinematic event variables: the missing transverse energy; the scalar sumof the jet transverse momentum (pT ); the scalar sum of the pT of all objects in the event; andthe pT of leptonically decaying W bosons from top quark decays [119]. Using 19.7 fb−1 , theymeasure the normalized differential cross section in the lepton+jets (e/µ+jets) and in the dilepton(e+ e− , µ+ µ− , and e± µ± ) decay channels as a function of the kinematic properties of the charged
leptons, the jets associated to b quarks, the top quarks, and the tt̄ system. The data are comparedwith several predictions from perturbative QCD up to approximate next-to-next-to-leading-orderprecision [127]. Using the same dataset, in the dilepton eµ channel, they measure normalized
double-differential cross sections for tt production as a function of various pairs of observables
characterizing the kinematics of the top quark and tt system [128]. This result has a significant
impact on the gluon distribution when included in PDF fits. Overall agreement is observed with thepredictions, which is improved when the latest parton distribution functions are used [128]. They
also perform a dedicated boosted-top analysis in the e or µ+jets channel where the hadronicallydecaying top quark is reconstructed as a single large-radius jet and identified as a top candidateusing jet substructure techniques [129].
√√s = 13 TeV measurements: At s = 13 TeV, ATLAS measures the differential tt crosssection in the lepton+jets and the dilepton channel as a function of the transverse momentum andabsolute rapidity of the top quark, and of the transverse momentum, absolute rapidity and invariant
mass of the tt system [130] [131] [91]. They find in general good agreement with the theory models
with the exception of the Powheg-Box+ Herwig++ predictions, which differ significantly from thedata in both the transverse momentum of the top quark and the mass of the tt system. ATLAS
measures the single- and double-differential tt̄ cross-section in the lepton + jets channel at particle
and parton level. Two topologies, resolved and boosted, are considered [132]. In the all-hadronic
channel, measurements are presented in the boosted regime [133] as well as in the resolved regime
with six separately resolved jets [134].
Using the full Run-2 datset of 140 fb−1 , ATLAS measures differential cross sections in the` + jets channel and fully hadronic channels in a boosted topology with at least one large-R“top-jet” from a hadronic decay with high-pT , also as a function of variables that characterise
the additional radiation in the events [135]. The measured distribution of the top-quark pT isused to set limits on the Wilson coefficients describing physics beyond the standard model. The
modelling of the additional radiation events show some mild disagreements to the data. Further
differential cross-section measurements were made that are specifically useful for MC generator
tuning. This includes the ATLAS measurement of the one- and two-dimensional differential crosssections for eight substructure variables, defined using only the charged components of the jets, ina particle-level phase space by correcting for the smearing and acceptance effects induced by the√

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detector [136] [94]. The QCD predictions for measures of energy-flow are found to be in good agreement with the measurements while variables sensitive to the three-body structure of the top-quark
jets exhibit some tensions with the measured distributions. In another example, a measurementof observables sensitive to effects of color reconnection in top-quark pair-production events is presented, in particular for the charged-particle multiplicity, the scalar sum of the transverse momentaof the charged particles, and the same scalar sum in bins of charged-particle multiplicity. Theseobservables are unfolded to the stable-particle level. The particle-level measurements are comparedwith different color reconnection models in Monte Carlo generators. These measurements disfavour
some of the color reconnection models and provide inputs to future optimisation of the parametersin Monte Carlo generators [137]. Furthermore, several observables sensitive to the fragmentationof b-quarks into b-hadrons are measured. Jets containing b-hadrons are used to construct observables that characterize the longitudinal and transverse momentum distributions of the b-hadron
within the jet. The measurements have been corrected for detector effects and provide a test ofheavy-quark-fragmentation modeling at the LHC in a system where the top-quark decay products
are color-connected to the proton beam remnants. The unfolded distributions are compared withthe predictions of several modern Monte Carlo parton-shower generators and generator tunes, anda wide range of agreement with the data is observed. These measurements complement similar
measurements from e+ e− collider experiments in which the b-quarks originate from a color-singlet
Z/γ ∗ [138].
CMS measures single- and double-differential tt̄ cross sections in the dilepton and the lepton+jets channel as a function of the kinematic properties of the leptons, jets from bottom quark
hadronization, top quarks, and top quark pairs and jet multiplicity [139–144]. While in general
good agreement is observed, in a dilepton analysis, significant disagreement is observed between
data and all predictions for several observables. The measurements are used to constrain the top
quark chromomagnetic dipole moment in an effective field theory framework at NLO in QCD and to
extract tt̄ and leptonic charge asymmetries [145]. In a later dilepton channel analysis, even a tripledifferential measurement is performed as a function of the invariant mass and rapidity of the tt̄system and the multiplicity of additional jets at particle level. The measurement is used to extract
the strong coupling constant and the top-quark pole mass and parton distribution functions [146].
In the all-hadronic and ` + jets events in a boosted topology with at least two large-R jets with ab-tag inside and pT > 400 GeV or one large-R jet, respectively, CMS measures the differential crosssection as a function of kinematic variables of individual top quarks or of the tt̄ system [147]. The
observed absolute cross sections are significantly lower than the predictions from theory. Using thefull Run-2 dataset of 137 fb−1 in ` + jets data, arranged in four regions according to the top pT ,boosted vs. resolved, and the b-tagging score, CMS measures the single- and double-differential tt̄
cross sections [99]. Here also the longitudinal momentum is measured well into the TeV range in
one measurement starting in the resolved regime.
61.2.1.3 tt̄ plus heavy flavor production processes
Further cross-section measurements are performed by ATLAS and CMS for tt̄+heavy flavor.
The measurement of the cross section for tt̄+heavy flavour [148] and tt̄+jets production as wellas the differential measurement of the jet multiplicity in tt̄ events is presented by ATLAS [149]and by CMS [120]. In addition, both experiments measure the production cross section of the tt̄bb̄
process as it is an interesting test of QCD due to the different mass scales involved. Furthermore,this process is of high relevance for top quark production as background to searches, for example√
for measurements of tt̄h production and measurements of 4-top quark production. At s = 8 TeV,
CMS measured the cross-section ratio σtt̄bb̄ /σtt̄jj using 19.6 fb−1 [150]. ATLAS also measured thett̄ production cross section along with the branching ratios into channels with leptons and quarks
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using 4.6 fb−1 of 7 TeV data [151]. They find agreement with the standard model at the level of afew percent.
Using 19.7 fb−1 of data recorded at 8 TeV, CMS measures the absolute and normalized differential cross section with respect to the jet multiplicity in tt̄+jets events in the dilepton channel. The
differential tt̄b and tt̄bb̄ cross sections are presented for the first time as a function of the kinematic
properties of the leading additional b jets [152].
Using 139 fb−1 of tt̄ → dilepton events, ATLAS distinguishes in a dedicated analysis muonsoriginating from W → µν decays and those from W → τ ν → µννν decays via their transverse
momentum spectrum and the impact parameter of the muon track, that reflects the tau lifetime,yielding high sensitivity. The measured ratio of R(τ /µ) = 0.992 ± 0.013 is in agreement with the
hypothesis of universal lepton couplings [153].
Using 36 fb−1 of dilepton events at 13 TeV, ATLAS also measures differential cross sections
with respect to high-resolution variables, constructed to characterize the longitudinal and transverse
momentum distributions of the b-hadron within the b-jets [138]. They are used to test the heavyquark-fragmentation modelling.
Using 137 fb−1 of dilepton events at 13 TeV, CMS measures differential cross sections withrespect to the mass of the tt̄ system and the rapidity difference of the top-quark and antiquark [154].
Exploiting their sensitivity to the top-quark Yukawa coupling yields a best fit value of Yt = 1.16+0.24−0.35 ,
bounding Yt < 1.54 at a 95% confidence level.
√At s = 13 TeV, ATLAS measures the tt̄bb̄ cross section and cross section ratios in the dilepton
and the ` + jets channels as inclusive and differential cross sections [155]. The measured inclusive
fiducial cross-sections generally exceed the tt̄bb̄ predictions from various NLO matrix element calculations matched to a parton shower. CMS measures the tt̄bb̄ cross section and cross section ratios inthe dilepton channel [156], in the dilepton and the lepton+jets channel [157], in the all-jet channel
by selecting events containing at least eight jets, of which at least two are identified as b-jets [158].
In the latter, a combination of multivariate analysis techniques is used to reduce the large background from multijet events not containing a top quark pair, and to help discriminate between jets
originating from top quark decays and other additional jets. In the all-hadronic channel, they latermeasured the tt̄ + bb̄ cross section to ≈ 25% precision employing a multivariate analysis techniqueand a 2-dimensional likelihood fit [159]. Using the full Run-2 dataset of 138 fb−1 , they measure
the inclusive and normalized differential tt̄bb̄ cross sections in the lepton+jets decay channel of the
top quark [160]. Measurements are made in four fiducial phase space regions, targeting different
aspects of the process. Distributions are unfolded to the particle level through maximum likelihood
fits, and compared with predictions from several event generators. In most cases, the measured
inclusive cross sections exceed the predictions with the chosen generator settings. The differential
cross sections show varying degrees of compatibility with the theoretical predictions.
CMS also measured the tt̄ + cc̄ cross section using 41.5 fb−1 of events with dileptonic final
states [161]. A multi-class neural network is employed to separate tt̄ + bb̄, tt̄ + cc̄ and tt̄ + ll. The
results are compatible with the prediction within 1 − 2 σ.
The production of four top-quarks is an interesting test of QCD in a very rare process and at
the same time sensitive to the top quark Yukawa coupling and to production mechanisms withnew mediators with strong couplings to top quarks. The latest cross section calculation yields−1
σtt̄tt̄ = 13.32+1.04−1.78 fb [44]. Using the full Run-II data set of 139 fb , ATLAS measures the four-tops
cross section in the two-lepton same sign or three-lepton channel with 13% branching ratio anddominant tt̄V background as σtt̄tt̄ = 24+7
−6 fb [162]. Using the same data set in the one-lepton or twolepton opposite-sign channel with 57% branching ratio and dominant tt̄ + heavy flavor background,+7
they measure σtt̄tt̄ = 26+17−15 fb [163]. The combination yields σtt̄tt̄ = 24−6 fb [163], corresponding
to an observed (expected) significance of 4.7 (2.6) σ significance. Using the full Run-2 dataset
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61. Top Quarkof 140 fb−1 , ATLAS presents the observation of the tt̄tt̄ production process in events containing
two leptons with the same electric charge or at least three leptons (e or µ). Event kinematics areused to separate signal from background through a multivariate discriminant based on graph neuralnetworks, and dedicated control regions are used to constrain the dominant backgrounds. The cross+6.6
section is measured to be σ(tt̄tt̄) = 22.5−5.5
fb [164], almost twice the Standard Model prediction
and compatible with it within 2 standard deviations. The observed (expected) significance of themeasured signal with respect to the standard model (SM) background-only hypothesis is 6.1 (4.3)
standard deviations. Data are also used to constrain the top-Higgs Yukawa coupling and effective
field theory operator coefficients.
After a search for four-top production in 35.8 fb−1 , in the one-lepton or two-lepton opposite-sign
channel [165], CMS uses the full Run-2 dataset of 137 fb−1 to measure the four-top cross section in
the two-lepton same sign or three-lepton channel, yielding σtt̄tt̄ = 12.6+5.8−5.2 fb [166], corresponding
to an observed (expected) significance of 2.6 (2.7) σ significance. In the full Run-2 dataset, they
manage to achieve evidence for the four-top production in events that have no leptons (all-hadronic),
one lepton, or two opposite-sign leptons, yielding σ(tt̄tt̄) = 36+12−11 fb [167], corresponding to an
observed significance of 3.9 standard deviations (1.5 expected). The combination with earlier CMS
results in other final states yields σ(tt̄tt̄) = 17±4(stat.)±3(syst.) fb, corresponding to a significanceof 4.0 standard deviations (3.2 expected).
Finally, CMS reports the observation of the four-tops production process based on events with
two same-sign, three, or four charged leptons (e and µ) and additional jets. Updated identification
techniques for charged leptons and jets originating from the hadronization of b quarks, as well
as a revised multivariate analysis strategy via a multi-class boosted decision tree to distinguishthe signal process from the main backgrounds, lead to an improved signal detection, yielding+2.3
σ(tt̄tt̄) = 17.7+3.7−3.5 (stat.)−1.9 (syst.) fb, corresponding to an observed significance of 5.6 standard
deviations (4.9 expected) [168].
61.2.1.4 Single-top production
Top-quarks cannot only be produced in pairs via the strong interaction, but also individually
via the electroweak interaction. This interaction is sensitive to the tW b coupling as well as to the
CKM-Matrix Element Vtb . The single-top quark production process was first observed in 2009 byDØ [169] and CDF [170, 171] at the Tevatron. The production cross section at the Tevatron isroughly half that of the tt cross section, but the final state with a single W -boson and typicallytwo jets, which tend to be emitted more in the forward direction, is less distinct than that for
tt and much more difficult to distinguish from the background of W +jets and other sources. A
comprehensive review of the first observation and the techniques used to extract the signal fromthe backgrounds can be found in [172]. A more recent one can be found in [173].
The dominant production at the Tevatron is through s-channel and t-channel W -boson exchange. Associated production with a W -boson (tW production) has a cross section that is too
small to observe at the Tevatron. The t-channel process is qb → q 0 t, while the s-channel process is
qq 0 → tb. The s- and t-channel productions can be separated kinematically. This is of particularinterest because potential physics beyond the Standard Model, such as fourth-generation quarks,
heavy W and Z bosons, flavor-changing-neutral-currents [37], or a charged Higgs boson, would
affect the s- and t-channels differently. However, the separation is difficult and initial observations
and measurements at the Tevatron by both experiments were of combined s + t-channel production. The two experiments combined their measurements for maximum precision with a resultings + t-channel production cross section of 2.76+0.58−0.47 pb [174], which agrees well with the theoretical+0.00
2
calculation at mt = 173 GeV/c of σs+t = 3.12−0.04(scale) ± 0.18(pdf ) pb (including both top andanti-top production) [35, 175].
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Using the full Run-II data set of up to 9.7 fb−1 , CDF and DØ have measured the t-channel
single-top quark production to be σt+t̄ = 2.25+0.29−0.31 pb [176, 177]. In the same publication, theyalso present the simultaneously measured s− and t−channel cross sections and the s + t combined
cross section measurement resulting in σs+t = 3.30+0.52−0.40 pb, without assuming the SM ratio ofσs /σt . The modulus of the CKM matrix element obtained from the s + t-channel measurement is|Vtb | = 1.02+0.06−0.05 and its value is used to set a lower limit of |Vtb | > 0.92 at 95% C.L. Those results arein good agreement with the theoretical value at the mass 172.5 GeV/c2 of σt = 2.08 ± 0.13 pb [175].
It should be noted that the theory citations here list cross sections for t or t alone, whereas theexperiments measure the sum. At the Tevatron, these cross sections are equal. The theory values
quoted here already include this factor of two.
Using datasets of 9.7 fb−1 each, CDF and DØ combine their analyses and report the firstobservation of single-top-quark production in the s-channel, yielding σs = 1.29+0.26−0.24 pb [178]. The
probability of observing a statistical fluctuation of the background of the given size is 1.8 × 10−10 ,corresponding to a significance of 6.3 standard deviations.
t-channel at the LHC:
At the LHC, the t-channel cross section is expected to be more than three times as large as s-channel
and tW production, combined.
√
At s = 5.02 TeV, very recently, ATLAS measures the t-channel single-top quark production+4.4
in a dedicated run using 255 pb−1 , yielding σ(tq + t̄q) = 27.1+4.4−4.1 (stat.)−3.7 (syst.) pb and a cross+1.43
section ratio between top an antitop production Rt = 2.73−0.82(stat.)+1.01−0.29 (syst.) [179]. This result+0.11
implies for the CKM-matrix element fLV · |Vtb | = 0.94−0.10 with fLV being a left-handed form
factor.
√At s = 7 TeV, using 4.59 fb−1 of data, ATLAS measures the t-channel single-top quarkcross section in the lepton plus 2 or 3 jets channel with one b-tag by fitting the distribution of amultivariate discriminant constructed with a neural network, yielding σt = 46±6 pb, σt̄ = 23±4 pb
with a ratio Rt = σt /σt̄ = 2.04 ± 0.18 and σt+t̄ = 68 ± 8 pb, consistent with SM expectations[180, 181]. CMS follows two approaches in 1.6 fb−1 of lepton plus jets events. The first approach
exploits the distributions of the pseudorapidity of the recoil jet and reconstructed top-quark massusing background estimates determined from control samples in data. The second approach isbased on multivariate analysis techniques that probe the compatibility of the candidate eventst−chan.
= 67.2 ± 6.1 pb, and |Vtb | = 1.020 ± 0.046(exp.) ± 0.017(th.)
with the signal. They find σt+t̄[182]. All combined measurements are consistent with their corresponding SM predictions and yield
67.5 ± 5.7 pb [183].
√
At s = 8 TeV, both experiments repeat and refine their measurements. ATLAS uses 20.2 fb−1of data. Total, fiducial and differential cross-sections are measured for both top-quark and topantiquark production [184]. An artificial neural network is employed to separate signal from background. The fiducial cross-section is measured with a precision of 5.8% (top quark) and 7.8% (topantiquark), respectively. The total cross-sections are measured to be σtt−chan. (tq) = 56.7+4.3−3.8 pb fort−chan.
+3.0
top-quark production and σt̄(t̄q) = 32.9−2.7 pb for top-antiquark production, in agreementwith the SM prediction. In addition, the ratio of top-quark to top-antiquark production crosssections is determined to be Rt = 1.72 ± 0.09. The total cross-section is used to extract the W tb
coupling: fLV · |Vtb | = 1.029 ± 0.048, which corresponds to |Vtb | > 0.92 at the 95% confidence level,
when assuming fLV = 1 and restricting the range of |Vtb | to the interval [0, 1]. The differential
cross-sections as a function of the transverse momentum and rapidity of both, top and antitop, aremeasured at both the parton and particle levels. The transverse momentum and rapidity differential
cross-sections of the accompanying jet from the t-channel scattering are measured at particle level.
All measurements are compared to various Monte Carlo predictions as well as to fixed-order QCD
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61. Top Quarkcalculations where available. The SM predictions provide good descriptions of the data. Using thesame dataset, ATLAS probes the W tb vertex structure from polarization observables in t-channel
single-top quark events. The observables are extracted from asymmetries in angular distributions
measured with respect to spin quantisation axes appropriately chosen for the top quark and the W boson and found to be in agreement with the Standard Model predictions [185]. CMS uses 19.7 fb−1
in the e or µ plus jets channel, exploiting the pseudorapidity distribution of the recoil jet. Theyfind σt = 53.8 ± 1.5(stat.) ± 4.4(syst.) pb and σt̄ = 27.6 ± 1.3(stat.) ± 3.7(syst.) pb, resulting in an
inclusive t-channel cross section of σt+t̄ = 83.6 ± 2.3(stat.) ± 7.4(syst.) [186]. They measure a crosssection ratio of Rt = σt /σt̄ = 1.95 ± 0.10(stat.) ± 0.19(syst.), in agreement with the SM. The CKM
matrix element Vtb is extracted to be |Vtb | = 0.998 ± 0.038(exp.) ± 0.016(th.). Later, CMS also provided a fiducial cross section measurement for t-channel single top in the same dataset in events withexactly one µ or e and two jets, one of which is associated with a b-hadron [187]. The total fiducial
cross section is measured using different generators at NLO plus parton-shower accuracy. Using as
reference the aMC@NLO MC predictions in the four-flavor scheme, σtfid = 3.38 ± 0.25(exp.) ± 0.20(th.)
pb is obtained, in good agreement with the theory predictions. All combined measurements are
consistent with their corresponding SM predictions and yield 87.7 ± 5.8 pb [183].
√
At s = 13 TeV, ATLAS uses 3.2 fb−1 to measure the t-channel cross section. Using abinned maximum-likelihood fit to the discriminant distribution of a neural network, the crosssections are determined to be σt (tq) = 156 ± 5(stat.) ± 27(syst.) ± 3(lumi.) pb and σ(t̄q) =91 ± 4(stat.) ± 18(syst.) ± 2(lumi.) pb [188]. The cross-section ratio is measured to be Rt =σt /σt̄ = 1.72 ± 0.09(stat.) ± 0.18(syst.). All results are in agreement with SM predictions. Using
the full Run-2 dataset of 140 fb−1 , ATLAS measures the t-channel cross sections to be σ(tq) =137 ± 8 pb and σ(t̄q) = 84+6
−5 pb for top-quark and top-antiquark production, respectively [189].
The combined cross-section is found to be σ(tq + t̄q) = 221 ± 13 pb and the cross-section ratio is
Rt = σ(tq)/σ(t̄q) = 1.636+0.036−0.034 , in good agreement with predictions made at NNLO in perturbation
theory. The results are also used to demonstrate the potential to constrain parton distributions(1,3)
functions and interpreted in terms of effective field theory operators −0.25 < CqQ < 0.12, andto derive the constraint |Vtb | > 0.95 at the 95% confidence level CMS uses 2.2 fb−1 for a firstmeasurement. Fits to the transverse W -mass and the output of an artificial neural network allow
the determination of the background and the signal contribution. The measured cross-section isσt = 238 ± 13(stat.) ± 29(syst.) pb [190]. The CKM matrix element is determined to |Vtb | =1.05 ± 0.07(exp.) ± 0.02(th.). Using 35.9 fb−1 of data, CMS refines their measurement. Eventswith one µ or e are selected, and different categories of jet and b-jet multiplicity and multivariate
discriminators are applied to separate the signal from the background, resulting in σt (tq) = 130 ±1(stat) ± 19(syst) pb and σt (t̄q) = 77 ± 1(stat) ± 12(syst) pb, respectively, and their ratio is1.68 ± 0.02(stat) ± 0.05(syst) [191]. The results are in agreement with the predictions from theStandard Model. This dataset is also used to measure differential cross sections in this channel [192].
CMS used the same dataset to measure the CKM matrix elements from their t-channel single-top
quark production cross section. In the standard model hypothesis of CKM unitarity, a lower limit
of |Vtb | > 0.970 is measured at the 95% confidence level. Several theories beyond the standard
model are considered, and by releasing all constraints among the involved parameters, the values|Vtb | = 0.988 ± 0.024, and |Vtd |2 + |Vts |2 = 0.06 ± 0.06 are measured [193].
tW -channel at the LHC:√
The predicted cross section for the associated tW process at the LHC at s = 7 TeV is 15.6 ±1.2 pb [36]. This is of interest because it probes the W tb vertex in a different kinematic region
than s- and t-channel production, and because of its similarity to the associated production of acharged-Higgs boson and a top quark. The signal is difficult to extract because of its similarity
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61. Top Quarkto the tt signature. Furthermore, it is difficult to uniquely define because at NLO a subset ofdiagrams has the same final state as tt and the two interfere [194]. The cross section is calculatedusing the diagram removal technique [195] to define the signal process. In the diagram removal
technique the interfering diagrams are removed, at the amplitude level, from the signal definition(an alternative technique, diagram subtraction removes these diagrams at the cross-section level
and yields similar results [195]). These techniques work provided the selection cuts are definedsuch that the interference effects are small, which is usually the case.
√At s = 7 TeV, both, ATLAS and CMS, provide evidence for the associated tW production [196, 197]. ATLAS uses 2.05 fb−1 in the dilepton plus missing ET plus jets channel, wherea template fit to the final classifier distributions resulting from boosted decision trees as signal
to background separation is performed. The result is incompatible with the background-only hypothesis at the 3.3σ (3.4σ expected) level, yielding σtW = 16.8 ± 2.9(stat.) ± 4.9(syst.) pb and−1 in the dilepton plus jets channel with at least one b-tag.
|Vtb | = 1.03+0.16−0.19 [196]. CMS uses 4.9 fb
A multivariate analysis based on kinematic properties is utilized to separate the tt̄ backgroundfrom the signal. The observed signal has a significance of 4.0σ and corresponds to a cross sectionof σtW = 16+5
−4 pb [197]. All combined measurements are consistent with their corresponding SM
predictions and yield 16.3 ± 4.1 pb [183].
√
At s = 8 TeV, both experiments repeated their tW -analyses. ATLAS uses 20.3 fb−1 to select
events with two leptons and one central b-jet. The tW signal is separated from the backgrounds
using boosted decision trees, each of which combines a number of discriminating variables into oneclassifier. Production of tW events is observed with a significance of 7.7σ. The cross section is
extracted in a profile likelihood fit to the classifier output distributions. The tW cross section,
inclusive of decay modes, is measured to be σtW = 23.0 ± 1.3(stat.)+3.2−3.5 (syst.) ± 1.1(lumi.) pb,
yielding a value for the CKM matrix element |Vtb | = 1.01 ± 0.10 and a lower limit of 0.80 at the
95% C.L. [198]. A fiducial cross section is also measured. ATLAS and CMS also combine theirearly measurements and obtain σtW = 16.3 ± 4.1 pb [199], in agreement with the NLO+NNLL
expectation. Later, ATLAS used 20.2 fb−1 in the single-lepton channel with at least three jets
to measure the W t production cross section. A neural network is trained to separate the tW
signal from the dominant tt̄ background. The cross-section is extracted from a binned profile
maximum-likelihood fit to a two-dimensional discriminant built from the neural-network output
and the invariant mass of the hadronically decaying W boson. The measured cross section isσtW = 26 ± 7 pb [200], in good agreement with the Standard Model expectation. CMS uses
12.2 fb−1 in events with two leptons and a jet originating from a b-quark. A multivariate analysis
based on kinematic properties is utilized to separate the signal and background. The tW associate
production signal is observed at the level of 6.1σ, yielding σtW = 23.4 ± 5.4 pb and |Vtb | =1.03 ± 0.12(exp.) ± 0.04(th.) [201].
ATLAS and CMS also combine their early measurements and obtain σtW = 23.1 ± 3.6 pb [183],
in agreement with the NLO+NNLL expectation. The product of a form factor with the CKM
matrix element Vtb is determined to be |Vtb | = 1.02 ± 0.04(meas.) ± 0.02(theo.) > 0.79.
√
At s = 13 TeV, ATLAS uses 3.2 fb−1 of events with two opposite sign isolated leptons and at
least one jet. They are separated into signal and control regions based on their jet multiplicity andthe number of jets with b-tags. Signal is separated from background in two regions using boosted
decision trees. The cross section is extracted by fitting templates to the data distributions, and ismeasured to be σtW = 94±10(stat.)+28−22 (syst.)±2(lumi.) pb [202]. The measurement is in agreementwith the SM prediction. CMS uses 36 fb−1 of events with two opposite sign isolated leptons, onetight and one loose jet and one b-tag. Signal and background is separated in categories dependingon the number of jets and the subset of b-tagged jets using a boosted decision tree. A maximum
likelihood fit yields σtW = 63.1 ± 1.8(stat.) ± 6.4(syst.) ± 2.1(lumi.) pb [203]. In this dataset, CMS
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61. Top Quark

also analyses the single-lepton channel, where a boosted decision tree is used to separate the tW
signal from the dominant tt̄ background, whilst the subleading W +jets and multijet backgrounds
are constrained using data-driven estimates. This result is the first observation of the tW process infinal states containing a single µ or single e and several jets, with a significance exceeding 5 standard
deviations. The cross section is determined to be σtW = 89 ± 4(stat) ± 12(syst) pb [204], consistent
with the Standard Model. Using the full Run-2 datset of 138 fb−1 , CMS measures the inclusive
and normalised differential cross sections. Events containing one e and one µ in the final state
are analysed. For the inclusive measurement, a multivariate discriminant, exploiting the kinematic
properties of the events is used to separate the signal from the dominant tt̄ background. A crosssection of 79.2 ± 0.9(stat)+7.7−8.0 (syst) ± 1.2(lumi) pb [205] is obtained, consistent with the predictionsof the standard model. For the differential measurements, a fiducial region is defined according
to the detector acceptance, and the requirement of exactly one jet coming from the fragmentationof a bottom quark. The resulting distributions are unfolded to particle level and agree with thepredictions at NLO in perturbative QCD.
s-channel at the LHC:√
At s = 7 TeV, the s-channel production cross section is expected to be 4.6 ± 0.3 pb for mt =173 GeV/c2 [35]. At ATLAS, a search for s-channel single top quark production is performed in
0.7 fb−1 using events containing one lepton, missing transverse energy and two b-jets. Using a
cut-based analysis, an observed (expected) upper limit at 95% C.L. on the s-channel cross-sectionof σs < 26.5 (20.5) pb is obtained [206].
√
At s = 8 TeV, ATLAS uses 20.3 fb−1 of data with one lepton, large missing transverse
momentum and exactly two b-tagged jets. They perform a maximum-likelihood fit of a discriminant
based on a Matrix Element Method and optimized in order to separate single top-quark s-channel
events from the main background contributions which are tt̄ and W +jets production. They findσs = 4.8 ± 0.8(stat.)+1.6−1.3 (syst.) pb with a signal significance of 3.2 standard deviations [207], which
provides first evidence for s-channel single-top production. The signal is extracted through amaximum-likelihood fit to the distribution of a multivariate discriminant defined using boosted
decision trees to separate the expected signal contribution from background processes. At 7 TeV
and 8 TeV, CMS uses 5.1 fb−1 and 19.3 fb−1 , respectively, and analyses leptonic decay modes
by performing a maximum likelihood fit to a multivariate discriminant defined using a Boosted
Decision Tree, yielding cross sections of σs = 7.1 ± 8.1 pb and σs = 13.4 ± 7.3 pb, respectively, anda best fit value of 2.0 ± 0.9 for the combined ratio of the measured σs values and the ones expectedin the Standard Model [208]. The signal significance is 2.5 standard deviations.
ATLAS and CMS present the combinations of their single-top-quark production cross-section
measurements, using Run-I data. For the s-channel cross-section, the combination yields 4.9±1.4 pb√
at s = 8 TeV. All combined measurements are consistent with their corresponding SM predictions[183].
√At s = 13 TeV, ATLAS uses 139 fb−1 to measure the s-channel cross section on events with ane or µ, missing transverse momentum and exactly two b-tagged jets in the final state. A discriminant
based on matrix element calculations is used to separate single-top-quark s-channel events fromthe main background contributions, which are top-quark pair production and W -boson productionin association with jets. The observed (expected) signal significance over the background-only+3.5
hypothesis is 3.3 (3.9) standard deviations, and the measured cross-section is σ = 8.2−2.9
pb,
+0.40
consistent with the Standard Model prediction of σSM = 10.32−0.36 pb [209].
Both, ATLAS and CMS, also measured the electroweak production of single top-quarks inassociation with a Z-boson, see section 61.2.5.4 of this review.
Fig. 61.2 provides a summary of all single top cross-section measurements at the LHC as afunction of the center-of-mass energy. All cross-section measurements are very well described by
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Inclusive cross-section [pb]21

ATLAS+CMS Preliminary

t-channel
ATLAS PRD90 (2014)112006, EPJC 77(2017) 531, ATLAS-CONF-2023-026*
CMS JHEP 12 (2012)035, JHEP 06(2014) 090, PLB800 (2019)135042
LHC comb. JHEP 05 (2019)088

LHCtop WG

Single top-quark production
June 2023

tW
ATLAS PLB716 (2012)142, JHEP 01(2016) 064, JHEP01(2018)063
CMS PRL 110 (2013)022003, PRL 112 (2014) 231802, arXiv:2208.00924
LHC comb. JHEP 05 (2019)088

t-channel

102s-channel
ATLAS PLB756 (2016)228, arXiv:2209.08990
CMS JHEP 09 (2016)027
LHC comb. JHEP 05 (2019)088

tW

stat. total

NNLO MCFM, JHEP 02 (2021) 040
PDF4LHC (CT18, MSHT20, NNPDF3.1)

scale ⊕ PDF ⊕ αs uncertainty

aNNLO + aN3LL JHEP 05 (2021) 278
PDF4LHC (CT18, MSHT20, NNPDF3.1)
tW: tt contribution removed

scale ⊕ PDF ⊕ αs uncertainty

10

NLO NPPS205 (2010) 10, CPC191(2015) 74
CT10nlo, MSTW2008nlo, NNPDF2.3nloµ = µ = mtop

s-channelRF

scale ⊕ PDF ⊕ αs uncertainty*Preliminary

7

8

13

s [TeV]

Figure 61.2: Measured and predicted single top production cross sections at LHC energies in pp
collisions. The plot is kindly provided by the LHCtopWG working group, status as of June 2023,
see https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCTopWGSummaryPlots.
the theory calculation within their uncertainty.
Thanks to the large statistics now available at the LHC, both CMS and ATLAS experiments also
performed differential cross-section measurements in single-top t-channel production [180], [210].
Such measurements are extremely useful as they test our understanding of both QCD and EW
top-quark interactions. Using the full Run-2 dataset of 139 fb−1 , ATLAS measures the threecomponents of the top-quark and top-antiquark polarisation vectors in t-channel single-top-quark
production simultaneously from the distributions of the direction cosines of the charged-lepton
momentum in the top-quark rest frame in single-lepton plus jets events. The three componentsof the polarisation vector for the selected top-quark event sample are Px0 = 0.01 ± 0.18, Py0 =−0.029±0.027, Pz 0 = 0.91±0.10 and for the top-antiquark event sample they are Px0 = −0.02±0.20,
Py0 = −0.007 ± 0.051, Pz 0 = −0.79 ± 0.16 [211]. They also present normalised differential crosssections corrected to a fiducial region at the stable-particle level as a function of the charged-lepton
angles for top-quark and top-antiquark events inclusively and separately, which are also used toderive bounds on the complex Wilson coefficient of the dimension-six OtW operator.
The CMS collaboration has measured differential single top quark t-channel production crosssections as functions of the transverse momentum and the absolute value of the rapidity of the top
quark. The analysis is performed in the leptonic decay channels of the top quark, with either amuon or an electron in the final state, using data collected with the CMS experiment at the LHC√
at s = 8 TeV and corresponding to an integrated luminosity of 19.7 fb−1 . Neural networks areused to discriminate the signal process from the various background contributions. The results arefound to agree with predictions from Monte Carlo generators [210]. Using the same data set andunder the assumption that the spin analyzing power of a charged lepton is 100% as predicted in theSM, they are also able to measure the spin asymmetry, sensitive to the top quark polarization of
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61. Top Quark

the top quark Aµ = 0.26 ± 0.03(stat) ± 0.10(syst) [212], which is compatible with a p-value of 4.6%,
equivalent to 2.0 standard deviation. At 13 TeV, using 35.9 fb−1 , CMS measures the differential
t-channel cross sections, for the first time in single-top production, and charge ratios for t-channel
single top quark production [192]. The results are found to be in agreement with SM predictions
using various NLO event generators and sets of parton distribution functions. Additionally, the spin
asymmetry, sensitive to the top quark polarization, is determined from the differential distributionof the polarization angle at parton level to be 0.440 ± 0.070, in agreement with the SM prediction.
This disfavours the results obtained at 8 TeV. ATLAS has measured the differential tW crosssection in 36.1 fb−1 at 13 TeV with respect to the energy of the b-jet, the energy of the system of
the two leptons and b-jet, and the transverse mass or mass of combinations of leptons, the b-jet
and neutrinos [213]. Using 35.9 fb−1 of eµ events, CMS measures the differential tW cross section.
A fiducial region is defined according to the detector acceptance, and the requirement of exactly
one b-tagged jet. The resulting distributions are unfolded to particle-level and compared withpredictions calculated at next-to-leading order in perturbative QCD. Within current uncertainties,
all the predictions agree with the data [214].
Further measurements of electroweak single-top quark production in association with addition
electroweak gauge bosons such as tZq or tγq production are covered in the section Top-Quark
Electroweak Charges and Couplings, Sec 61.2.5.4.
61.2.2 Top-Quark Asymmetries
A forward-backward asymmetry in tt production at a pp collider arises starting at order αS3
in QCD from the interference between the Born amplitude qq → tt with 1-loop box production
diagrams and between diagrams with initial- and final-state gluon radiation. The asymmetry, AF B ,is defined byN (∆y > 0) − N (∆y < 0),(61.5)AF B =N (∆y > 0) + N (∆y < 0)where ∆y = yt − yt is the rapidity difference between the top- and the anti-top quark. Calculations
at αS3 predict a measurable AF B at the Tevatron. The most recent calculations up to order αS4 ,including electromagnetic and electroweak corrections, yield a predicted asymmetry of ≈(9.5±0.7)%[215]. This is about 10% higher than the previous calculation at NLO [216, 217], and improves theagreement with experiment.
Contrary to most measurements in the top sector, many measurements in this section are
statistically limited. This is true - by construction - in the measurements in extreme corners ofphase space (i.e. boosted measurements) and in rare production processes like ttW and ttγ. The
progress in these measurements is expected to be achieved quite rapidly, as Run-3 athe the LHC
and subsequent runs deliver more data.
Both CDF and DØ measured asymmetry values in excess of the SM prediction, fueling speculation about exotic production mechanisms (see, for example, [218] and references therein). The
first measurement of this asymmetry by DØ in 0.9 fb−1 [219] found an asymmetry at the detector
level of (12 ± 8)%. The first CDF measurement in 1.9 fb−1 [220] yielded (24 ± 14)% at partonlevel. Both values were higher, though statistically consistent with the SM expectation. With theaddition of more data, the uncertainties have been reduced, and the central values, if somewhat
smaller, have remained consistent with the first measurements. At the same time, the improved
calculations from theory have increased the predicted asymmetry values, improving the agreement
between theory and experiment.
√
CDF and DØ have combined results using the full Tevatron dataset at s = 1.96 TeV [221].
Three combined asymmetries are reported: Att
F B as defined in Eq. 61.5 for fully-reconstructed
tt events, a single-lepton asymmetry, A`F B defined as in Eq. 61.5 but with ∆y replaced by the
31st May, 2024

61. Top Quark

23

product of the lepton charge and pseudo-rapidity, and a dilepton asymmetry, A``F B , defined asin Eq. 61.5 but with ∆y replaced by ∆η between the two leptons. The combined results are
AFtt B = 0.128 ± 0.021 ± 0.014, A`F B = 0.073 ± 0.016 ± 0.012, and A``
F B = 0.108 ± 0.043 ± 0.016,
where the first uncertainty is statistical and the second systematic. These are to be compared to SM
predictions at NNLO QCD and NLO electroweak of AFtt B = 0.095±0.007 [215], A`F B = 0.038±0.003,
and A``F B = 0.048 ± 0.004 [217], respectively. Both experiments have also measured differential
asymmetries, in bins of Mtt , ∆y, q` × η` , and ∆η`` , with consistent results, though the growth ofAtt
F B with increasing Mtt and ∆y appears somewhat more rapid than the SM prediction [221].
At the LHC, where the dominant tt production mechanism is the charge-symmetric gluongluon fusion, the measurement is more difficult. For the sub-dominant qq production mechanism,
the symmetric pp collision does not define a forward and backward direction. Instead, the charge
asymmetry, AC , is defined in terms of a positive versus a negative t − t rapidity difference, ∆yAttC=N (∆|y| > 0) − N (∆|y| < 0).
N (∆|y| > 0) + N (∆|y| < 0)(61.6)

Both CMS and ATLAS have measured AC in the LHC dataset. Using lepton+jets events√in 4.7 fb−1 of data at s = 7 TeV, ATLAS measures Att
C = (0.6 ± 1.0)% [222]. ATLAS has√reported on the same measurement performed at s = 8 TeV with 20.3 fb−1 of data, with a√s = 8 TeV, ATLAS measures [224]
result of Att
C = (0.9 ± 0.5)% [223]. In the dilepton channel at
tt``
AC = (2.1 ± 1.6)%, and AC = (0.8 ± 0.6)% (defined in terms of the ∆η of the two leptons)
in agreement with the SM predictions of (1.11 ± 0.04)% and (0.64 ± 0.03)%, respectively [217].
√
Using lepton+jets events CMS has measured AC at both s = 7 and 8 TeV. They measure−1 at √s = 7 TeV andAtt
and Att
C = (0.4 ± 1.5)%
C = (0.33 ± 0.26(stat.) ± 0.33(syst.))% in 5.0 fb√
in 19.7 fb−1 at s = 8 TeV, respectively [225, 226]. Both measurements are consistent with the√√s = 7 TeV and (1.11 ± 0.04)% at s = 8 TeV [217],
SM expectations of Att
C = (1.23 ± 0.05)% at
although the uncertainties are still too large for a precision test. In 19.5 fb−1 of dilepton events at√
tt = (1.1 ± 1.3)% and A`` = (0.3 ± 0.7)% [227], consistent with SM
s = 8 TeV, CMS measures AC
C
expectations [228].
In their 7 and 8 TeV analyses, ATLAS and CMS also provide differential measurements asa function of Mtt and the transverse momentum pT and rapidity y of the tt system. To reduce
model-dependence, the CMS collaboration has performed a measurement in a reduced fiducial
phase space [229], with a result of AC = (−0.35 ± 0.72(stat.) ± 0.31(syst.))%, in agreement withSM expectations.
To specifically address the dependence of the asymmetry on Mtt , ATLAS has performed a√
measurement in boosted tt events [230]. In 20.3 fb−1 of data at s = 8 TeV, in events with
tt = (4.2 ± 3.2)% compared to a NLO SM
Mtt > 0.75 TeV, and |(∆|y|)| < 2, ATLAS measures AC
prediction of (1.60 ± 0.04)%. The measurement is also presented in three bins of Mtt , each inagreement, though with large uncertainties, with the SM expectations.
Both ATLAS and CMS have measured asymmetries in the distribution of leptons from tt decays.
√
ATLAS, in 4.6 fb−1 of s = 7 TeV data, has measured A`` = (2.4 ± 1.5(stat.) ± 0.9(sys.))% in
dilepton events [231]. Using a neutrino weighting technique in the same dataset to reconstruct the√
top quarks, ATLAS measures AC = (2.1±2.5 (stat.)±1.7 (sys.))%. CMS, in 5.0 fb−1 of s = 7 TeV
data, uses dilepton events to measure AC = (1.0±1.5 (stat.)±0.6 (sys.))%, where a matrix weighting
technique is used to reconstruct the top quarks, and A`` = (0.9 ± 1.0 (stat.) ± 0.6 (sys.))% [232]. An
earlier result using lepton+jets events from the same CMS dataset found AC = (0.4 ± 1.0 ± 1.1)%√[225]. Combined results from ATLAS and CMS have now been released [233]. At s = 7 TeV√
the combined result is AC = (0.5 ± 0.7 (stat.) ± 0.6 (sys.))%, and at s = 8 TeV it is AC =31st May, 2024

24

61. Top Quark(0.55 ± 0.23 ± 0.25)%. These results are all consistent, within their large uncertainties, with the
SM expectations of A`` = (0.70 ± 0.03)% and AC = (1.23 ± 0.05)% [217].
√
ATLAS has released a charge asymmetry measurement at s = 13 TeV using the full 139 fb−1
dataset, which combines data in the single-lepton and dilepton channels, and employs reconstruction
techniques adapted to both the resolved and boosted topologies. A Bayesian unfolding procedure
is performed to correct for detector resolution and acceptance effects. The combined inclusivett̄ charge asymmetry is measured to be AC= 0.0068 ± 0.0015, which differs from zero by 4.7tt̄
standard deviations. Differential measurements are performed as a function of the invariant mass,transverse momentum and longitudinal boost of the tt̄ system. Both the inclusive and differential
measurements are found to be compatible with the Standard Model predictions, at NLO in QCD
with NLO electroweak corrections [234]. The measurements are interpreted in the framework of theStandard Model effective field theory, placing competitive bounds on several Wilson coefficients.
A model-independent comparison of the Tevatron and LHC results is made difficult by thediffering tt production mechanisms at work at the two accelerators and by the symmetric nature of
the pp collisions at the LHC. A recent result from the CMS Collaboration [235] in 35.9 fb−1 of lepton√
plus jets events at s = 13 TeV, uses a likelihood analysis to separate the q q̄ process from production
via gluon-gluon and gluon-quark interactions and extract AF B = (4.8+8.8−8.4 (stat.) ± 2.8 (sys.))%.
In addition, given a particular model of BSM physics, a comparison can be obtained through theresulting asymmetry predicted by the model at the two machines, see for example [230].
Using 139 fb−1 of data at 13 TeV in the lepton plus jets channel, ATLAS presents a measurementof the charge asymmetry in tt̄ production in association with a photon. While the tt̄ asymmetry isdiluted in inclusive measurements at the LHC owing to the large fraction of gluon–gluon-initiated tt̄
events, it is enhanced in other topologies such as tt̄γ due to an increased fraction of the quark initiated production mode. The charge asymmetry is obtained from the distribution of the difference of
the absolute rapidities of the top quark and antiquark using a profile likelihood unfolding approach.
It is measured to be AC = −0.003 ± 0.029 in agreement with the Standard Model expectation [236],
where the precision is limited by the presently available statistics.
In a similar fashion and using the same dataset, ATLAS also searches for the leptonic charge
asymmetry (A`C ) of tt̄ pair production in association with a W boson (tt̄W ) in event final stateswith exactly three charged light leptons (electrons or muons). Here, the events are also enhanced
in quark-initiated production processes. Additionally, the W boson in the initial state causespolarisation of the tt̄ pair, which further leads to a sizeable asymmetry. A profile-likelihood fit to
the event yields in multiple regions corresponding to positive and negative differences between thepseudorapidities of the charged leptons from top-quark and top-antiquark decays is used to extract
the charge asymmetry. At reconstruction level, the asymmetry is found to be −0.12 ± 0.14(stat.) ±0.05(syst.). An unfolding procedure is applied to convert the result at reconstruction level into acharge-asymmetry value in a fiducial volume at particle level with the result of −0.11±0.17(stat.)±0.05(syst.). The Standard Model expectations for these two observables are calculated using Monte
Carlo simulations with NLO plus parton shower precision in QCD and including NLO electroweak+0.007
corrections. They are 0.084+0.005−0.003 (scale)±0.006(M Cstat.) and 0.063−0.004 (scale)±0.004(M Cstat.),respectively, and in agreement with the measurements [237].
ATLAS explores a so-called ‘energy asymmetry’ in tt production in association with a high-pT
jet (ttj production). The energy asymmetry is defined as a difference between the top and anti-top
quarks’ energies, and is measured in ATLAS in three bins of the associated high-pT jet angle, θj .
Both, the energies and jet angle, are measured in the tt̄j rest frame. A Bayesian unfolding method
corrects for resolution and acceptance effects. The measurement is in agreement with the Standard
Model at NLO accuracy [238].
In an early analysis of the Run-2 data, CMS analyzed 35.9 fb−1 of 13 TeV data, in par31st May, 2024

61. Top Quark

25

ticular using tt̄ events decaying to muon or electron and jets in final states with low and highLorentz boosts. Events are reconstructed using a fit of the kinematic distributions of the decay products to those expected for tt̄ final states. The values found for the asymmetry parame+0.020
ters are AF B = 0.048+0.095−0.087 (stat)−0.029 (syst), for the anomalous chromomagnetic dipole moment+0.013+0.016tµ = −0.024−0.009 (stat)−0.011 (syst), and a limit is placed on the magnitude of a possible anomalouschromoelectric dipole moment |dt | < 0.03 at 95% confidence level [239].
The measurement of the charge asymmetry in tt̄ events with highly Lorentz-boosted top quarks
decaying to a single, nonisolated lepton and overlapping jets is presented by CMS using the complete
Run-2 dataset of 138 fb−1 of 13 TeV data. The top quark charge asymmetry is measured for eventswith a tt̄ invariant mass larger than 750 GeV, most relevant for BSM searches, and corrected for
detector and acceptance effects using a binned maximum likelihood fit. The measured top quark
charge asymmetry of (0.69+0.65−0.69 )% is in good agreement with the standard model prediction at
NNLO in QCD with NLO electroweak corrections. The result is also presented for two invariant
mass ranges, 750 – 900 and > 900 GeV [240].
61.2.3 Top Quark Spin Correlations, Polarization, and Entanglement
One of the unique features of the top quark is that it decays before its spin can be flipped bychromomagnetic interactions. Thus the top quark polarization is directly observable via the angular
distribution of its decay products and it is possible to define and measure observables sensitive to the
top quark spin and its production mechanism. Although the top- and antitop-quarks produced bystrong interactions in hadron collisions are essentially unpolarized, the spins of t and t̄ are correlated.
For QCD production at threshold, the tt̄ system is produced in a 3 S1 state with parallel spins forq q̄ annihilation or in a 1 S0 state with antiparallel spins for gluon-gluon fusion. The situations at
the Tevatron, where the production is primarily from q q̄ annihilation, and at the LHC, where theproduction is primarily from gluon-gluon fusion, are therefore somewhat complementary. However,at the LHC production of tt̄ pairs at large invariant mass occurs primarily via fusion of gluons
with opposite helicities, and the tt̄ pairs so produced have parallel spins as in production at theTevatron via q q̄ annihilation. The direction of the top quark spin is 100% correlated to the angular
distributions of the down-type fermion (charged leptons or d-type quarks) in the decay. The joint
angular distribution [241–243]
1
d2 σ
1= (1 + B+ cos θ+ + B− cos θ− + κ · cos θ+ · cos θ− ),σ d(cos θ+ )d(cos θ− )4

(61.7)

where θ+ and θ− are the angles of the daughters in the top-quark rest frame with respect to aparticular spin quantization axis (assumed here to be the same for θ+ and θ− ), is a very sensitive
observable. The maximum value for κ, 0.782 at NLO at the Tevatron [244], is found in the offdiagonal basis [241], while at the LHC the value at NLO is 0.326 in the helicity basis [244]. The
coefficients B+ and B− are near zero in the SM because the top quarks are unpolarized in tt̄
production. In place of κ, Aα+ α− is often used, where αi is the spin analyzing power, and A is thespin correlation coefficient, defined asA=N (↑↑) + N (↓↓) − N (↑↓) − N (↓↑),
N (↑↑) + N (↓↓) + N (↑↓) + N (↓↑)

(61.8)

where the first arrow represents the direction of the top quark spin along a chosen quantization
axis, and the second arrow represents the same for the antitop-quark. The spin analyzing power αi
is +0.998 for positively charged leptons, -0.966 for down-type quarks from W decays, and -0.393
for bottom quarks [245]. The sign of α flips for the respective antiparticles. The spin correlation
could be modified by a new tt̄ production mechanism such as through a Z 0 boson, Kaluza-Klein
gluons, a dark-matter mediator, or a Higgs boson.
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61. Top Quark

The experiments typically use a Monte Carlo to provide templates for the measured distributions, or alternatively a matrix-element technique, and fit a parameter f , representing the fractionof events with the expected Standard Model correlation, with (1 − f ) the fraction with no correlation. The correlation coefficient is extracted via Ameas = f · ASM . A ‘fraction’ f > 1 means thatthe measured correlation coefficient is larger than the Standard Model expectation.
For a more complete introduction and discussion of the spin density matrix, see reference [246].
CDF and DØ have studied spin correlations in tt̄ production in the dilepton and lepton+jets
channel with limited sensitivity, showing first evidence (see the PDG listings for details).
Spin correlations have been conclusively measured at the LHC by both the ATLAS and CMS
collaborations. In the dominant gluon fusion production mode for tt̄ pairs at the LHC, the angular
distribution between the two leptons in tt̄ decays to dileptons is sensitive to the degree of spincorrelation [247].
Measurements have been made at 7, 8, and now 13 TeV. While there is some interest in the√s dependence of the correlations as a test of the production mechanism (q q̄ vs gluon-gluon andpossible sensitivity to new physics) the earlier measurements at 7 and 8 TeV [248–253] had relatively
large uncertainties and have now been overtaken by the high-statistics 13 TeV measurements, which
we review here.
√
In an ATLAS measurement at s = 8 TeV [254], the spin-correlation coefficient κ is measured
in the helicity basis to be κ = 0.296 ± 0.093 in good agreement with the SM expectation of 0.318(corresponding to a central value of f of 0.931). The polarization coefficients, B, in Eq. 61.7 aremeasured, also in the helicity basis, to be B+ = −0.044±0.038 and B− = −0.064±0.040, consistent
with the SM predictions of 0.0030 ± 0.0010 and 0.0034 ± 0.00104, respectively.
√
The most recent result from ATLAS, in 36.1 fb−1 at s = 13 TeV, uses ∆φ, the azimuthal
angle between the two charged leptons in eµ events in an analysis that also measures the differential
cross sections in ∆φ and ∆η between the two leptons [255]. The result, measured by comparison
with NLO Monte Carlo generators, is f = 1.249 ± 0.024 ± 0.061+0.067−0.090 , where the uncertainties are
statistical, systematic, and theoretical, is again greater than 1.0. Whereas the previous results were
statistically consistent with the Standard Model expectation of 1.0, this result is slightly higher
than the expectation and hence inconsistent at the level of 2.2σ. The NLO generators are NLO in
QCD only (and only at the production level). Including electroweak couplings produces an expectedStandard Model distribution consistent with the data, but results in a large scale uncertainty, giving
f = 1.03 ± 0.13.
√
In 35.9 fb−1 of data at s = 13 TeV, CMS has studied spin correlations in dilepton events
via the measurement of parton-level normalized differential cross sections, sensitive to each of the
independent coefficients of the spin-dependent parts of the tt̄ production density matrix. The
measured distributions and extracted coefficients are compared with standard model predictions
from simulations at NLO accuracy in QCD, and from NLO QCD calculations including electroweak
corrections. The normalized differential cross sections are used in fits to constrain the anomalouschromomagnetic and chromoelectric dipole moments of the top −0.24 < CtG /Λ2 < 0.07 TeV−2 andI /Λ2 < 0.20 TeV−2 , respectively, at 95% confidence level [256]. These results are part of−0.33 < CtG√
a complete study of the top quark spin density matrix at s = 13 TeV, through the measurementof the coefficients of Eq. 61.7.
Entanglement is a striking feature of quantum mechanics [257–259]. If two particles are entangled, the state of one particle cannot be described independently from the other. More precisely, anentangled state is one that cannot be written as a convex combination of product states of density
matrices [260,261]. It has been observed in a wide variety of systems, ranging from the microscopic
to the macroscopic scale. However, up to now entanglement has remained largely unexplored at
high-energy colliders, except for flavor entanglement in Υ (4S) → B0 B̄0 decays [262] and a study of
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61. Top Quark

Bell inequality violation in B0 → J/Ψ K ∗ (892)0 decays [263]. Entanglement in top quark pairs has
now been proposed to be studied for the first time via their spin correlation [264–271].
At the LHC, tt̄ pairs are produced mainly via gluon-gluon fusion. When they are produced
close to their production threshold, that is, when their invariant mass (mtt̄ ) is close to twice
the mass of the top quark (mtt̄ ≈ 2 · mt ≈ 350 GeV), they exist nearly in a spin singlet state,
which is therefore expected to be maximally entangled. After averaging over all possible top-quark
directions, entanglement only survives at threshold because there the tt̄ pairs are produced in a spin
singlet, which is rotationally invariant. The rotational invariance of a spin singlet implies that thetrace of the spin correlation matrix C is a good entanglement witness. It is an observable that cansignal the presence of entanglement without any assumption on the particular form of the quantum
state, with tr[C] + 1 < 0 as a sufficient condition for entanglement. It is more convenient to define
an entanglement witness using
D = tr[C]/3,(61.9)

D = −3 · hcos φi,(61.10)which can be experimentally measured as:

where hcos φi is the average of the angle between the charged lepton directions in each one of theparent top quark and antitop quark rest frames which can be experimentally measured from anensemble dataset. The existence of an entangled state is demonstrated if the measurement satisfies
D < −1/3.
Using 139 fb−1 of Run-2 data, recorded at 13 TeV, ATLAS reports the highest-energy observation of entanglement so far in top–antitop quark events produced at the Large Hadron Collider.
Spin entanglement is now detected from the measurement of a single observable D, inferred by
the angle between the charged leptons in their parent top- and antitop-quark rest frames. The
observable is measured on a narrow interval around the tt̄ production threshold, where the entanglement detection is expected to be significant. The entanglement observable is measured
in a fiducial phase-space with stable particles. The entanglement witness is measured to be
D = −0.547 ± 0.002(stat.) ± 0.021(syst.) for 340 < mtt̄ < 380 GeV [272]. The large spreadin predictions from several mainstream event generators indicates that modelling this property
is challenging. The predictions depend in particular on the parton-shower algorithm used. The
observed result is more than five standard deviations from a scenario without entanglement andhence constitutes the first observation of entanglement in a pair of quarks, and the observation ofentanglement at the highest energy to date.
61.2.4 W -Boson Helicity in Top-Quark Decay
The Standard Model dictates that the top quark has the same vector-minus-axial-vector (V −A)
charged-current weak interactions −i √g2 Vtb γ µ 21 (1 − γ5 ) as all the other fermions. In the SM, thefraction of top-quark decays to longitudinally polarized W bosons is proportional to its Yukawa
coupling and hence enhanced with respect to the weak coupling. It is expected to be [273] F0SM ≈
2 (F SM ∼ 70% for m = 173 GeV/c2 ). Fractions of left-handed, rightx/(1 + x), x = m2t /2MWt0handed, or longitudinal W bosons are denoted as F− , F+ , and F0 respectively. In the SM, F− isexpected to be ≈ 30% and F+ ≈ 0%. Predictions for the W polarization fractions at NNLO in
QCD are available [274].
The Tevatron and the LHC experiments use various techniques to measure the helicity of theW boson in top-quark decays, in both the lepton+jets and in dilepton channels in tt̄ production.
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61. Top Quark

The first method uses a kinematic fit, similar to that used in the lepton+jets mass analyses,
but with the top-quark mass constrained to a fixed value, to improve the reconstruction of finalstate observables, and render the under-constrained dilepton channel solvable. Alternatively, in the
dilepton channel the final-state momenta can also be obtained through an algebraic solution of thekinematics. The distribution of the helicity angle (cos θ∗ ) between the lepton and the b quark in
the W rest frame provides the most direct measure of the W helicity. In a simplified version of thisapproach, the cos θ∗ distribution is reduced to a forward-backward asymmetry.
The second method (p`T ) uses the different lepton pT spectra from longitudinally or transversely
polarized W -decays to determine the relative contributions.
2)
A third method uses the invariant mass of the lepton and the b-quark in top-quark decays (M`b∗as an observable, which is directly related to cos θ .
At the LHC, top-quark pairs in the dilepton channels are reconstructed using the neutrino
weighting technique, see section 61.2.5.1.
Finally, the Matrix Element Method (MEM) has also been used [275], in which a likelihood isformed from a product of event probabilities calculated from the MEM for a given set of measured
kinematic variables and assumed W -helicity fractions.
The results of recent CDF, DØ, ATLAS, and CMS analyses are summarized in Table 61.2. The
datasets are now large enough to allow for a simultaneous fit of F0 , F− and F+ , which we denote by‘3-param’ or F0 and F+ , which we denote by ‘2-param’ in the table. Results with either F0 or F+
fixed at its SM value are denoted ‘1-param’. For the simultaneous fits, the correlation coefficient
between the two values is about −0.8. A complete set of published results can be found in the
Listings. All results are in agreement with the SM expectation.
CDF and DØ combined their results based on 2.7 − 5.4 fb−1 [276] for a top-quark mass of√
172.5 GeV/c2 . ATLAS presents results from 1.04 fb−1 of s = 7 TeV data using a template
method for the cos θ∗ distribution and angular asymmetries from the unfolded cos θ∗ distribution
in the lepton+jets and the dilepton channel [277]. CMS performs a similar measurement basedon template fits to the cos θ∗ distribution with 5.0 fb−1 of 7 TeV data in the lepton+jets final
state [278]. As the polarization of the W bosons in top-quark decays is sensitive to the W tb vertex
Lorentz structure and anomalous couplings, both experiments also derive limits on anomalous
contributions to the W tb couplings. CMS and ATLAS collaborations have also combined theirresults from 7 TeV data to obtain values on the helicity fractions as well as limits on anomalous
couplings [279].
At 8 TeV, ATLAS came out with a measurement of the W-helicity fractions in 20.2 fb−1 in
lepton+jets events with at least one b-tag [280]. Using 19.8 fb−1 of 8 TeV data, CMS measured theW-helicity in lepton + 4 jet events with two b-tags [281] as well as in events with two opposite-sign
leptons (electron or muon) in the final state, applying six kinematic constraints on the kinematicsof the produced particles [282]. Also, using the same dataset, a first measurement of the W boson helicity in top-quark decays was made in electroweak single top production [283], yielding
similarly precise and consistent results. The 8 TeV results obtained in tt̄ and single-top eventsby ATLAS and CMS have also been combined recently [284]. These results are in agreementwith the standard model predictions at next-to-next-to-leading order in perturbative QCD andrepresent an improvement in precision of 25 (29)% for F0 (FL ) with respect to the most precise
single measurement. A limit on anomalous right-handed vector (VR ), and left- and right-handed
tensor (gL , gR ) tW b couplings and on corresponding Wilson coefficients is set.
Recently, ATLAS used 139 fb−1 of data recorded at 13 TeV in dilepton events with at least twob-tags to measure the normalised differential tt̄ cross section with respect to cos θ∗ at parton leveland from that, based on template fits, extract the helicity fractions. The results are complementary
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61. Top Quark29

to previous results and compatible with Standard Model expectations [285].
Table 61.2: Measurement and 95% C.L. upper limits of the W helicity in top-quark decays. The
table includes both preliminary, as of September 2023, and published results. A full set of publishedresults, including the results obtained at the Tevaton, is given in the Listings.
W Helicity
F0 = 0.67 ± 0.07
F0 = 0.682 ± 0.045
F0 = 0.626 ± 0.059
F0 = 0.709 ± 0.019
F0 = 0.681 ± 0.026
F0 = 0.653 ± 0.029
F0 = 0.720 ± 0.054
F0 = 0.693 ± 0.014
F0 = 0.684 ± 0.015
F+ = 0.01 ± 0.05
F+ = 0.008 ± 0.018
F+ = 0.015 ± 0.034
F+ = −0.008 ± 0.014
F+ = −0.004 ± 0.015
F+ = 0.018 ± 0.027
F+ = −0.018 ± 0.022
F+ = −0.008 ± 0.007
F+ = −0.002 ± 0.014

RLdt(fb−1 )ATLAS (7 TeV)
1.0
CMS (7 TeV)
5.0
ATLAS+CMS (7 TeV) 2.2
ATLAS (8 TeV)
20.2
CMS (8 TeV)
19.8
CMS (8 TeV)
19.7
CMS (8 TeV)
19.7
ATLAS+CMS (8 TeV) 20
ATLAS (13 TeV)139
ATLAS (7 TeV)
1.0
CMS (7 TeV)
5.0
ATLAS+CMS (7 TeV) 2.2
ATLAS (8 TeV)
20.2
CMS (8 TeV)
19.8
CMS (8 TeV)
19.7
CMS (8 TeV)
19.7
ATLAS+CMS (8 TeV) 20
ATLAS (13 TeV)
139
SourceRef.

Method

[277]
[278]
[279]
[280]
[281]
[282]
[283]
[284]
[285]
[277]
[278]
[279]
[280]
[281]
[282]
[283]
[284]
[285]

cos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-paramcos θ∗ 3-param

61.2.5 Top-Quark Properties
61.2.5.1 Top-Quark Mass Measurements
The most precisely studied property of the top quark is its mass. The top-quark mass has beenmeasured in the lepton+jets, the dilepton, and the all-jets channel by all four Tevatron and LHC
experiments, and now in single-top events at the LHC. The latest and/or most precise results are
summarized in Table 61.3. The lepton+jets channel yields the most precise single measurements
because of good signal to background ratio (in particular after b-tagging) and the presence of onlya single neutrino in the final state. The momentum of a single neutrino can be reconstructed (upto a quadratic ambiguity) via the missing ET measurement and the constraint that the lepton andneutrino momenta reconstruct to the known W boson mass. In the large data samples available atthe LHC, measurements in the dilepton channel can be competitive and certainly complementary
to those in the lepton+jets final state.
A large number of techniques have now been applied to measuring the top-quark mass. The original ‘template method’ [286], in which Monte Carlo templates of reconstructed mass distributions
are fit to data, has evolved into a precision tool in the lepton+jets channel, where the systematic
uncertainty due to the jet energy scale (JES) uncertainty is controlled by a simultaneous, in situ
fit to the W → jj hypothesis [287]. All the latest measurements in the lepton+jets and the all-jets√
channels use this technique in one way or another. In 20.2 fb−1 of data at s = 8 TeV in the
lepton+jets channel, ATLAS achieves a total uncertainty of 0.53% with a statistical component of
0.23% [288]. The measurement is based on a 3-dimensional template fit, determining the top-quark
31st May, 2024

30

61. Top Quark

mass, the global jet energy scale and a b-to-light jet energy scale factor. The most precise CMS
result in the lepton+jets channel uses an ideogram method and comes from a so-called ‘hybrid’
approach in which the prior knowledge about the jet energy scale is incorporated as a Gaussianconstraint, with a width determined by the uncertainty on the jet energy corrections. In 19.7 fb−1√of s = 8 TeV data, CMS achieves a total uncertainty of 0.30% with a statistical component of
0.09% with the hybrid approach [289]. Using this same method, CMS has released a top-mass√measurement from s = 13 TeV data. Using 35.9 fb−1 of lepton+jets events they measure the top
mass with a precision of 0.36%, with a statistical component of 0.05% [290]. The measurements at√
s = 13 TeV include, for the first time, an uncertainty due to ‘color reconnection’ [291,292]. In thissame dataset, CMS has extracted a top mass from highly boosted top-quark decays by selecting
events in which the hadronic-side top decay is reconstructed as a single jet with PT > 400 GeV.
The cross section as a function of jet mass is unfolded at the particle level to extract a top mass
with a precision of 1.4% [293].
The template method is complemented by the ‘matrix element’ method. This method was
first applied by the DØ Collaboration [294], and is similar to a technique originally suggested by
Kondo et al. [275] and Dalitz and Goldstein [295]. In the matrix element method a probability foreach event is calculated as a function of the top-quark mass, using a LO matrix element for the
production and decay of tt̄ pairs. The in situ calibration of dijet pairs to the W → jj hypothesis
is now also used with the matrix element technique to constrain the jet energy scale uncertainty.
In the lepton+jets channel, DØ uses the full Tevatron dataset of 9.7 fb−1 and yields an uncertainty
of about 0.43% [296].
In the dilepton channel, the signal to background is typically very good, but reconstruction of
the mass is non-trivial because there are two neutrinos in the final state, yielding a kinematicallyunconstrained system. A variety of techniques have been developed to handle this. An analytic
solution to the problem has been proposed [297], but this has not yet been used in the massmeasurement. One of the most precise measurements in the dilepton channel comes from using theinvariant mass of the charged lepton and b-quark system (M`b ), which is sensitive to the top-quark√
mass and avoids the kinematic difficulties of the two-neutrino final state. In 4.6 fb−1 of s = 7
TeV data, ATLAS has measured the top-quark mass in the dilepton channel to a precision of 0.53%√
using a template fit to the M`b distribution [298]. Using 19.7 fb−1 of data at s = 8 TeV, CMS has
released [299] a mass measurement in the dilepton channel based on a simultaneous fit to M`b anda transverse-mass-like variable MT 2 [300]. The most precise result in this analysis, which comesfrom a linear combination of fits with the jet energy scale fixed at its nominal value and one thatsimultaneously determines the top mass and jet energy scale, has a total uncertainty of 0.54%. At
the LHC, because of their precision, these techniques have largely displaced a number of earlier
techniques in the dilepton channel, though these techniques are still included, and described, in the
combined results from CMS, reported in Ref. [289].
In the neutrino weighting technique, used by CDF to analyze the full Run 2 dilepton dataset of
9.1 fb−1 , a weight is assigned by assuming a top-quark mass value and applying energy-momentum
conservation to the top-quark decay, resulting in up to four possible pairs of solutions for theneutrino and anti-neutrino momenta. The missing ET calculated in this way is then compared tothe observed missing ET to assign a weight [305]. The CDF result achieves a precision of 1.8%
using a combination of neutrino weighting and an “alternative mass”, which is insensitive to thejet energy scale [306]. The alternative mass depends on the angles between the leptons and theleading jets and the lepton four-momenta.
In the all-jets channel there is no ambiguity due to neutrino momenta, but the signal to background is significantly poorer due to the severe QCD multijets background. The emphasis therefore
has been on background modeling, and reduction through event selection. The most recent mea31st May, 2024

61. Top Quark

31

Table 61.3: Measurements of top-quark mass from Tevatron and LHC. The results are a selection of both published and preliminary (not yet submitted for publication as of September 2023)
measurements. For a complete set of published results see the Listings. Statistical uncertainties
are listed first, followed by systematic uncertainties.
mt (GeV/c2 )172.08 ± 0.25 ± 0.41
172.44 ± 0.13 ± 0.47
172.35 ± 0.16 ± 0.48
172.34 ± 0.20 ± 0.70
173.72 ± 0.55 ± 1.01
172.25 ± 0.08 ± 0.62
172.6 ± 0.4 ± 2.4
172.13 ± 0.32+0.69−0.70
174.30 ± 0.35 ± 0.54
173.34 ± 0.27 ± 0.71
172.52 ± 0.14 ± 0.30

Source
ATLAS
CMS
CMS
CMS
ATLAS
CMS
CMS
CMS
CDF,DØ (I+II)
Tevatron+LHC
ATLAS+CMS

Ldt fb−1
20.2
19.7
19.7
35.9
20.2
35.9
35.9
35.9
≤9.7
≤8.7+≤4.9≤5+≤20
R

Ref.
[288]
[289]
[289]
[301]
[302]
[290]
[293]
[303]
[304]
[29]
[1]

Channel`+jets+``+All jets`+jets+``+All jets`+jets``All jets`+jetsBoosted jets
Single top
publ. or prelim.
publ. or prelim.
prelim.

√surement in the all-jets channel, by CMS in 35.9 fb−1 of s = 13 TeV data [301], uses an ideogram
method and a 2-dimensional simultaneous fit for mt and the jet energy scale to extract the topquark mass and achieves a precision of 0.36%. A measurement from ATLAS [302] uses a template
fit to the ratio of three-jet (mt ) to two-jet (MW ) mass in the all-hadronic channel, the two-jet de√nominator provides an in situ, fit to the W → jj hypothesis. In 20.2 fb−1 of data at s = 8 TeV,
the result has a precision of 0.65%. A measurement from CDF in 9.3 fb−1 uses a two-dimensional
template fit and achieves a precision of 1.1% [307].
The CMS Collaboration extracted a top-quark mass measurement from single-top events, something not previously done because of the poor signal to background ratio. The mass is extracted
from the invariant mass of the muon, bottom quark, and missing transverse energy. The first mea√
surement with 19.7 fb−1 of data at s = 8 TeV, achieved a precision of 0.71% [308]. A more recent√
measurement in 35.9 fb−1 of data at s = 13 TeV achieves 0.44% precision [303].
A dominant systematic uncertainty in these methods is the understanding of the jet energy
scale, and so several techniques have been developed that have little sensitivity to the jet energy
scale uncertainty. In addition to Reference [306] mentioned above, these include the measurement of
the top-quark mass using the following techniques: Fitting of the lepton pT spectrum of candidate
events [309]; fitting of the transverse decay length of the b-jet (Lxy ) [310]; fitting the invariant
mass of a lepton from the W -decay and a muon from the semileptonic b decay [311, 312], kinematic
properties of secondary vertices from b-quark fragmentation [313], the invariant mass of the J/ψ + `system in events in which a b-quark fragments to a J/ψ particle [314], fitting the b-jet energy
peak [315], and dilepton kinematics in eµ events [316].
Several measurements have now been made in which the top-quark mass is extracted from themeasured tt cross section using the theoretical relationship between the mass and the production
cross section. These determinations make use of predictions calculated at higher orders, where
the top mass enters as an input parameter defined in a given scheme. At variance with the usual
methods, which involve the kinematic properties of the final states and therefore the pole mass,
this approach can also directly determine a short-distance mass, such as the MS mass [317]. Withan alternative method ATLAS extracted the top-quark pole mass using tt events with at least one
additional jet, basing the measurement on the relationship between the differential rate of gluon
31st May, 2024

32

61. Top Quark

radiation and the mass of the quark [318]. A similar analysis by CMS used the differential crosssection as a function of the invariant mass of the tt system and the leading jet not associated withthe top decays [319].
Each of the experiments has produced a measurement combining its various results. The combined measurement from CMS with up to 19.7 fb−1 of data achieves statistical and systematic
uncertainties of 0.08% and 0.27%, respectively [289]. The combined measurement from ATLAS,
with up to 20.3 fb−1 yields statistical and systematic uncertainties of 0.14% and 0.24%, respectively [288]. CDF has combined measurements with up to 9.3 fb−1 [320] and achieves a statisticalprecision of 0.33% and a systematic uncertainty of 0.43%. DØ achieves a 0.33% statistical+JES
and a 0.28% systematic uncertainty by combining results in 9.7 fb−1 [321].
Combined measurements from the Tevatron experiments and from the LHC experiments take
into account the correlations between different measurements from a single experiment and between
measurements from different experiments. The Tevatron average [304], using up to 9.7 fb−1 ofdata, now has a precision of 0.37%. The LHC combination, using up to 4.9 fb−1 of data, has a
precision of 0.56% [322], where more work on systematic uncertainties is required. A TevatronLHC combination has been released, combining the results of all four experiments, using the full√
Tevatron dataset and the s = 7 TeV LHC data, with a resulting precision of 0.44% [29]. Recently,
ATLAS and CMS have released a combinations of fifteen individual top quark mass measurements
in semi-leptonic and hadronic decays of the top quark, and a measurement using events enrichedin single top quark production via the electroweak t-channel. The data sets used correspond to
an integrated luminosity of up to 5 and 20 fb−1 , recorded at 7 and 8 TeV, respectively, yielding aprecision of 0.33 GeV (0.2%) [1].
The direct measurements of the top-quark mass, such as those shown in Table 61.3, correspondto the parameter used in the Monte Carlo generators, which is closely related to the pole mass [8].
The relation between the pole mass and short-distance masses, such as MS, is affected by nonperturbative effects. Recent calculations evaluate the size of this ambiguity to be below 250 MeV
and therefore still smaller than the current measurement uncertainty [323,324]. ATLAS has recently
performed a ‘calibration’ of the top mass parameter in Powheg + Pythia 8 with respect to theso-called ‘MSR’ mass scheme [325]. Using simulated lepton+jets events and the mass distributionof large-radius jets containing the three quarks from the hadronically decaying top quark, theyfind a mass difference between the Monte Carlo mass and the MSR mass of 80 MeV with large
uncertainties [326].
As a result of renormalization at higher-orders in perturbation theory, the top quark mass depends on the scale at which it is evaluated. The CMS collaboration has made the first measurementof the so-called running of the top-quark mass in the MS scheme [327]. The running mass is extracted from a measurement of the differential cross section as a function of the tt̄ invariant mass,
unfolded back to the parton level, in eµ final states. The running mass varies by about 15% fromMtt̄ = 400 GeV to Mtt̄ ≈ 1 TeV, in good agreement with the renormalization group calculation
at one-loop level. Compared to the hypothesis of no running, the significance of the measured
running is 2.6σ. However, caveats of such an interpretation have been raised as a result of the large
theoretical uncertainties [328].
With the discovery of a Higgs boson at the LHC with a mass of about 125 GeV/c2 [329, 330],
the precision measurement of the top-quark mass takes a central role in the question of the stabilityof the electroweak vacuum because top-quark radiative corrections tend to drive the Higgs quartic
coupling, λ, negative, potentially leading to an unstable vacuum. A calculation at NNLO [2] leads
to the conclusion of vacuum stability for a Higgs mass satisfying MH ≥ 129.4 ± 5.6 GeV/c2 [331].
Given the uncertainty, a Higgs mass of 125 GeV/c2 satisfies the limit, but the central values of the
Higgs and top-quark masses put the electroweak vacuum squarely in the metastable region. The
31st May, 2024

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61. Top Quark

uncertainty is dominated by the precision of the top-quark mass measurement and its interpretation
as the pole mass. For more details, see the Higgs boson review in this volume.
As a test of the CP T -symmetry, the mass difference of top- and antitop-quarks ∆mt = mt −mt̄ ,which is expected to be zero, can be measured. CDF measures the mass difference in 8.7 fb−1 of
1.96 TeV data in the lepton+jets channel using a template methode to find ∆mt = −1.95 ±1.11(stat.) ± 0.59(syst.) GeV/c2 [332] while DØ uses 3.6 fb−1 of lepton+jets events and the matrix
element method with at least one b-tag. They find ∆mt = 0.8±1.8(stat.)±0.5(syst.) GeV/c2 [333].
In 4.7 fb−1 of 7 TeV data, ATLAS measures the mass difference in lepton+jets events with adouble b-tag requirement and hence very low background to find ∆mt = 0.67 ± 0.61(stat.) ±0.41(syst.) GeV/c2 [334]. CMS measures the top-quark mass difference in 5 fb−1 of 7 TeV datain the lepton+jets channel and finds ∆mt = −0.44 ± 0.46(stat.) ± 0.27(syst.) GeV/c2 [335]. They
repeat this measurement with 19.6 fb−1 of 8 TeV data to find ∆mt = −0.15 ± 0.19(stat.) ±0.09(syst.) GeV/c2 [336]. Now that the top mass has been measured in single-top events, themass difference can be measured by tagging the top- or anti-top quark with the lepton charge. In
35.9 fb−1 of 13 TeV single-top candidate events CMS measures the mass ratio and difference to+0.77
be 0.995+0.005−0.006 and 0.83−1.01 GeV, respectively [303]. All measurements are consistent with the SM
expectation.
61.2.5.2 Width
Observation of top-quark spin correlations requires a top-quark lifetime less than the spin decorrelation timescale [337]. The top-quark width, inversely proportional to its lifetime, is expected
to be of order 1 GeV/c2 (Eq. 1). Early measurements made at CDF [338] and CMS [339] established confidence-level intervals for the width, but did not have the sensitivity to make a direct
measurement.
The first direct measurement comes from an ATLAS analysis that directly fits reconstructed√2
lepton+jets events in 20.2 fb−1 of data at s = 8 TeV. They find Γt = 1.76±0.33+0.79−0.68 GeV/c [340].
√−1
A more recent measurement from ATLAS with 139 fb
of data at s = 13 TeV [341], uses
a template fit to the lepton-b-quark invariant mass in dilepton final states. The result, Γt =(1.9 ± 0.5) GeV/c2 , is the most precise measurement to date.
The total width of the top-quark can also be determined from the partial decay width Γ (t →W b) and the branching fraction B(t → W b). DØ obtains Γ (t → W b) from the measured t-channel
cross section for single top-quark production in 5.4 fb−1 , and B(t → W b) is extracted from ameasurement of the ratio R = B(t → W b)/B(t → W q) in tt̄ events in lepton+jets channels with 0,
1 and 2 b-tags. Assuming B(t → W q) = 1, where q includes any kinematically accessible quark, the+0.90
2−25 s.
result is: Γt = 2.00+0.47−0.43 GeV/c which translates to a top-quark lifetime of τt = (3.29−0.63 )×10
0
Assuming a high mass fourth generation b quark and unitarity of the four-generation quark-mixing
matrix, they set the first upper limit on |Vtb0 | < 0.59 at 95% C.L. [342]. A similar analysis has√
performed by CMS in 19.7 fb−1 of s = 8 TeV data. It provides a better determination of the total2
width with respect to the measurement by DØ giving Γt = 1.36 ± 0.02(stat.)+0.14−0.11 (syst.) GeV/c[110].
61.2.5.3 Yukawa coupling
The top-Higgs Yukawa coupling is expected to be the largest among all Yukawa couplings. It
can be accessed directly by measurements of the tt̄ cross section in association with a Higgs boson,tt̄h, or indirectly via loop processes in h → γγ or h → W W decays or in the rare process of tt̄tt̄
production. A discussion of the former can be found in this review, See Sec. 11.3.3 of "Status ofHiggs Boson Physics", in this Review. Searches for and recently the observation of tt̄tt̄ production
is discussed in 61.2.1.3.
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61. Top Quark

61.2.5.4 Top-Quark Electroweak Charges and Couplings
The top quark is the only quark whose electric charge has not been measured through production
at threshold in e+ e− collisions. Furthermore, it is the only quark whose electromagnetic couplinghas not been observed and studied until recently. Since the CDF and DØ analyses on top-quark
production did not associate the b, b̄, and W ± uniquely to the top or antitop, decays such as
t → W + b̄, t̄ → W − b were not excluded. A charge 4/3 quark of this kind is consistent with current
electroweak precision data. The Z → `+ `− and Z → bb̄ data, in particular the discrepancy between
0,`
ALR from SLC at SLAC and A0,b
F B of b-quarks and AF B of leptons from LEP at CERN, can be fittedwith a top quark of mass mt = 270 GeV/c2 , provided that the right-handed b quark mixes with theisospin +1/2 component of an exotic doublet of charge −1/3 and −4/3 quarks, (Q1 , Q4 )R [343,344].
Also the third component of the top quark’s weak isospin has not been measured so far.
DØ studied the top-quark charge in double-tagged lepton+jets events, CDF did it in single
tagged lepton+jets and dilepton events. Assuming the top- and antitop-quarks have equal but
opposite electric charge, then reconstructing the charge of the b-quark through jet charge discrimination techniques, the |Qtop | = 4/3 and |Qtop | = 2/3 scenarios can be differentiated. For the exotic
model of Chang et al. [344] with a top-quark charge |Qtop | = 4/3, CDF excluded the model at
99% C.L. [345] in 5.6 fb−1 , while DØ excluded the model at a significance greater than 5 standard
deviations using 5.3 fb−1 and set an upper limit of 0.46 on the fraction of such quarks in the selected
sample [346]. These results indicate that the observed particle is indeed consistent with being a
SM |Q| = 2/3 quark.
√
In 2.05 fb−1 at s = 7 TeV, ATLAS performed a similar analysis, reconstructing the b-quark
charge either via a jet-charge technique or via the lepton charge in soft muon decays in combination
with a kinematic likelihood fit. They measure the top-quark charge to be 0.64 ± 0.02(stat.) ±0.08(syst.) from the charges of the top-quark decay products in single lepton tt̄ events, and hence
exclude the exotic scenario with charge −4/3 at more than 8σ [347].
√
In 4.6 fb−1 at s = 7 TeV, CMS discriminates between the SM and the exotic top-quark charge
scenario in the muon+jets final states in tt̄ events. They exploit the charge correlation between
high-pt muons from W -boson decays and soft muons from B-hadron decays in b-jets. Using an
asymmetry technique, where A = −1 represents the exotic Q = −4/3 scenario and A = +1 theSM Q = +2/3 scenario, they find Ameas = 0.97 ± 0.12(stat.) ± 0.31(sys.), which agrees with theStandard Model expectation and excludes the exotic scenario at 99.9% C.L. [348].
tt̄γ production:
The electromagnetic or the weak coupling of the top quark can be probed directly by investigatingtt̄ events with an additional gauge boson, such as tt̄γ, tt̄W , and tt̄Z events. The corresponding
coupling can be extracted from the corresponding cross section, cross section ratios with respect
to the tt̄ cross section or extracted from effective field theory (EFT) fits to various measured
distributions and differential cross sections.
CDF performed a first search for tt̄γ producton in events containing a lepton, a photon, significant missing transverse momentum, and a jet identified as containing a b-quark and at least threejets and large total transverse energy in 6.0 fb−1 . They reported evidence for the observation of tt̄γ
production with a cross section σtt̄γ = 0.18 ± 0.08 pb and a ratio of σtt̄γ /σtt̄ = 0.024 ± 0.009 [349].
√
ATLAS performed a first measurement of the tt̄γ cross section in pp collisions at s = 7 TeV
using 4.6 fb−1 of data. Events are selected that contain a large transverse momentum electron ormuon and a large transverse momentum photon. The production of tt̄γ events was observed witha significance of 5.3 standard deviations. The resulting cross section times branching ratio into thesingle lepton channel for tt̄γ production with a photon with transverse momentum above 20 GeV is
σ f id. (tt̄γ) × BR = 63 ± 8(stat.)+17−13 (syst.) ± 1(lumi.) pb per lepton flavor [350], which is consistent
with leading-order theoretical calculations.
31st May, 2024

35

61. Top Quark

At 8 TeV, ATLAS has used 20.2 fb−1 of data to measure the tt̄γ cross section with a photon
above 15 GeV and |η| < 2.37. The fiducial cross section is measured to be 139 ± 18 fb [351], ingood agreement with the NLO prediction [352]. Using 19.7 fb−1 of data at 8 TeV, CMS performeda similar measurement of the tt̄γ production cross section in the lepton+jets decay mode witha photon transverse momentum above 25 GeV and |η| <1.44. They obtain a normalized crosssection R = σtt̄+γ /σtt̄ = (5.7 ± 1.8) × 10−4 in e+jets and (4.7 ± 1.3) × 10−4 in µ+jets. The
fiducial tt̄γ cross section is obtained by multiplying by the measured tt̄ fiducial cross section of
244.9 ± 1.4(stat.)+6.3−5.5 (sys.) ± 6.4(lumi.) pb. Extrapolating to the full phase space, the result is
σtt̄γ ×BR=(515 ± 108) fb, per lepton+jets final state [353], in good agreement with the theoreticalprediction.
√
At s = 13 TeV, using 36.1 fb−1 of single-lepton and dilepton events with exactly one photon,
ATLAS measures the tt̄γ cross section. They employ neural network algorithms to separate thesignal from the backgrounds. The fiducial cross-sections are measured to be 521 ± 9(stat.) ±41(sys.) fb and 69 ± 3(stat.) ± 4(sys.) fb for the single-lepton and dilepton channels, respectively.
The differential cross-sections are measured as a function of photon transverse momentum, photon
absolute pseudorapidity, and angular distance between the photon and its closest lepton in bothchannels, as well as azimuthal opening angle and absolute pseudorapidity difference between the
two leptons in the dilepton channel. All measurements are in agreement with the theoreticalpredictions [354].
√
ATLAS uses 139 fb−1 of s = 13 TeV eµ + γ events with at least two jets, out of which atleast one is b-tagged, to measure the inclusive and differential cross-sections for the productionof a top-quark pair in association with a photon. This analysis is sensitive to both processes,
tt̄γ + tW γ. The fiducial cross-section is measured to be 39.6+2.7−2.3 fb in good agreement with the
dedicated theoretical calculation provided by the authors of refs. [355, 356], which predicts a value+1.04
of σf id = 38.50+0.56−2.18 (scale)−1.18 (PDF) fb for the chosen fiducial phase space. Differential crosssections as functions of several observables are compared to state-of-the-art Monte Carlo simulations
and NLO theoretical calculations. These include cross-sections as functions of the photon transverse
momentum and absolute pseudorapidity and angular variables related to the photon and the leptons
and between the two leptons in the event. All measurements are in agreement with the predictions[357].
Recently, CMS used 137 fb−1 of data to measure the tt̄γ cross section. In the lepton-plus-jets
channel, they perform measurements in a fiducial volume defined at the particle level. Events with
an isolated, highly energetic lepton, at least three jets from the hadronization of quarks, among
which at least one is b-tagged, and one isolated photon are selected. The inclusive fiducial tt̄γ
cross section, for a photon with transverse momentum greater than 20 GeV and pseudorapidity|η| < 1.4442, is measured to be σtt̄γ = 798 ± 7(stat) ± 48(syst) fb, in good agreement with theprediction from the standard model at NLO in QCD [358]. The differential cross sections are alsomeasured as a function of several kinematic observables such as the transverse momentum of thephoton, its rapidity, or the opening angle between the photon and the lepton. The measurements
on detector-level are also interpreted in terms of limits on the Wilson coefficients in the context
of the standard model effective field theory. The confidence intervals for the Wilson coefficients
ctZ and cItZ are the most stringent to date. Using the same dataset, in the dilepton channel, an
inclusive cross section of 174.4 ± 2.5(stat) ± 6.1(syst) fb is measured in a signal region with at least
one b-tagged jet and exactly one photon with transverse momentum above 20 GeV [359]. In thesame analysis, differential cross sections are measured as a function of several kinematic observablesof the photon, leptons, and jet, and compared to standard model predictions. Combinations of themeasurements in the l+jets and the dilepton channels are also interpreted in the standard model
effective field theory framework, yielding the most stringent limits for the Wilson coefficients ctZ
31st May, 2024

36

61. Top Quarkand cItZ to date.
tqγ production:
Using the full Run-2 data set of 139 fb−1 at 13 TeV, ATLAS observes the production of single top
quark together with a photon. The analysis uses the presence of a forward jet, characteristic of tchannel production, and separates the signal from the background with neural networks. Requiringa photon with transverse momentum larger than 20 GeV and within the detector acceptance, thefiducial cross section is measured to be 688 ± 23(stat.)+75−71 (syst.) fb, to be compared with theStandard Model prediction of 515+36
fb
at
NLO
in
QCD
[360].
In 35.9 fb−1 of lepton-plus-photon−42
plus-jets events, CMS manages to establish the first evidence for the associated production of a√single-top quark and a photon at s = 13 TeV. They employ a multivariate discriminant based on
topological and kinematic event properties to separate signal from background processes. An excess
above the background-only hypothesis is observed, with a significance of 4.4 standard deviations.
A fiducial cross section is measured for isolated photons with transverse momentum greater than
25 GeV in the central region of the detector. The measured product of the cross section andbranching fraction is σ(pp → tγj)B(t → µγb) = 115 ± 17(stat) ± 30(syst) fb, which is consistent
with the SM prediction [361]. A precision test of the vector and axial vector couplings in tt̄γ eventsor searches for possible tensor couplings of top-quarks to photons will only be feasible with an
integrated luminosity of several hundred fb−1 in the future [362].
tt̄Z and tt̄W production:
ATLAS and CMS have also studied the associate production of top-antitop quark pairs along with
an electroweak gauge boson, tt̄W or tt̄Z, where in the Standard Model the W -boson is expected to
be produced via initial state radiation, while the Z-boson can also be radiated from a final-state
top-quark and hence provides sensitivity to the top-quark neutral current weak gauge coupling,which implies a sensitivity to the third component of the top-quark’s weak isospin, which has notbeen measured so far.
√
CMS performed measurements of the tt̄W and tt̄Z cross section at s = 7 TeV with 5 fb−1 ,
+0.09
+0.14
+0.06
yielding σtt̄V = 0.43+0.17−0.15 (stat.)−0.07 (syst.) pb (V = Z, W ) and σtt̄Z = 0.28−0.11 (stat.)−0.03 (syst.) fb,
at about 3 standard deviations significance [363] and compatible with the SM expectations of+0.0120.306+0.031−0.053 pb and 0.137−0.016 pb, respectively [364,365]. ATLAS performed a similar analysis with
4.7 fb−1 in the three-lepton channel and set an upper limit of 0.71 pb at 95% C.L. [366].
Using 20.3 fb−1 of 8 TeV data, ATLAS performs a simultaneous measurement of the tt̄W andtt̄Z cross section. They observe the tt̄W and tt̄Z production at the 5.0σ and 4.2σ level, respectively,+58
yielding σtt̄W = 369+100−91 fb and σtt̄Z = 176−52 fb [367]. CMS performs an analysis where signal
events are identified by matching reconstructed objects in the detector to specific final state particles
from tt̄W and tt̄Z decays using 19.5 fb−1 of 8 TeV data. They obtain σtt̄W = 382+117−102 fb and
σtt̄Z = 242+65
fb,
yieldingasignificance
of
4.8
and
6.4
standard
deviation,
respectively[368].
−55
These measurements are used to set bounds on five anomalous dimension-six operators that would
affect the tt̄W and tt̄Z cross sections.
The most recent measurements in these channels are made at 13 TeV from ATLAS and CMS
in multilepton final states. ATLAS made a measurement using 36.1 fb−1 of events with two, threeor four leptons. In multiple regions, the tt̄Z and tt̄W cross sections are simultaneously measured
using a combined fit to all regions, yielding σtt̄Z = 0.95 ± 0.08(stat) ± 0.10(syst) pb and σtt̄W =0.87 ± 0.13(stat) ± 0.14(syst) pb [369] to be compared with the NLO+NLL (QCD) and NLO (EW)
+11%
−1 in
SM predictions, σtt̄W = 579+14%−9% fb and σtt̄Z = 811−10% fb [43]. Recently, ATLAS uses 139 fb
three and four lepton events to measure the inclusive and differential tt̄Z cross section. The inclusive
cross section is measured to be σtt̄Z = 0.99 ± 0.05(stat.) ± 0.08(syst.) pb [370], in agreement withthe most precise theoretical predictions. The differential measurements are presented as a functionof a number of kinematic variables which probe the kinematics of the tt̄Z system. Overall, good
31st May, 2024

37

61. Top Quark

agreement is observed between the unfolded data and the predictions. Using the same dataset of
140 fb−1 , ATLAS performs an improved measurement in both, the inclusive and differential tt̄Z
production cross sections. Final states with two, three and four isolated leptons (electrons or muons)
are targeted. The inclusive cross section is measured to be σtt̄Z = 0.86 ± 0.04(stat.) ± 0.04(syst.) pb
and found to be in agreement with the most advanced Standard Model predictions [371]. The
improvement with respect to the previous measurement using the same dataset is mainly in a bettermachine learning-based separation of signal and background, the addition of a 2-lepton signal region,and better modelling. The differential measurements are presented as a function of a number ofobservables that probe the kinematics of the tt̄Z system. Both absolute and normalised differential
cross section measurements are performed at particle- and parton-level for specific fiducial volumes,
and are compared with theoretical predictions at NLO+NNLL. The results are interpreted in theframework of the Standard Model Effective Field Theory and used to set limits on a large number of√dimension-6 operators involving the top quark. CMS uses 35.9 fb−1 of s = 13 TeV data to measure
+0.13
+0.09
+0.12
σtt̄W = 0.77+0.12−0.11 (stat.)−0.12 (syst.) pb and σtt̄Z = 0.99−0.08 (stat.)−0.10 (syst.) pb production crosssections, and significances over the background-only hypotheses of 5.5σ and 9.5σ, respectively [372],
firmly establishing the observation of these processes. CMS measured the inclusive tt̄Z cross section
in 77.5 fb−1 of events with three or four charged leptons, and the Z boson is detected throughits decay to an oppositely charged lepton pair. The production cross section is measured to beσ(tt̄Z) = 0.95 ± 0.05(stat) ± 0.06(syst) pb. This measurement includes differential cross sections asfunctions of the transverse momentum of the Z boson and the angular distribution of the negatively
charged lepton from the Z boson decay, which characterise the tt̄Z process in detail for the firsttime, as well as stringent direct limits on the anomalous tZ couplings [373]. Very recently, using thecomplete Run-2 dataset of 138 fb−1 , CMS searches for signs of new physics, interpreted in effective
field theory, in tt̄ events produced in association with a Lorentz-boosted Z or Higgs boson [374].
Selected events contain a single lepton and hadronic jets, including two identified with the decayof bottom quarks, plus an additional large-radius jet with high transverse momentum identified asa Z or Higgs boson decaying to a bottom quark pair. Machine learning techniques are employed todiscriminate between tt̄Z or tt̄H events and events from background processes, which are dominatedby tt̄+jets production. No indications of new physics are observed. The signal strengths of boosted
tt̄Z and tt̄H production are measured, and upper limits are placed on the tt̄Z and tt̄H differential
cross sections as functions of the Z or Higgs boson transverse momentum, expressed as limits oneight possible dimension-six operators.
Recently, CMS measured the tt̄W cross section in 138 fb−1 at 13 TeV in events with two or
three leptons (electrons and muons) and additional jets. In events with two leptons, a multiclassneural network is used to distinguish between the signal and background processes. Events withthree leptons are categorized based on the number of jets and of jets originating from b quark
hadronization, and the lepton charges. The inclusive tt̄W production cross section in the full phasespace is measured to be 868 ± 40(stat) ± 51(syst) fb. The tt̄W + and tt̄W − cross sections are alsomeasured as 553 ± 30(stat) ± 30(syst) fb and 343 ± 26(stat) ± 25(syst) fb, respectively, and thecorresponding ratio of the two cross sections is found to be 1.61 ± 0.15(stat)+0.07−0.05 (syst) [375]. The
measured cross sections are larger than but consistent with the standard model predictions within
two standard deviations. Also ATLAS presents both, the inclusive and differential cross-sections oftt̄W production in 140 fb−1 of 13 TeV data using final states with two same-sign or three isolated
leptons (electrons or muons). The inclusive production cross-section is measured to be 890 ± 80 fb,
which turns out a bit high compared to the new reference theoretical prediction at NNLO in QCD
of 745.3±49.9(scale)±13.4(P DF ) fb [46]. Differential cross-section measurements characterise thisprocess in detail for the first time. Several particle-level observables are compared to a variety oftheoretical predictions which are generally in good agreement with the normalised differential cross31st May, 2024

38

61. Top Quark

section results [376]. They also measure the tt̄W + and tt̄W − cross section individually, yielding a+0.16
ratio of R = 1.95+0.21−0.18 (stat.)−0.13 (syst.).
single-top + W/Z production:
The electroweak couplings can also be probed in single-top production in association with a Z
boson. The pp → tZq process at the LHC probes both the W W Z coupling in the case where
the Z emerges from the t-channel W in single-top production and, in the case where the Z isradiated from the top quark, the tZ coupling. A CMS search at 8 TeV using 19.7 fb−1 produceda hint of a tZq signal in tri-lepton events, with a significance compared to the background-only
hypothesis of 2.4σ [377]. Very recently, CMS and ATLAS collaborations used 139 fb−1 at 13 TeV
+7.5
+7.3
in three-lepton events to measure tZ(→ `+ `− )q. CMS obtains σtZq = 87.9−7.3(stat)−6.0(syst) fb
for m(``) > 30 GeV [378], following the evidence [361] of the observation of the process [379]. The
ratio between the cross sections for the top quark and the top antiquark production in association+0.27
with a Z boson is measured as 2.37+0.56−0.42 (stat)−0.13 (syst). Differential measurements at parton andparticle levels are performed for the first time. Additionally, the spin asymmetry, which is sensitive
to the top quark polarization, is determined from the differential distribution of the polarization
angle at parton level to be 0.58+0.15−0.16 (stat) ± 0.06 (syst), in agreement with SM predictions at nextto-leading order. Using neural networks, ATLAS improves the background rejection and extracts
the signal. The measured cross-section for m(``) > 30 GeV is 97 ± 13(stat.) ± 7(syst.) fb, consistent
with the Standard Model prediction [380].
tW Z production:
Using 138 fb−1 at 13 TeV, CMS presents the first evidence for the standard model production of
a top quark in association with a W and a Z boson in multilepton final states. The Z boson isreconstructed via its decays to electron or muon pairs. The measured cross section amounts to
0.37 ± 0.05(stat) ± 0.10(syst) pb, and corresponds to an observed (expected) significance of 3.5(1.4) standard deviations [381].
Searches for and now also measurements of the associate production of a top-antitop quark pairalong with a Higgs boson, tt̄h, with various subsequent decays provide sensitivity to the top-Higgs
Yukawa coupling. For further details, see the review on “Status of Higgs boson physics”.
61.2.6 New Physics
The top quark plays a special role in the SM. Being the only quark with a coupling to the
Higgs boson of order one, it provides the most important contributions to the quadratic radiative
corrections to the Higgs mass exposing the issue of the naturalness of the SM. It is therefore very
common for models where the naturalness problem is addressed to have new physics associated withthe top quark. In SUSY, for instance, naturalness predicts the scalar top partners to be the lightest
among the squarks and to be accessible at the LHC energies (see the review “Supersymmetry:
Theory”). In models where the Higgs is a pseudo-Goldstone boson, such as Little Higgs models,
naturalness predicts the existence of partners of the top quarks with the same spin and color,but with different electroweak couplings, the so-called vectorial t0 . Stops and t0 ’s are expected tohave sizeable branching ratios to top quarks. Another intriguing prediction of SUSY models with
universal couplings at the unification scale is that for a top-quark mass close to the measured value,
the running of the Yukawa coupling down to 1 TeV naturally leads to the radiative breaking of
the electroweak symmetry [382]. In fact, the top quark plays a role in the dynamics of electroweak
symmetry breaking in many models [383]. One example is topcolor [384], where a large top-quark
mass can be generated through the formation of a dynamic tt̄ condensate, X, which is formed by a
new strong gauge force coupling preferentially to the third generation. Another example is topcolorassisted technicolor [385], predicting the existence of a heavy Z 0 boson that couples preferentiallyto the third generation of quarks. If light enough such a state might be directly accessible at the
31st May, 2024

61. Top Quark

39

present hadron collider energies, or if too heavy, lead to four-top interactions possibly visible in thett̄tt̄ final state. This final state has been observed by CMS [168] and by ATLAS [164].
61.2.6.1 Direct Searches for Physics Beyond the Standard ModelIn this section we review the latest direct searches for Physics Beyond the Standard Model(PBSM) in top-quark production and decay. These direct search come in two categories: tt resonance searches and searches for rare non-SM interactions involving top quarks, including FlavorChanging-Neutral-Current (FCNC) searches. Top-sector resonance searches come in two categories,
tt resonances in which a presumed heavy particle X decays into a tt pair, and searches in which a
non-SM decay product of the top quark is observed via its resonant decay. The most recent results
are of the latter category. We refer the reader to Refs. [386–388] for X → tt̄ searches. Searches forrare non-SM interactions and FCNC final states are interpreted using the EFT approach describedin Section 61.1.1.2. In this section we focus on the branching-ratio limits from these searches, while
the EFT interpretations are cited in Section 61.2.6.4.
61.2.6.2 FCNC and Rare non-SM Interaction Searches
The most recent FCNC searches target a t → qH decay in tt production, or an FCNC vertex
in single-top production together with a Higgs boson. The ATLAS search in Ref. [389] looks for
H → τ τ in both cases. A small, 2.3σ excess of events is observed and limits on t → qH branchingratios are set. The most recent CMS result uses Higgs decays to vector bosons in addition toτ τ . That result is combined with results from Refs. [390] and [391] that use the bb̄ and γγ decay
channels of the Higgs [392]. Table 61.4 shows the most recent independent limits for q = u or q = c
and assume the other branching ratio is zero. Other results can be found in the Listings.
Table 61.4: 95% C.L. limits on branching ratios (BR) of the top quark for FCNC and other rare
non-SM interactions.
bht! Processt → cHt → cH Combinedt → uHt → uH Combinedt → Zu LH
t → Zc LH
t → uγ LH
t → cγ LH
t → ugt → cgt → eµu (Scalar)t → eµu (Vector)t → eµu (Tensor)t → eµc (Scalar)t → eµc (Vector)t → eµc (Tensor)
t → µτ q

BR limit
9.4 × 10−4
4.3 × 10−4
3.7 × 10−4
6.9 × 10−4
7.2 × 10−4
1.9 × 10−4
6.2 × 10−5
1.3 × 10−40.85 × 10−5
4.2 × 10−50.61 × 10−4
3.7 × 10−4
0.07 × 10−6
0.13 × 10−6
0.25 × 10−6
0.89 × 10−6
1.31 × 10−6
2.59 × 10−6
11 × 10−7

Reference
[389]
[392]
[392]
[389]
[392]
[392]
[393]
[393]
[394]
[394]
[395]
[395]
[396]
[396]
[396]
[396]
[396]
[396]
[397]

Searches targeting tZq couplings use leptonic decays of the Z-boson and a trilepton final state.
31st May, 2024

61. Top Quark40

In tt events, the signal occurs through the FCNC decay t → Zq, in single-top the signal occurs
through the associated production of a top quark and a Z-boson. The branching-ratio limits shownin Table 61.4 are for tZu and tZc left-handed couplings and assume, for tZu, that the tZc couplingis zero and vice versa. Reference [393] also presents limits for right-handed couplings, which areclose to the values quoted in Table 61.4 for left-handed couplings
Searches targeting tγq couplings focus on a high-PT photon in the final state. As with tZq
couplings, signal events occur through top-quark decay in tt and through associated production of
a top quark and a photon in single-top events. In Ref. [394] limits are found for the EFT couplings
shown in Table 61.7, and the limits shown in Table 61.4 are derived from the limits on the WCs.
The table shows the limits assuming a left-handed coupling. Limits on right-handed couplings arealso give in Ref. [394] and are only slightly weaker than those determined for left-handed couplings.
In Ref. [395] FCNC couplings tgq between a top quark, a gluon, and an up or charm quark arelooked for in single-top production. The couplings increase the single-top production cross section
and, in the case of the tgc coupling, also affect the rapidity distribution of the produced top quark
because of the different PDFs for valence and sea quarks.
CMS searches for charged-lepton-flavor-violating interactions in both production, q → eµt, anddecay, t → eµq, with q = u or c [396]. The branching ratio limits set are included in Table 61.4
and the Wilson coefficients constrained are listed in Table 61.6.
ATLAS has searched for charged-lepton-flavor-violating µτ qt interactions which are sensitive
to the two-quark-two-lepton operators of Table 61.1 [397]. The branching ratio limit set is includedin Table 61.4 and the Wilson coefficients constrained are listed in Table 61.6.
61.2.6.3 Resonance Searches
While technically an FCNC search, a decay of the type t → qX where q = u or c, could be
missed when X is not the expected quark or boson. ATLAS has searched for t → qX where X
is a light scalar with a mass below the top quark that decays to bb [398]. Such phenomena exist
in composite Higgs models [403]. The ATLAS search used tt events and separated signal from
Table 61.5: Wilson coefficients (WC) corresponding to boson operators and related PBSM searchreferences.
bht! WC
CtW

CtZ

CbW
CtG

CtB
CHt
1
CHQ
3
CHQ

Process
Single-top polarization
ttZ, tZ
Boosted ttZ, ttH
t+ additional leptons
ttZ
ttZ, tZ
ttZ, ttH
t+ additional leptons
Boosted ttZ, ttH
Boosted tt
tt charge asymmetry
ttZ
ttZ
ttZ
ttZ
ttZ
31st May, 2024

Citations
[211]
[399]
[374]
[400]
[371]
[399]
[374]
[400]
[374]
[401]
[234]
[371]
[371]
[371]
[371]
[371]

61. Top Quark

41

Table 61.6: Wilson coefficients (WC) corresponding to four-fermion operators and related PBSM search references.
WC
11
CQq
18
CQq

1
Ctq

8
Ctq

1
Ctu

1
Ctd
8
Ctu

8
Ctd

8
CQd

8
CQu

1
CQu
1
CQd
31
CQq
38
CQq

3(2313)C`equ1(2323)
C`equ
Ceµtu
Ceµtc

Process
tt charge asymmetry
tt energy asymmetry in ttj
ttZ
tt charge asymmetry
tt energy asymmetry in ttj
Boosted all-hadronic tt
ttZ
tt charge asymmetry
tt energy asymmetry in ttj
ttZ
tt charge asymmetry
tt energy asymmetry in ttj
Boosted all-hadronic tt
Boosted tt
ttZ
tt charge asymmetry
tt energy asymmetry in ttj
ttZ
tt charge asymmetry
ttZ
tt charge asymmetry
tt energy asymmetry in ttj
Boosted all-hadronic tt
ttZ
tt charge asymmetry
Boosted all-hadronic tt
ttZ
tt charge asymmetry
Boosted all-hadronic tt
ttZ
tt charge asymmetry
Boosted all-hadronic tt
ttZ
tt charge asymmetry
ttZ
tt charge asymmetry
ttZ
ttZ
tt charge asymmetry
Boosted all-hadronic tt
ttZ
t → µτ ut → µτ c
top production & decay
top production & decay

Citations
[234]
[238]
[371]
[234]
[238]
[402]
[371]
[234]
[238]
[371]
[234]
[238]
[402]
[401]
[371]
[234]
[238]
[371]
[234]
[371]
[234]
[238]
[402]
[371]
[234]
[402]
[371]
[234]
[402]
[371]
[234]
[402]
[371]
[234]
[371]
[234]
[371]
[371]
[234]
[402]
[371]
[397]
[397]
[396]
[396]

background by categorizing events according to the number of jets and the number of jets tagged
as originating from b-quarks. The observed limits correspond to the product of the BR t → qX
31st May, 2024

42

61. Top Quarkand X → bb. The limit in the t → uX(t → cX) channel is 0.019%(0.018%) for MX = 20 GeV and
0.062%(0.078%) for MX = 160 GeV.
61.2.6.4 Effective Field Theory Results
As described in Section 61.1.1.2, EFTs have become a primary tool for evaluating the outcomeof top PBSM searches. EFT provides both model-independent limits, a straightforward way tocompare and contrast search results from different processes and different experiments, and aguide to the full space of possible top-quark-related PBSM. In a nice pedagogical paper [404],
Zhang and Willenbrock elucidate the advantages of the EFT approach compared to the vertexfunction approach for searching for PBSM in top-quark interactions, including the fact that the
EFT approach incorporates the SM gauge symmetry and contact interactions that are neglectedin the vertex-function approach. As a result of these advantages, EFTs have become the dominant
technique for evaluating search limits, and we review the most recent results in this section.
As ATLAS and CMS do, we categorize the top-EFT operators as follows: four-fermion operators, vector-boson operators and scalar-boson operators. Operators can change the overall rateof top-quark production, modify the kinematics of production and/or decay, or produce new interactions, such as flavor-changing neutral currents (FCNC). To date, all results are consistent
with the SM expectation of zero for each Wilson coefficient. The numerical values of the limits are not intuitively meaningful, especially given that they correspond to an arbitrarily chosenmass scale of Λ = 1 TeV. Therefore, rather than providing a table of confidence intervals, we refer
the interested reader to the LHC Top Working Group page of summary plots where the limits
on the Wilson coefficients are presented graphically [405], and to the references given below. Instead, the tables below provide the most recent relevant references (i.e. those using the full LHC
dataset of 139 fb−1 ) for limits on each coefficient wherein measurement, fitting, and limit derivation techniques can be found. Additional limits and references can be found in the listings and inreferences [359, 374, 396, 399, 400, 406–408].
Table 61.7: Wilson coefficients (WC) corresponding to flavor-changing-neutral-current (FCNC)
operators and related PBSM search references.
WC
32 + C 32
CuW
uB
(23)∗
(23)∗
CuW + CuB
31 + C 31
CuW
uB
(13)∗
(13)∗
CuW + CuB
32 , C 32
CuW
uB
(23)∗
(23)∗
CuW , CuB
31 , C 31
CuW
uB
(13)∗
(13)∗
CuW , CuB
CuG
CcG
Cuφ
Ccφ

Process
tqγ
tqγ
tqγ
tqγ
tZc
tZc
tZu
tZu
tgu
tgc
tHu
tHc

Citations
[394]
[394]
[394]
[394]
[393]
[393]
[393]
[393]
[395]
[395]
[389]
[389]

61.3 Outlook
Top quark physics at hadron colliders has developed into precision physics. Various propertiesof the top quark have been measured with high precision, where the LHC has by now surpassed
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43

61. Top Quark√
the Tevatron precision and reach in the majority of relevant observables. Several s-dependent
physics quantities, such as the production cross-section, have been measured at several energies at
the Tevatron and the LHC. Up to now, all measurements are consistent with the SM predictions
and allow stringent tests of the underlying production mechanisms by strong and weak interactions.
Given the very large event samples available at the LHC, top-quark properties will be further
determined in tt̄ as well as in electroweak single top-quark production. At the Tevatron, the t−
and s−channels for electroweak single top-quark production have been estblished separately. At the
LHC, quick progress has been achieved in the last years yielding more than 3 sigma significance ofthe s-channel and more than 5 sigma significance for the t-chnnel and Wt-production. Furthermore,tt̄γ, tt̄Z, and tt̄W together with tt̄H associated production have started to provide key informationon the top-quark electroweak couplings. Corresponding effective field theory (EFT) fits for the
coupling extraction are being developed. At the same time various models of physics beyond the
SM involving top-quark production are being constrained. While a majority of the Run-II data
recorded at 13 TeV has been analysed or is in an advanced stage, the beginning of the Run-III at√
s = 13.6 to 14 TeV and an expected integrated luminosity of 160 − 200 fb−1 , doubling the Run-I
plus Run-II data set, is immanent. With the first results being released, top-quark physics has thepotential to shed light on open questions and new aspects of physics at the TeV scale.
CDF and DØ notes can be retrieved fromhttps://inspirehep.net
with the search command "find CDF-NOTE-XXXXX" or "find D0 Note XXXX",
and ATLAS note references fromhttps://twiki.cern.ch/twiki/bin/view/AtlasPublic/TopPublicResults,
and CMS note references fromhttps://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsTOP,
and plots provided by the LHC Top Working Group fromhttps://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCTopWGSummaryPlots.
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