The electro-weak couplings of the top and bottom quarks — Global fit and future prospects

JHEP12(2019)098 Published for SISSA by Springer Received:August 28, 2019 Revised:November 4, 2019 Accepted:November 25, 2019 Published:December 12, 2019 The electro-weak couplings of the top and bottom quarks — Global fit and future prospects Gauthier Durieux,aAdrian Irles,bV´ıctor Miralles,cAna Pe˜nuelas,cMart´ın Perell´o,c Roman P¨oschlband Marcel Vosc aPhysics Department, Technion — Israel Institute of Technology, Technion City, Haifa 3200003, Israel bLaboratoire de l’Acc´elerateur Lin´eaire (LAL), CNRS/IN2P3 et Universit´e de Paris-Sud XI, Centre Scientifique d’Orsay Bˆatiment 200, BP 34, F-91898 Orsay CEDEX, France cInstituto de F´ısica Corpuscular (IFIC, UV/CSIC), Calle Catedr´atico Jos´e Beltr´an 2, E-46071, Paterna, Valencia, Spain E-mail: [email protected],[email protected], [email protected],[email protected], [email protected],[email protected], [email protected] Abstract: We evaluate the implications of LHC and LEP/SLC measurements for the electro-weak couplings of the top and bottom quarks. We derive global bounds on the Wilson coefficients of ten two-fermion operators in an effective field theory description. The combination of hadron collider data with Z-pole measurements is found to yield tight limits on the operator coefficients that modify the left-handed couplings of the bottom and top quark to the Zboson. We also present projections for the high-luminosity phase of the LHC and for future electron-positron colliders. The bounds on the operator coefficients are expected to improve substantially during the remaining LHC programme, by factors of 1 to 5 if systematic uncertainties are scaled as statistical ones. The operation of an e+e− collider at a center-of-mass energy above the top-quark pair production threshold is expected to further improve the bounds by one to two orders of magnitude. The combination of measurements in pp and e+e−collisions allows for a percent-level determination of the top-quark Yukawa coupling, that is robust in a global fit. Keywords: Phenomenology of Field Theories in Higher Dimensions ArXiv ePrint: 1907.10619 Open Access,c The Authors. Article funded by SCOAP3.https://doi.org/10.1007/JHEP12(2019)098 JHEP12(2019)098 Contents 1 Introduction 1 2 Effective field theory and fit setup 2 2.1 Effective field theory 2 2.2 Operator basis 3 2.3 Fit setup 5 2.4 Implementation of the fit 5 3 Measurements 6 3.1 Top-quark neutral-current interactions 6 3.2 Top-quark charged-current interactions 7 3.3 Measurements in bottom-quark production 7 3.4 Indirect constraints 7 3.5 Summary of measurements 8 3.6 Sensitivity to operator coefficients 9 4 Present constraints 10 4.1 Fit to LHC and LEP/SLC data 10 4.2 Impact of Λ−4terms 12 5 Future collider prospects 13 5.1 High-luminosity phase of the LHC 13 5.2 Future e+e−collider: ILC 14 5.3 Global fit on prospects 16 5.4 Validity of the EFT framework 17 5.5 Four-fermion operators of the form e+e−Q¯ Q18 6 The top-quark Yukawa coupling 20 6.1 Indirect and direct bounds 20 6.2 Associated t¯ tH production at the LHC 21 6.3 HL-LHC prospects 21 6.4 ILC prospects 22 6.5 Summary of results 22 7 Conclusions 24 A Observables parameterization 26 A.1 LHC @13TeV 26 A.2 t→W+b27 A.3 LEP/SLC @91GeV 27 A.4 e−e+→b¯ b28 A.5 e−e+→t¯ tH 32 B Conversion to LHC TOP WG EFT conventions 32 – i – JHEP12(2019)098 C Covariance matrices 32 C.1 Present constraints 32 C.2 Future prospects 33 C.2.1 LEP/SLC + LHC Run2 33 C.2.2 LEP/SLC + LHC S1 35 C.2.3 LEP/SLC + LHC S2 35 C.2.4 LEP/SLC + LHC S2 + ILC250 35 C.2.5 LEP/SLC + LHC S2 + ILC250 + ILC500 35 C.2.6 LEP/SLC + LHC S2 + ILC250 + ILC500 + ILC1000 36 1 Introduction With the discovery of the Higgs boson [1,2] at the LHC, the particle content of the Standard Model (SM) is experimentally confirmed. Measurements are performed in a very broad range of production processes to characterize the interactions among all currently known particles. Precision measurements may be affected by the presence of new particles or interactions and thus provide an indirect probe of new physics. While the SM seems to stand all tests so far, experiments keep searching for subtle deviations from its predictions. In this paper, we study the electro-weak (EW) couplings of the third-generation quarks which have particular relevance in many extensions of the SM. In particular, the EW couplings of the top and bottom quarks have an exquisite sensitivity to a broad class of composite Higgs/extra dimension scenarios [3,4]. As the top quark escaped scrutiny at the previous generation of electron-positron colliders, the LHC measurements analyzed in this paper provide the first constraints on its EW couplings. We include measurements by ATLAS and CMS at a center-of-mass energy of 13 TeV of the associated t¯ tX production rate (with X=γ, W, Z, H), the single top-quark production cross section in the t-channel, Wt associated production and tZq production as well as the Whelicity fractions in top-quark decay. As the left-handed top and bottom quarks are part of the same doublet, their couplings are related [5,6]. We include measurements in bottom-quark pair production at LEP and SLC in the fit. The precise measurements at the Z-pole of the ratio Rband the b-quark asymmetry parameter, Ab, which is extracted from measurements of the leftright and forward-backward asymmetries in bottom-quark pair production, provide strong constraints. An effective field theory (EFT) is employed to parameterize the effects of new physics arising at scales higher than that of the considered measurements. The ten CP-conserving operator coefficients modifying t¯ tZ,b¯ bZ,t¯ bW and t¯ tH interactions are simultaneously constrained in a global analysis of LHC and LEP/SLC data. Our results apply to newphysics models in which deviations to the measurements considered are dominated by these ten parameters. Other contributions are sometimes already well constrained. Those – 1 – JHEP12(2019)098 of four-fermion operators are notably not tightly bound yet, but inclusion of the effect of all dimension-six operators in a fully global analysis is beyond the scope of this work. The fitting code, publicly available [7], is implemented in the HEPfit [8] package which uses a Markov-Chain Monte-Carlo implementation based on the Bayesian Analysis Toolkit [9]. In the next decade the LHC program is expected to sharpen the limits considerably. We define several scenarios for the expected measurement precision after completing the LHC program, including the high-luminosity phase (HL-LHC [10]). We also assess the potential of a future e+e−collider (either linear colliders, such as the International Linear Collider ILC [11], the Compact Linear Collider CLIC [12], or circular colliders such as FCCee [13] or CEPC [14]). A Higgs factory operated at center-of-mass energy of 250 GeV will improve the constraints on the bottom-quark operator coefficients [15] significantly. Operation above the top-quark pair production threshold is part of the initial stage of the CLIC project [16] and later stages of the ILC and FCCee. In this paper the potential of operation at a center-of-mass energy of 500 GeV is studied, where very tight constraints on the top-quark operators are expected [6,17]. This study represents the most complete characterization of the EW interactions of the bottom and top quarks to date. Our fit yields more stringent constraints than previous work [18–20]. We moreover present the first comparison of the HL-LHC and ILC [11] potential for precision measurements that constrain the top and bottom-quark EW couplings. This paper is organized as follows. The effective-field-theory and fitting frameworks are presented in section 2. The measurements at the LHC and LEP/SLC that are included in the fit are introduced in section 3. The results from the fit to existing data are presented in section 4. Projections for the potential of the HL-LHC and the ILC are presented in section 5. The results and prospects for the extraction of the top-quark Yukawa coupling are discussed in section 6. The findings are summarized in section 7. 2 Effective field theory and fit setup This section presents the framework in which we develop our fit to the data. 2.1 Effective field theory We adopt an EFT approach to parameterize systematically the effects of physics beyondthe-SM (BSM) at a high scale. The Wilson coefficients of each higher-dimensional operator can be related to the parameters of concrete BSM realizations with a matching procedure (i.e. bounds on Wilson coefficients are mapped onto the coupling and mass of new heavy states). The EFT description preserves the gauge symmetries of the SM and is a proper quantum field theory. As such, the EFT predictions can be improved systematically in a perturbative order-by-order expansion. The EFT expands the SM Lagrangian in terms of a new physics scale Λ: Leff =LSM +1 Λ2X i CiOi+OΛ−4.(2.1) – 2 – JHEP12(2019)098 Operators of odd dimension violate baryon or lepton numbers and are ignored. The interferences of SM amplitudes with those involving an insertion of dimension-six operators gives rise to the leading Λ−2terms. We also include terms of order Λ−4arising from the squares of amplitudes where dimension-six operators are inserted once, or from the interference of amplitudes featuring two dimension-six operator insertions with SM ones. The contributions of dimension-eight operators are not included, even though they first arise at the same Λ−4order. The convergence of the EFT expansion hinges on the smallness of Ci/Λ2. For typical choices of the coefficient Ci∼1 the new physics scale Λ has to exceed several TeV for the effective operator paradigm to hold. Following the recommendation of the LHC TOP Working Group [21], fits with and without Λ−4contributions are compared to assess the convergence of the expansion. A strong impact of the Λ−4terms on the fit results is an indication that one must carefully check the validity of the EFT expansion when recasting the bounds on concrete SM extensions [22]. We therefore discuss their impact explicitly in sections 4and 5. 2.2 Operator basis The number of operators involved in the most general EFT description is daunting even at the first order of the expansion. We therefore isolate a smaller subset that provides an adequate basis for a study of BSM effects in the top and bottom-quark EW couplings. This analysis is relevant for scenarios where the dominant BSM effects in the measurements considered appear in these operators. We focus on the set of operators with leading contributions to the available measurements, restricting the study to dimension-six operators. We also limit the fit to two-fermion operators, as a fully general treatment including the four-fermion operators is impossible with the current data set.1Finally, we ignore the imaginary part of the operator coefficients. These lead to CP-violating interactions of the top quark and are efficiently constrained using dedicated analyses at colliders [23,24] and low-energy probes [25]. O1 ϕQ ≡y2 t 2¯ qγµqϕ†i ←→ Dµϕ, O3 ϕQ ≡y2 t 2¯ qτIγµqϕ†i ←→ DI µϕ, Oϕu ≡y2 t 2¯ uγµuϕ†i ←→ Dµϕ, Oϕd ≡y2 t 2¯ dγµdϕ†i ←→ Dµϕ, Oϕud ≡y2 t 2¯ uγµdϕTiDµϕ, OuW ≡ytgW¯ qτIσµνuϕ∗WI µν, OdW ≡ytgW¯ qτIσµνdϕ∗WI µν, OuB ≡ytgY¯ qσµνuϕ∗Bµν, OdB ≡ytgY¯ qσµνdϕ∗Bµν, Ouϕ ≡¯ qu ϕ∗ϕ†ϕ, Odϕ ≡¯ qd ϕ∗ϕ†ϕ, (2.2) 1The reason for this omission is purely practical: the current data offer insufficient constraints for a global fit including these operator coefficients. We discuss the possibility of extending the fit to CP-conserving four-fermion operators in section 5.5. – 3 – JHEP12(2019)098 In the Warsaw basis [26] (see also refs. [27,28]), the two-fermion operators that affect top and bottom-quark interactions with vector, tensor, or scalar Lorentz structures are listed in eq. (2.2), where we have defined q≡(uL, VCKMdL)T,u≡uR, and d≡dR. The matrix VCKM is the Cabibbo-Kobayashi-Maskawa [29,30] matrix, while ≡(0 −11 0) acts on SU(2)Lindices. The operators O1 ϕQ and O3 ϕQ modify the left-handed couplings of the Zboson to downtype and up-type quarks. At leading order, the effect on the left-handed coupling of the top quark is proportional to the difference of the Wilson coefficients, δgt L=−(C1 ϕQ − C3 ϕQ)m2 t/Λ2, that on the left-handed coupling of the bottom quark depends on the sum: δgb L=−(C1 ϕQ +C3 ϕQ)m2 t/Λ2. The simultaneous fit of the coefficients C1 ϕQ and C3 ϕQ is the main rationale to combine the bottom and top-quark operators in the fit. Two further operators Oϕu and Oϕd modify the right-handed couplings of the bottom and top quark to the Zboson, respectively, δgt R=−Cϕu m2 t/Λ2and δgb R=−Cϕd m2 t/Λ2. The operators labeled OuW ,OdW ,OuB and OdB in eq. (2.2) are EW dipole operators. The OuW and OuB give rise to tensor couplings of the photon and Zboson to the up-type quarks. Non-zero values of the Wilson coefficients CuW and CuB induce an anomalous dipole moment of the top quark. Similarly, the operators OdW and OdB give rise to tensor couplings of down-type quark to the photon and Zboson and induce an anomalous dipole moment in the bottom quark. The O3 ϕQ and OuW operators also modify the charged-current interactions of the top quark with a Wboson and left-handed b-quark. The Oϕud and OdW operators, give rise to interactions between the top quark, the right-handed b-quark, and the Wboson. Finally, the last two operators, Ouϕ and Odϕ, lead to a shift in the Yukawa couplings of up-type and down-type quarks. The operator Ouϕ affects several observables included in the analysis. We discuss their potential to constrain Cuϕ in section 6. A truly global treatment of this operator must take advantage of the measurements of the Higgs boson production and decay rates. Such a combined fit of the top-quark, EW and Higgs EFTs is beyond the scope of the current work and is left for a future publication. The observables included in the analysis are not sensitive to Odϕ, so this operator is ignored in the following. We do not consider the chromo-magnetic dipole operators OuG ≡ytgs¯ qσµνuϕ∗Gµν and OdG ≡ytgs¯ qσµνdϕ∗Gµν, or the four-fermion operators of the q¯qt¯ ttype. The former and a certain number of combinations of the later are better constrained by measurements of the pp →t¯ t/b¯ bprocesses not considered here. Top and bottom-quark pair production may however not be able to tightly constrain all the numerous q¯qt¯ toperators simultaneously. Their contributions to associated pp →t¯ tX production processes considered here could then be sizeable. Reciprocally, the measurement of associated production processes could play an important role in probing all combinations of q¯qt¯ toperator coefficients. Again, since we do not include such operators in our analysis, our results will apply to BSM scenarios in which they induce subleading contributions. In the context of the fit to top and bottom-quark data we use the notation OtW ,OtB and ObW ,ObB for the dipole operators. We will use the notation Oϕt,Oϕb, and Oϕtb when referring to the operators that modify the right-handed couplings of the top and bottom quark and the notation Otϕ for the operator that modifies the top-quark Yukawa coupling. The Wilson coefficients are normalized to the TeV scale. – 4 – JHEP12(2019)098 The top-quark EFT conventions adopted here are different from the standard established by the LHC TOP Working Group in ref. [21]. In appendix Bwe provide the conversion to these standards. 2.3 Fit setup The dependence of the observables included in the fit on the Wilson coefficients is calculated at leading order with the Monte Carlo generator MG5 aMC@NLO [31]. The TEFT EW UFO model [32] is used for most of the operators. Exceptions are Ctϕ for which the dim6top UFO model [21] is used, and CbW and CbB for which we use the SMEFTsim UFO model [33]. The following values of the input parameters are used in the calculation: α= 1/127.9, GF= 1.16637 ×10−5GeV−2, mZ= 91.1876 GeV , mH= 125 GeV , mb= 0 GeV , mt= 172.5 GeV . The dependence of observables on the Wilson coefficients admits the following expansion: o=oSM +1 Λ2X i Cioi+1 Λ4X jX k CjCkojk +O(Λ−4).(2.3) The leading EFT term proportional to Λ−2reflects the interference of SM amplitudes with those featuring one dimension-six operator insertion. The terms proportional to Λ−4stem from the square of the amplitudes involving one insertion of dimension-six operators, or from amplitudes involving two such insertions in interference with SM ones. Terms of order Λ−4due to dimension-eight operators are ignored. The parameterized relations between observables and Wilson coefficients are given in appendix A. For several combinations of operators and observables the term proportional to Λ−2 in eq. (2.3) is suppressed. The Λ−4terms then plays an important role and the EFT expansion is not valid in full generality. A well-known example is the dependence of the associated production processes pp → t¯ tX on the top-quark dipole operators. The σµνqνstructure involves the momentum of the Zboson or photon, which leads to a suppression because the radiated Zboson or photon tends to be soft [32]. In this case, other processes can be found, where the Λ−2term dominates the sensitivity: the inclusion of charged-current interactions and e+e−→t¯ t production restores the validity of the fit for CtW and CtB. Several operators affecting the bottom-quark EW couplings lead to amplitudes whose interferences with SM ones are suppressed by the small bottom-quark mass. The ObW and Oϕtb operators induce a t¯ bW interaction involving a right-handed bottom quark. The ObB operator also generate a chirality flipping b¯ bZ dipolar interactions. The interferences of the amplitudes they generate with SM ones thus vanish in the mb→0 approximation adopted in this paper. For these operators, a strong dependence of the fit results on the Λ−4terms remains even after the ILC programme. 2.4 Implementation of the fit The fit to data is performed using the open source HEPfit package [34,35]. HEPfit is a general tool designed to combine direct and indirect constraints, in EFTs or particular – 5 – JHEP12(2019)098 SM extensions. Its flexibility allows to easily implement any BSM model or observable. HEPfit is available under the GNU General Public License. The developers’ version can be downloaded at [7]. The fit is performed as a Bayesian statistical analysis of the model. HEPfit includes a Markov-Chain Monte-Carlo implementation provided by the Bayesian Analysis Toolkit [9] to explore the parameter space. Similar fits using the HEPfit package have been performed for different models [36,37] and for effective field theories [38,39]. The results in this paper were verified with an independent fitting code based on the Minuit minimization package in ROOT [40]. The results for individual limits agree to 1%. For the comparison of the global limits we perform an ad-hoc fit in which we reduce the number of parameters and observables. In this case the results agree to 10%. In general we find HEPfit is more robust when dealing with several local minima, so all final results are obtained using HEPfit. The fit is based on the Bayesian approach of statistics and the interpretation differs slightly from the frequentist interpretation. The fit results are given as intervals on the operator coefficients with a given posterior probability, typically 68%. 3 Measurements The measurements that form the input to the fit are presented in this section. 3.1 Top-quark neutral-current interactions •pp →t¯ th production. The production of a Higgs boson in association with a topquark pair was observed by ATLAS and CMS in 2018 [41,42]. The production rate is sensitive to the coefficient Ctϕ of the operator that shifts the value of the top-quark Yukawa coupling. •pp →t¯ tZ/W production. The associated production of top quarks with a Zboson gives access to all operators that modify the coupling of the top quark with neutral EW gauge bosons and is therefore a key channel in a combined fit [32]. The ATLAS and CMS measurements of the inclusive cross section using 36 fb−1of data at 13 TeV have reached a precision of approximately 15–20% [43,44]. The results on pp → t¯ tW production are also included in the fit. A recent preliminary result [45], with an integrated luminosity of 78 fb−1and a relative uncertainty of less than 10%, is not included. •pp →t¯ tγ production. The rate of the pp →t¯ tγ process depends on the CtW and CtB coefficients of EW dipole operators. ATLAS has published a measurement of the pp →t¯ tγ fiducial cross-section [46] at √s= 13 TeV. •Single top-quark production in association with a Zboson has been observed by ATLAS and CMS. For the pp →tZq process the first cross-section measurements have reached a precision of approximately 15–35% [47,48]. •pp →γ∗/Z∗→t¯ tproduction. The neutral-current pair production process q¯q→ Z/γ →t¯ tis overwhelmed by the QCD process and has not been isolated. This – 6 – JHEP12(2019)098 contribution to the inclusive pp →t¯ tprocess leads to a dependence of the rate on the EW operators considered, but in practice this contribution can be ignored. 3.2 Top-quark charged-current interactions •Top-quark decay, t→Wb. The charged-current t¯ bW vertex is accessible at hadron colliders in top-quark decay. The t→Wb decay has a branching ratio of nearly 100%. The helicity fractions of the Wboson produced in top-quark decay can be predicted to excellent precision [49]. The measurements by ATLAS and CMS [50– 53] at √s= 7 and 8 TeV reach a precision of several percent. The combination of precise predictions and measurements converts these measurements in true hadron collider precision measurements and in sensitive probes to new physics affecting the t¯ bW vertex [23]. We include the 8 TeV measurements of FLand F0, that yield a tight limit on CtW . •Single-top-quark production. A second handle on the t¯ bW vertex is found in chargedcurrent single top-quark production. The t-channel process has a sizeable cross section, which has been measured to better than 10% precision [54,55] at √s= 13 TeV. ATLAS and CMS have also published precise measurements of the rate for the Wt associated production channel [56,57]. •Top-quark decay in single top-quark production. A measurement of the W-boson helicity in a sample of polarized top quarks yields further limits on anomalous topquark couplings [58–60]. These are however not considered here, as they are primarily competitive for the (CP-violating) imaginary parts of the operator coefficients that we do not include in our study. 3.3 Measurements in bottom-quark production •e+e−→b¯ bproduction. The LEP and SLC measurements of bottom-quark pair production provide a powerful, complementary handle on the operator coefficients C1 ϕQ and C3 ϕQ. Combining measurements of bottom-quark production at LEP/SLC with measurements in top-quark production yield solid constraints on both operator coefficients in a global fit [6]. We consider the measurements of Rband Abb F BLR at the Zpole [61]. •pp →b¯ bZ production. The associated production processes pp →b¯ bZ and pp → b¯ bγ at the Tevatron and LHC probe the b¯ bZ and b¯ bγ vertices. The ATLAS and CMS experiments have measured the cross section for the associated production of aZboson and at least one b-quark [62,63] in early LHC runs. The constraints derived from these measurements are not currently competitive with the LEP and SLC measurements. We therefore ignore them in the following. 3.4 Indirect constraints For reference, we collect here several observables that can be used to derive indirect constraints to top-quark couplings. A more complete discussion can be found in appendix A of ref. [21]. – 7 – JHEP12(2019)098 It is instructive to compare the S2 scenario to more detailed projections. ATLAS and CMS have provided detailed prospect studies for some analyses [82]. Other groups have published independent prospect studies, see in particular ref. [83] for t¯ tZ production and ref. [23] for top-quark decay. The production of a top-quark pair in association with a gauge boson plays an important role in the fit. In the ATLAS and CMS measurements we consider, the theory uncertainty (typically of the order of 10%) is similar in size to the experimental uncertainty. In the S2 scenario, the experimental uncertainties are improved very substantially. The theory uncertainties are then expected to be limiting by the end of the HL-LHC. This indeed seems the most likely scenario. The factor two improvement in the theory uncertainty envisaged in the S2 scenario could well be achieved by improving the description from the current NLO to NNLO in QCD, which seems feasible on the time scale of the HL-LHC programme. A promising avenue for many of the associated production processes is a differential analysis. In the current data set, the precision is still very limited for rare processes. However, with a hundred-fold increase in the data sample, differential analyses at the HLLHC are expected to provide powerful constraints [83,84]. This is particularly relevant for the dipole operators. In figure 3, the sensitivity of the differential pp →t¯ tγ cross section is seen to increase strongly with the transverse momentum of the photon pT. A shape analysis of the spectrum may yield a powerful constraint, possibly even exceeding the prospects of the S2 scenario. The case of the W-boson helicity fraction measurement in top-quark decays is an example where the S2 scenario is probably overly optimistic. The theory uncertainty is currently significantly below the experimental precision, so that it does not limit the precision for this projection. The strong improvement in the precision envisaged by the S2 scenario is optimistic in comparison with the outlook in ref. [23]. In practice, the impact on the overall prospects is limited. The measurements in top-quark decay are most relevant for the constraint on CtW /Λ2, that is sensitive to several other measurements. In case the measurements in top-quark decay should fail to improve as expected in S2, other measurements (such as single top-quark production with a Zboson) can take over its role in the global fit. We expect, therefore, that the overall results presented in this section are not affected too much, even if the top-quark decay measurements improve less than envisaged. 5.2 Future e+e−collider: ILC At an electron-positron collider bottom and top-quark pair production through the exchange of a photon or Zboson are among the dominant processes. A future high-energy e+e−collider thus provides an ideal laboratory to characterize the Z/γ b¯ band Z/γ t¯ tvertices. Single top-quark production could also bring valuable constraining power [85] but no quantitative prospect is currently available. So we do not consider this process. The potential of the ILC for the measurement of the EW couplings of the bottom quark is studied in detail in refs. [15,86]. These studies consider measurements of the cross-section and forward-backward asymmetry in the nominal ILC running scenario [87], – 14 – JHEP12(2019)098 ) [GeV]γ ( T p 20 - 35 35 - 50 50 - 65 65 - 80 80 - 95 95 - 110 110 - 140 140 - 180 180 - 300 300 - 500 > 500 tB cross-section sensitivity to C 2− 10 1− 10 γInclusive tt γDifferential tt Figure 3. The sensitivity of the differential pp →t¯ tγ cross section to the operator coefficient CtB/Λ2. The sensitivity is defined as the relative change in the cross section due to a unit change in CtB/Λ2. with an integrated luminosity of 2000 fb−1at √s= 250 GeV. The electron and positron beams are polarized, with a polarization of ±80% and ±30%, respectively. The luminosity is divided equally among the left-right and right-left configurations. The authors perform a full-simulation study, including the relevant SM backgrounds, and a realistic jet charge identification strategy based on the use of Kaon and vertex-charge tags. We adopt the uncertainty estimates of ref. [86], that include statistical and systematic uncertainties. For the 500 GeV run a complete analysis does not yet exist. We adopt the acceptance times efficiency estimate of 25% based on full simulation by the same authors. The statistical uncertainties for the cross-section and forward-backward asymmetry for the leftright and right-left beam polarizations at √s= 500 GeV are estimated assuming a total integrated luminosity of 4 ab−1. To produce top-quark pairs, an e+e−collider must be operated at a center-of-mass energy above twice the top-quark mass. Runs above the pair-production threshold are envisaged in the CLIC initial program and in later stages of the ILC and FCCee. Beam polarization, foreseen in ILC and CLIC, allows to disentangle the photon and Z-boson vertices [17,88]. In a multi-parameter EFT fit, the initial-state polarization is helpful to simultaneously constrain the coefficients of OtB and OtW [6]. For the sake of brevity we focus on the ILC scenario.2We again consider the nominal operating scenario [87], with an integrated luminosity of 4 ab−1at √s= 500 GeV with two different beam polarizations, P(e−, e+) = (−0.8,+0.3) and P(e−, e+) = (+0.8,−0.3). The projections for the e−e+→t¯ tprocess are based on the statistically optimal observables motivated in ref. [6]. These observables are optimized to fully exploit the bW+¯ bW−differential information (in the narrow top-quark width approximation) and 2The potential of the 500 GeV ILC and the initial stage at √s= 380 GeV of the CLIC project [12,16, 89] is found to be very similar for the relevant two-fermion operators, when rescaled by the appropriate integrated luminosity [4]. – 15 – JHEP12(2019)098 tϕ C3 Qϕ C1 Qϕ CtW CtB Cϕt Cbϕ CbW CbB Ctbϕ C ] -2 [ TeV 2 Λ i C ∆ 3− 10 2− 10 1− 10 1 10 2 10 LEP/SLC + LHC Run 2 + HL-LHC S1 + HL-LHC S2 + ILC250 + ILC500 Figure 4. Prospects for the precision of the Wilson coefficients in future high-luminosity operation of the LHC and at a high-energy e+e−collider. Assumptions on the operating scenarios and details of the uncertainty estimates are given in text. The solid section of the bars represents the individual constraints, where each parameter is fitted in isolation, the full length indicates the marginalized constraint in a ten-parameter fit. The complete covariance matrices of the fits that are presented in this figure are available in appendix C.2. extract the tightest constraints on parameters with linear dependence. In our case, these optimal observables place bounds on subset of operators that affect the top-quark EW couplings; Cϕt,C− ϕQ,CtW and CtB. Ref. [6] demonstrates that at least two center-of-mass energies are needed if one wants to constrain all two-fermion and four-fermion operators coefficients simultaneously. The experimental uncertainties are studied in full simulation in refs. [16,17]. Statistical uncertainties are estimated including the relevant branching ratios for the lepton+jets final state, the effect of the luminosity spectrum and a t¯ treconstruction efficiency of 50%. This yields an effective efficiency of 10% that multiplies the e+e−→t¯ t cross-section (see ref. [6] for more details). 5.3 Global fit on prospects In figure 4, we present the global fit results for the future collider scenarios introduced in the previous sections. The complete covariance matrices for all the fits are provided in appendix C.2. In figure 4the uncertainty ∆Cion the operator coefficients is shown. This uncertainty is estimated as half of the 68% probability interval. In order to compare all projects on an equal footing, the central value of all measurements, including the existing LHC and LEP/SLC results, is set to the SM value. For each Wilson coefficient, the first vertical bar represents the current data. In the second and third bars, the measurements envisaged in the S1 or S2 scenario for the HL-LHC are added. The fourth bar includes the LEP/SLC data, the data of the HL-LHC S2 scenario and the ILC run at √s= 250 GeV. The fifth bar adds also the 500 GeV run at the ILC. A discusstion of the extraction of the top-quark Yukawa coupling is postponed to section 6. For the first HL-LHC scenario, S1, we find that, due the conservative assumptions on systematic uncertainties, the bounds on the Wilson coefficient improve only marginally. In – 16 – JHEP12(2019)098 the S2 scenario, almost all limits are considerably tighter. For the dipole operator OtB the constraint remains very poor due the limited sensitivity of the LHC observables. This could be improved by the addition of the differential t¯ tγ measurement, as discussed in section 5.1. The individual and marginalized limits for the operators that affect only the top-quark sector are very similar. Most operators are constrained from several angles, by different LHC observables (see figure 1). This limits the correlation in the global fit. In the bottomquark sector, the sensitivity is dominated by the Rbmeasurement, giving rise to a strong correlation and considerably larger differences between individual and marginalized limits. Adding the e+e−→b¯ bdata at √s= 250 GeV provides an improvement for the pure bottom-quark operators by an order of magnitude. The top-quark operators improve somewhat as well, due to a reduction of the correlation with the bottom-quark operators. Finally, we consider the ILC500 scenario. At this energy, the sensitivity to the bottomquark operators is very similar to that at √s= 250 GeV. As the b¯ bproduction cross section decreases with the center-of-mass energy, the addition of the 500 GeV data does not provide an important improvement on the bottom-quark coefficients limits. On the contrary, the addition of the e+e−→t¯ tdata leads to a very pronounced improvement of the constraints on the top-quark operator coefficients, by one or two orders of magnitude. The direct access to the Z/γ t¯ tvertex provides very tight constraints. Also the bounds on C1 ϕQ/Λ2and C3 ϕQ/Λ2are expected to improve by an order of magnitude. The combination of high-precision constraints on the two linear combinations (C1 ϕQ +C3 ϕQ, that affects bottom-quark pair production, and the difference, C1 ϕQ −C3 ϕQ, that affects top-quark pair production) finally lift the degeneracy that affects the LHC/LEP/SLC fit of section 4. 5.4 Validity of the EFT framework In section 4.2, the terms of order Λ−4were found to have a considerable impact on the fit to current LHC and LEP/SLC data. This limits the generality of the interpretation to extensions of the SM where the contribution of the dimension-eight terms we have ignored is less important than that of the dimension-six operators we have included. With the increasing precision of the measurements at the LHC and at future facilities, this tension in the EFT description is expected to decrease. In the second HL-LHC scenario, S2, the difference between the nominal fit and a fit based on a parameterization that only considers the Λ−2terms is indeed reduced significantly. In fact, for most of the observables the former gives better constraints (by a factor 3 at most) due to the fact that the observables depend on less parameters because of the vanishing Λ−4terms for CbW ,CbB and Cϕtb in the mb→0 limit. However, the Λ−4term still plays an important role for CtB due to the suppression of the linear term explained in section 2. The high-precision measurements in e+e−collisions improve the bounds by at least an order of magnitude and bring most operator coefficients safely into the range where the EFT expansion is valid in full generality. The difference between the nominal fit and the fit based on only Λ−2terms is reduced to less than 20%. – 17 – JHEP12(2019)098 5.5 Four-fermion operators of the form e+e−Q¯ Q In this subsection, we discuss the perspective for an extension of the fit to the complete set of CP-conserving dimension-six operators that affect the bottom and top-quark EW couplings. The two-lepton-two-quark operators contributing to e+e−t¯ tand e+e−b¯ b(as well as νe−t¯ b) interactions are the following: O1 lq ≡1 2¯ qγµq¯ lγµl, O3 lq ≡1 2¯ qτIγµq¯ lτIγµl, Olu ≡1 2¯ uγµu¯ lγµl, Old ≡1 2¯ dγµd¯ lγµl, Oeq ≡1 2¯ qγµq¯ eγµe, Oeu ≡1 2¯ uγµu¯ eγµe, Oed ≡1 2¯ dγµd¯ eγµe, OT lequ ≡¯ qσµνu¯ lσµνe, OS lequ ≡¯ qu ¯ le, Oledq ≡¯ dq ¯ le, (5.1) where l≡(VPMNSνL, eL)T,e≡eR, and VPMNS is the Pontecorvo-Maki-NakagawaSakata [90–92] matrix. We define O+ lq =O1 lq +O3 lq which mediates b¯ bproduction and O− lq =O1 lq −O3 lq for t¯ tproduction in e+e−collisions. The seven operators in the left column of eq. (5.1) have vector Lorentz structures similar to SM gauge interactions. Three further scalar and tensor operators, have non-standard Lorentz structures and can effectively be constrained with specialized observables [6] and runs with left-left or right-right beam polarization [87]. In the following, we therefore focus on the seven vector operators. The primary handle to constrain the two-fermion and four-fermion operators in a global fit is the energy dependence. The sensitivity to four-fermion operators grows very strongly with energy, while that to the two-fermion operators is essentially flat. At hadron colliders, the four-fermion operators of e+e−t¯ tform can, at least in principle, be constrained by a differential analysis of the cross section of the pp →t¯ t e+e− process versus the invariant mass and transverse momentum of the e+e−system [32]. The fit can then disentangle the photon, Z-boson, and the contact interaction contributions. No such analysis has been made public, so far. A future e+e−collider with multiple energy stages is expected to provide a powerful bound on the four-fermion operator coefficients. In ref. [6], a ten-parameter fit of the two-fermion and four-fermion operator coefficients that affect the EW couplings of the top quark is shown to provide stringent bounds when at least two well-separated energy stages are available. To estimate the effect of the inclusion of the four-fermion operators, we extend the fit with seven additional degrees of freedom. At the same time, the prospects for mea- – 18 – JHEP12(2019)098 10-parameter fit 17-parameter fit ILC250 + ILC500 + ILC1000 Cϕt/Λ20.01 0.09 C3 ϕQ/Λ20.005 0.04 C1 ϕQ/Λ20.005 0.04 CtW /Λ20.02 0.014 CtB/Λ20.02 0.015 Ctϕ/Λ20.54 0.54 Cϕb/Λ20.007 0.008 CbW /Λ20.09 0.17 CbB/Λ20.13 0.17 Cϕtb/Λ21.9 1.9 Ceu/Λ2— 0.0006 Ced/Λ2— 0.0005 Ceq/Λ2— 0.0004 Clu/Λ2— 0.0006 Cld/Λ2— 0.0009 C− lq /Λ2— 0.0006 C+ lq /Λ2— 0.0005 Table 3. The marginalized 68% probability bounds on the dimension-six operator coefficients in units of TeV−2. The results in the first column are based on a ten-parameter fit on pseudo-data from two ILC runs, with an integrated luminosity of 2 ab−1at 250 GeV and 4 ab−1at √s= 500 GeV. These results are identical to those of the ILC500 entry in figure 4. The second column presents the results of the seventeen-parameter fit. It includes an additional run, with an integrated luminosity of 8 ab−1at √s= 1 TeV and seven additional degrees of freedom corresponding to two-lepton-twothird-generation-quark operators. surements at √s= 1 TeV, with an integrated luminosity of 8 ab−1, are added to the HL-LHC+ILC250+ILC500 scenario. For the top-quark operators we again adopt the projections of ref. [6], for bottom-quark operators, statistical uncertainties on the crosssection and AF B are propagated, assuming a conservative acceptance times selection efficiency of 10%. The results of this extended fit are shown in table 3. The marginalized 68% probability bounds are compared to those obtained in the ten-parameter fit (i.e. the results labeled ILC500 in figure 4). This seventeen-parameter fit yields excellent limits on the four-fermion operators, below 10−3TeV−2. The bounds agree with those of ref. [6] when the larger integrated luminosity in the 1 TeV scenario is accounted for. The bounds on the dipole operators are similar to those of the ten-parameter fit: the bounds on the coefficients CtW /Λ2and CtB/Λ2of the top-quark dipole operators improve somewhat, as the sensitivity of the optimal observables grows with increasing center-of- – 19 – JHEP12(2019)098 mass energy. The bound on CbW /Λ2derives from cross-section and AF B in e+e−→ b¯ bmeasurements. It does therefore not improve at higher center-of-mass energies and moreover suffers somewhat from the introduction of additional e+e−b¯ bdegrees of freedom. The largest difference between the two fits is found for the two-fermion operators that modify the left-handed couplings of the top and bottom-quark to the Zboson or the right-handed coupling of the top quark to the Zboson. The presence of the four-fermion operators degrades the excellent limits on Cϕt/Λ2and C1,3 ϕQ/Λ2by a factor eight. We conclude, therefore, that a global EFT fit, including all dimension-six operators that affect the top and bottom-quark EW interactions, is feasible provided data is collected at two sufficiently distinct centre-of-mass energies above the top-quark pair production threshold. 6 The top-quark Yukawa coupling In this section, we extract the top-quark Yukawa coupling from LHC data and the prospects for measurements at the HL-LHC and ILC. 6.1 Indirect and direct bounds The top-quark Yukawa coupling is one of the most intriguing parameters in the SM. With a value close to 1 it is the largest of all Yukawa couplings. New physics scenarios such as two-Higgs-doublet models, supersymmetric scenarios with small tan β, and composite Higgs models [93] could lead to sizeable shifts from the SM prediction. A precise and robust measurement is therefore one of the main targets of high-energy physics experiments in the next decades. The measurements of the Higgs boson decays and production rates other than t¯ tH yield indirect constraints on the top-quark Yukawa coupling. A model-dependent bound can be derived from the loop-induced gg →H,H→Zγ and H→γγ rates. In the SM, the top-quark loop is the dominant contribution to these rates, but the effective couplings to the photon and the gluon could also receive contributions from new particles. In the κ fit framework employed in early Higgs coupling fits, these BSM contributions are assumed to be absent and the gg →Hand H→γγ rates yield a tight constraint on the factor κt=κc=κuthat multiplies the Yukawa couplings of the up-type quarks. The legacy result of LHC Run 1 is κt= 1.40+0.24 −0.21 [94]. Significantly sharper results are available from Run 2 measurements [95,96]. These indirect bounds tend to weaken considerably in a global fit. An e+e−collider also offers several handles on the top-quark Yukawa coupling. The same indirect methods are available at center-of-mass energies below the t¯ tH production threshold. In the κframework with κu=κc=κt, the precise determination of the H→c¯cdecay rate yields a tight bound on that parameter. The Yukawa coupling can also be extracted indirectly from the measurement of the Hgg and Hγγ couplings, with 1% precision after 2 ab−1at √s= 250 GeV [75]. A global effective field theory (EFT) analysis of the indirect sensitivity of Higgs and diboson measurements to EW top-quark couplings, including the top-quark Yukawa coupling, is performed in ref. [76]. It is found – 20 – JHEP12(2019)098 that differential measurements are crucial to simultaneously disentangle all tree and looplevel contributions. Several attempts have been made to disentangle the contributions of different operators that contribute to the gg →H(and H→γγ) rates (see ref. [97] and references therein) with additional probes, such as boosted Higgs+jet production, di-Higgs boson production, off-shell Higgs production. None of these seem sufficiently sensitive to lift the degeneracy between the operator that modifies the top-quark Yukawa coupling and operators representing Hgg (or Hγγ) contact interactions. Therefore, we focus on the direct bound from t¯ tH production in this paper. 6.2 Associated t¯ tH production at the LHC The observation of the associated production process of a top-quark pair with a Higgs boson [41] provides a direct demonstration of the interaction of the Higgs boson with the top quark. The ratio µt¯ tH of the measured cross section and the SM prediction is determined with a precision approaching 20%. With an uncertainty of 8%, the NLO QCD prediction in the SM is also relatively precise. The extraction of the top-quark Yukawa coupling from the pp →t¯ tH rate could thus yield a competitive and robust result, provided all other EFT contributions are sufficiently well constrained. The fit presented in section 4includes the LHC measurement of the pp →t¯ tH production cross section. A single-parameter fit yields an individual 68% probability bound on the operator coefficient Ctϕ that shifts the value of the top-quark Yukawa coupling: Ctϕ/Λ2∈[−4.4,0]TeV−2(individual). Due to a small quadratic term in the dependence of the t¯ tH cross section on Ctϕ, the fit finds a second minimum very far from the SM value. Here we only treat the minimum which is closer to the SM value. The bound becomes only slightly weaker in the ten-parameter fit: Ctϕ/Λ2∈[−4.6,0.1]TeV−2(marginalized). The individual and marginalized results are very close to each other, an indication that the constraint from the t¯ tH rate is very robust against the effect of the operators that modify top-quark EW couplings. The dependence of pp →t¯ tH on other top-quark EW operators arises mainly from q¯q-initiated production which is subdominant compared to the gg-initiated process. The correlation of Ctϕ/Λ2with CtW /Λ2,C3 ϕQ/Λ2,CtB/Λ2and CbW /Λ2is small, below 0.1%. We note, however, that including four-fermion q¯qt¯ toperators can have a significant impact on the extraction of the top-quark Yukawa coupling from pp →t¯ tH measurement. 6.3 HL-LHC prospects The fit is repeated on projections to assess the expected precision after the complete data set collected during the high-luminosity phase of the LHC. As before, we focus on the S2 scenario, based on an integrated luminosity of 3 ab−1at √s= 14 TeV. In this scenario, the statistical uncertainty on the t¯ tH cross section becomes negligible and the precision is – 21 – JHEP12(2019)098 primarily limited by the precision of the theory prediction (currently 8% and assumed to improve to 4%). The precision of the global fit improves considerably, reducing the 68% probability interval to [−0.55,+0.55]. This result agrees with the S2 prospects in ref. [81]. 6.4 ILC prospects The direct measurement of the Yukawa coupling in e+e−→t¯ tH production requires operation at a center-of-mass energy above the t¯ tH production threshold. The cross section turns on sharply at around √s= 500 GeV. The unpolarized cross section reaches a maximum of 2 fb at a center-of-mass energy of approximately 800 GeV. The t¯ tH production rate is two orders of magnitude lower than that for top-quark pair production rate, which forms the most important background for the H→b¯ banalysis. The cross section of the irreducible t¯ tb¯ bbackground, either from associated t¯ tZ production or a hard gluon splitting to a b¯ bpair, is similar to that of the signal. Full-simulation studies of the potential of the linear collider [16,98–101] have been performed at center-of-mass energies from 500 GeV to several TeVs. They include realistic descriptions of the t¯ tand t¯ tZ backgrounds, of the detector response, flavour tagging and jet clustering. Projections for the nominal ILC programme [87], with 4 ab−1of integrated luminosity collected at 500 GeV are presented in ref. [102]. An uncertainty of 13% is expected on the t¯ tH cross section, limited by statistics. As the nominal ILC energy is very close to the t¯ tH production threshold, operation at a slightly higher energy improves the precision considerably. Increase of the center-of-mass energy by 10% (i.e. to √s= 550 GeV) enhances the cross section by a factor of four and the precision on the Yukawa coupling by a factor two, for the same integrated luminosity [102]. We base our projection for 1 TeV operation on the analysis of ref. [98] of t¯ tH production followed by H→b¯ bdecay. The expected uncertainty on the t¯ tH cross section for an integrated luminosity of 8 ab−1is of 3.2%, obtained by scaling the signal and background yields with a flat luminosity factor. To match the statistical precision, the systematic uncertainties must be controlled to a challenging level. At 1 TeV the signal efficiency and background yield must be known to approximately 1%, which seems feasible with data-driven estimation in control regions. The theory uncertainty in the cross section at √s= 1 TeV must be reduced to the level of 1–2%, a factor two with respect to currently available calculations [103]. On the other hand, it is likely that the analysis can be further improved, by reoptimizing the selection, with the inclusion of other Higgs decay channels and of the τ-lepton plus jets final state. Significant additional improvements are possible with improved jet clustering algorithms and the use of kinematic fits. 6.5 Summary of results In table 4, we present the individual and marginalized 68% probability bounds on Ctϕ/Λ2 from the fits to LEP/SLC+LHC data and to the future collider scenarios. For comparison to the literature, the same results are also provided in terms of the precision with which – 22 – JHEP12(2019)098 scenario LHC Run 2 HL-LHC S2 ILC500 ILC550 ILC500 +LEP/SLC +LEP/SLC +ILC1000 √s,RL13TeV, 36 fb−114TeV, 3 ab−1500 GeV, 4 ab−1550 GeV, 4 ab−1+1 TeV, +8 ab−1 68% probability interval for effective operator coefficient Ctϕ/Λ2[TeV−2] individual [−4.4,+0.0] [−0.55,+0.55] [−1.06,+1.06] [−0.50,0.50] [−0.27,+0.27] marginalized [−4.6,−0.2] [−0.55,+0.55] [−1.07,+1.07] [−0.52,+0.52] [−0.32,+0.32] corresponding relative uncertainty on top-quark Yukawa coupling ∆yt/yt[%] individual 13.2 3.3 6.4 3.0 1.62 marginalized 13.2 3.3 6.4 3.1 1.96 Table 4. The 68% probability intervals for Ctϕ/Λ2and the corresponding precision on the topquark Yukawa coupling. The results of the first four columns correspond to the ten-parameter fit that we used to obtain the results of figure 4. The results for the scenario with ILC runs at two different center-of-mass energies in the last column were obtained with the extended seventeenparameter fit presented in section 5.5. the Yukawa coupling can be extracted, using the simple relation: δyt=−Ctϕv2 Λ2.(6.1) The results of the first four columns correspond to the ten-parameter fit that we used to obtain the results of figure 4. The results for the scenario with ILC runs at two different center-of-mass energies in the last column were obtained with the extended seventeenparameter fit presented in section 5.5. Before turning to a discussion of the global fit results, we compare the individual limits to the literature. The HL-LHC result in table 4agrees with the HL-LHC projection of ref. [81]. The ILC results at 500 GeV agree —by construction— with the summary of the Higgs/EW group for the 2020 update of the European strategy for particle physics in ref. [104]. The results for operation at 550 GeV and 1 TeV extend the study to higher energy. We find that in nearly all cases the individual and marginalized results agree very closely. This implies that the operators that modify the top-quark EW couplings do not affect the extraction of the top-quark Yukawa coupling. In the LHC and HL-LHC fits, despite the relatively poor constraints on the EW couplings of the top quark, the bounds on Ctϕ/Λ2are not affected by the presence of the additional degrees of freedom. In this case, it is important to note, however, that the operators that affect the QCD interactions of the top quark, such as CtG/Λ2and four-fermion operators of the form q¯qt¯ t, are not included in the fit. These can in principle be constrained using precise measurements of the differential t¯ tcross section. A recent global fit of the top-quark sector on LHC data [20] finds, however, that the marginalized limit on Ctϕ is approximately a factor 10 weaker than the individual limit, due to strong correlations between operator coefficients. The addition of Tevatron results or future differential measurements could help reducing this degeneracy. It is nevertheless likely that a combination of pp →t¯ tand pp →t¯ tX measurements could be needed to constrain simultaneously all q¯qt¯ toperators. In this respect, the extraction of the top-quark Yukawa coupling at future lepton colliders so far seems more robust. – 23 – JHEP12(2019)098 AF B −+,250[%] = 69.6 + 1TeV Λ2          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          0.3 0.3 −2.2 · · 1.8 3.8 −29.5 8.57           +1TeV Λ4          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · −2.2 1.02 · · · · · · · · −0.16 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·                     C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           (A.18) AF B +−,250[%] = 35.9 + 1TeV Λ2          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          −7.7 −7.7 −4.5 · · 62 119 −4.6 7.9           +1TeV Λ4          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · −0.10 −0.14 · · · · · · · · −0.95 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·                     C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           (A.19) AF B −+,500[%] = 67.7 + 1TeV Λ2          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          0.2 0.2 −2.3 · · 1.2 8 −139 40.3           +1TeV Λ4          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · −5.8 3.09 · · · · · · · · −0.47 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·                     C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           (A.20) – 30 – JHEP12(2019)098 AF B +−,500[%] = 46.7 + 1TeV Λ2          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          −7 −7 −3.5 · · 219 380 −26.6 28.4           +1TeV Λ4          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · −0.67 0.09 · · · · · · · · −2.8· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·                     C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           (A.21) AF B −+,1000[%] = 57 + 1TeV Λ2          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          0.48 0.48 −2.7 · · 3.4 37.4 −593 145           +1TeV Λ4          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · −10 4.83 · · · · · · · · −0.7· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·                     C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           (A.22) AF B +−,1000[%] = 34.6 + 1TeV Λ2          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          −6.8 −6.8 −3.6 · · 826 1611 −120 6.5           +1TeV Λ4          C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           T          · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · −1.34 0.1· · · · · · · · −3.35 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·                     C3 ϕQ C1 ϕQ Cϕb CbW CbB Ced Ceq Cld C+ lq           (A.23) – 31 – JHEP12(2019)098 A.5 e−e+→t¯ tH Pol. √s[GeV] SM Cϕt C− ϕQ CtW CtB Ctϕ C− lq Clu Ceq Ceu −+ 500 0.49 −0.026 −0.028 0.44 0.13 −0.063 −1.5 −1.4 −0.06 −0.04 +−500 0.23 −0.015 0.014 0.016 0.18 −0.03 −0.09 −0.09 −0.94 −0.98 −+ 550 1.9 −0.1 −0.1 1.8 0.56 −0.23 −7.12 −6.56 −0.24 −0.3 +−550 0.91 0.059 0.049 0.073 0.73 −0.11 −0.39 −0.42 −4.2 −4.7 −+ 1000 3.37 −0.11 −0.21 4.37 1.39 −0.39 −43 −29.5 −1.05 −1.7 +−1000 1.75 0.12 0.049 0.22 1.8 −0.2 −2.3 −1.77 −18.1 −29.9 Table 5. Linear dependence of the cross-section [pb] for the process e−e+→t¯ tH.P(e−, e+) = (−0.8,+0.3) is noted as −+, and P(e−, e+) = (+0.8,−0.3) is noted as +−. B Conversion to LHC TOP WG EFT conventions The conversion between our conventions for top-quark operator coefficients and the LHC TOP WG standards of ref. [21] is the following:                       cϕt c3 ϕQ c− ϕQ ctW ctZ ctϕ cϕtb c(1) Qe c(1) tl c(1) te c−(1) Ql                       =                      y2 t0 0 0 0 0 0 0 0 0 0 0y2 t0 0 0 0 0 0 0 0 0 0−y2 ty2 t0 0 0 0 0 0 0 0 0 0 0 ytgW0 0 0 0 0 0 0 0 0 0 ytgWcW−ytgYsW0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 −y2 t0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1                                           Cϕt C3 ϕQ C1 ϕQ CtW CtB Ctϕ Cϕtb Ceu Ceq Clu C− lq                      . (B.1) No standard have been established for the bottom-quark operator coefficients Cϕb,CbW , CbB,Ced,Ceq,Cld,C+ lq . A conversion of our results to these standards is provided, for convenience, in the form of a Mathematica notebook as supplementary material. C Covariance matrices C.1 Present constraints FIgure 5shows the projection of the fit posterior on planes formed by each pair of operator coefficient (top-quark Yukawa excluded) for section 4analysis of LEP/SLC and LHC Run 2 data. The associated mean values,uncertainties and correlation matrices, for (Cϕt, C3 ϕQ, C1 ϕQ, CtW , CtB, Ctϕ, Cϕb, CbW , CbB, Cϕtb)/Λ2in units of TeV−2, are – 32 – JHEP12(2019)098 the following: mean values = 1.4 0.018 0.018 −0.1 4.6−2.4−0.104 0.75 −0.25 −1.7 uncertainties = 6.8 0.75 1.4 0.3 6.2 2.2 2.8 2.4 19 5.4 corr =                        1−0.071 0.087 −0.0068 −0.0056 0.0014 0.079 −0.0071 0.041 0.0031 −0.071 1 −0.056 0.068 −0.017 0.00054 0.25 0.14 0.12 0.00098 0.087 −0.056 1 −0.0039 0.012 −0.0014 0.9 0.34 0.47 0.014 −0.00068 0.068 −0.0039 1 0.023 0.0018 0.026 0.0015 0.018 0.00045 −0.0056 −0.017 0.012 0.023 1 0.0047 0.004 0.0033 0.0051 0.0014 0.0014 0.00054 −0.0014 0.0018 0.0047 1 0.0013 0 0.0016 −0.0018 0.079 0.25 0.9 0.026 0.004 −0.0013 1 0.31 0.6 0.0094 −0.0071 0.14 0.34 0.0015 0.0033 0 0.31 1 0.26 0.1 0.041 0.12 0.47 0.018 0.0051 0.0016 0.6 0.26 1 0.014 0.0031 0.00098 0.014 0.00045 0.0014 −0.0018 0.0094 0.1 0.014 1                        (C.1) Note that non-Gaussianities imply that the above information only permits an approximate reconstruction of the posterior probability. A Mathematica notebook with these numerical values and a conversion to LHC TOP WG standards is provided as supplementary material. C.2 Future prospects We provide here the uncertainties and correlation matrices of section 5study of future prospects (summarized in figure 4) on (Cϕt, C3 ϕQ, C1 ϕQ, CtW , CtB, Ctϕ, Cϕb, CbW , CbB, Cϕtb)/Λ2operator coefficients in units of TeV−2. This information, together with a conversion to LHC TOP WG standards, is also provided for convenience in a Mathematica notebook as supplementary material. C.2.1 LEP/SLC + LHC Run2 uncertainties = 6.8 0.72 0.96 0.32 5.2 2.1 1.4 2.2 14 4.8 corr =                        1−0.14 0.15 −0.012 −0.0021 −0.00082 0.09 0.016 0.055 0 −0.14 1 −0.32 0.056 −0.036 0.0045 0.23 0.067 0.062 0.0015 0.15 −0.32 1 −0.027 0.02 0.032 0.78 0.26 0.35 −0.0036 −0.012 0.056 −0.027 1 −0.0076 0.002 0.011 −0.011 0.0054 −0.0024 −0.0021 −0.036 0.02 −0.0076 1 −0.0029 −0.00097 0.0062 0.0023 0.00028 −0.00082 0.0045 0.032 0.002 −0.0029 1 0.028 −0.0068 −0.0032 0.00089 0.09 0.23 0.78 0.011 −0.00097 0.028 1 0.29 0.53 −0.0037 0.016 0.067 0.26 −0.011 0.0062 −0.0068 0.29 1 0.22 0.02 0.055 0.062 0.35 0.0054 0.0023 −0.0032 0.53 0.22 1 −0.0043 0 0.0015 −0.0036 −0.0024 0.00028 0.00089 −0.0037 0.02 −0.0043 1                        (C.2) These values differ slightly from those of eq. (C.1) since all measurements have here been assumed to reproduce the SM prediction. – 33 – JHEP12(2019)098 Figure 5. Allowed regions after the fit to the LHC and LEP/SLC measurements in table 1. The 68% and 95% probability regions are shown for each pair of the ten effective operator coefficients that affect the electro-weak interactions of the top and bottom quarks. The top-quark Yukawa operator is marginalized over. All Wilson coefficients are in units of TeV−2. – 34 – JHEP12(2019)098 C.2.2 LEP/SLC + LHC S1 uncertainties = 6.3 0.63 0.71 0.26 4.8 2 0.99 1.9 12 4.2 corr =                      1−0.19 0.19 −0.013 −0.0046 −0.0019 0.071 0.011 0.031 0.0021 −0.19 1 −0.48 0.048 −0.038 −0.00027 0.26 0.077 0.079 0.0047 0.19 −0.48 1 −0.024 0.042 0.001 0.65 0.21 0.24 −0.014 −0.013 0.048 −0.024 1 −0.0055 0.0061 0.019 −0.00031 0.00055 0.0017 −0.0046 −0.038 0.042 −0.0055 1 0.0075 0.012 −0.00032 0.00058 0.0026 −0.0019 −0.00027 0.001 0.0061 0.0075 1 0.0064 0.0025 0.01 0.00042 0.071 0.26 0.65 0.019 0.012 0.0064 1 0.29 0.48 −0.012 0.011 0.077 0.21 −0.00031 −0.00032 0.0025 0.29 1 0.21 −0.0046 0.031 0.079 0.24 0.00055 0.00058 0.01 0.48 0.21 1 −0.017 0.0021 0.0047 −0.014 0.0017 0.0026 0.00042 −0.012 −0.0046 −0.017 1                      (C.3) C.2.3 LEP/SLC + LHC S2 uncertainties = 2.7 0.17 0.3 0.06 3.8 0.54 0.6 1.4 8.2 3  corr =                      1−0.083 0.26 −0.023 −0.049 −0.0024 0.27 0.012 0.067 0.0073 −0.083 1 −0.4−0.031 −0.0086 −0.0009 0.046 0.0073 −0.021 −0.00016 0.26 −0.4 1 0.0046 −0.0096 −0.0055 0.8 0.15 0.16 0.0025 −0.023 −0.031 0.0046 1 −0.03 −0.00047 0.00029 −0.0011 0.0019 −0.0015 −0.049 −0.0086 −0.0096 −0.03 1 0.018 −0.02 0.0037 −0.0065 −0.00064 −0.0024 −0.0009 −0.0055 −0.00047 0.018 1 −0.0056 0.0035 0.0017 −0.0027 0.27 0.046 0.8 0.00029 −0.02 −0.0056 1 0.17 0.27 0.0028 0.012 0.0073 0.15 −0.0011 0.0037 0.0035 0.17 1 0.11 0.022 0.067 −0.021 0.16 0.0019 −0.0065 −0.0017 0.27 0.11 1 0.012 0.0073 −0.00016 0.0025 −0.0015 −0.00064 −0.0027 0.0028 0.022 0.012 1                      (C.4) C.2.4 LEP/SLC + LHC S2 + ILC250 uncertainties = 1.7 0.15 0.15 0.06 3.8 0.54 0.016 0.17 0.24 3  corr =                      1 0.18 −0.18 −0.045 0.024 −0.0034 −0.0016 0.0028 −0.0029 0.0071 0.18 1 −1−0.031 −0.013 −0.0056 −0.025 −0.0038 −0.0013 −0.01 −0.18 −1 1 0.031 0.013 0.0056 −0.0099 0.0035 0.00081 0.01 −0.045 −0.031 0.031 1 −0.034 −0.0011 −0.00067 0.0064 0.0083 −0.0042 0.024 −0.013 0.013 −0.034 1 0.017 0.0012 −0.0015 0.0025 −0.0059 −0.0034 −0.0056 0.0056 −0.0011 0.017 1 −0.00097 0.00079 −0.00014 −0.0013 −0.0016 −0.025 −0.0099 −0.00067 0.0012 −0.00097 1 0.012 0.0098 0.0034 0.0028 −0.0038 0.0035 0.0064 −0.0015 0.00079 0.012 1 0.3 0.001 −0.0029 −0.0013 0.00081 0.0083 0.0025 −0.00014 0.0098 0.3 1 −0.00071 0.0071 −0.01 0.01 −0.0042 −0.0059 −0.0013 0.0034 0.001 −0.00071 1                      (C.5) C.2.5 LEP/SLC + LHC S2 + ILC250 + ILC500 uncertainties = 0.01 0.0054 0.0054 0.02 0.019 0.54 0.0068 0.088 0.12 1.8 corr =                      1−0.74 0.74 0.93 −0.9 0.00045 −0.0019 −0.0012 0.00058 0.0011 −0.74 1 −0.72 −0.87 0.86 0.0014 0.065 0.0014 0.0003 −0.0014 0.74 −0.72 1 0.87 −0.86 0.00058 0.06 0.00016 0.0022 −0.00049 0.93 −0.87 0.87 1 −0.97 0.00024 −0.0022 −0.00059 0.0012 0.00084 −0.9 0.86 −0.86 −0.97 1 1.8×10−50.0025 0.00039 −0.00094 −0.00097 0.00045 0.0014 0.00058 0.00024 1.8×10−51 0.0018 −0.00016 −0.0012 −0.00036 −0.0019 0.065 0.06 −0.0022 0.0025 0.0018 1 −0.0017 −0.0061 −0.0027 −0.0012 0.0014 0.00016 −0.00059 0.00039 −0.00016 −0.0017 1 0.38 0.0067 0.00058 0.0003 0.0022 0.0012 −0.00094 −0.0012 −0.0061 0.38 1 0.0039 0.0011 −0.0014 −0.00049 0.00084 −0.00097 −0.00036 −0.0027 0.0067 0.0039 1                      (C.6) – 35 – JHEP12(2019)098 C.2.6 LEP/SLC + LHC S2 + ILC250 + ILC500 + ILC1000 The study of section 5.5 leads to the following uncertainties and correlation matrix on (Cϕt, C3 ϕQ, C1 ϕQ, CtW , CtB, Ctϕ, Cϕb, CbW , CbB,Cϕtb, Ced, Ceq, Cld, C+ lq , Ceu, Clu, C− lq )/Λ2operator coefficients in units of TeV−2: uncertainties = 0.088 0.04 0.04 0.014 0.015 0.9 0.008 0.17 0.17 1.9 0.0005 0.0004 0.0009 0.0005 0.0006 0.0006 0.0006  corr =                                           1−0.27 0.27 0.0014 −0.0033 0.0021 −0.0038 −0.0017 0.0034 −0.0021 0.0096 −0.0038 0.0046 0.0055 −0.00077 0.0045 −0.0018 −0.27 1 −0.99 −0.0049 0.0062 7.2×10−50.025 0.0013 −0.0013 0.0029 0.016 0.015 0.0044 −0.0048 −0.0037 −0.0037 0.0019 0.27 −0.99 1 0.0051 −0.0065 0 0.013 −0.0023 0.00059 −0.003 0.039 0.015 0.008 −0.0016 0.0022 0.0035 −0.0023 0.0014 −0.0049 0.0051 1 −0.84 −0.0015 −0.0014 −0.0028 −0.00056 0 0.0018 −0.0027 0.0023 0.0018 −0.001 −0.00013 −0.00083 0.0033 0.0062 −0.0065 −0.84 1 0.0029 −0.00027 0.0023 −0.0017 0.00039 −0.0012 0.0022 −0.00084 −0.0023 −0.00098 0.00042 0.00036 0.0021 7.2×10−50−0.0015 0.0029 1 0.0011 −0.00067 0.0032 0.0019 −0.00022 −0.0014 −0.0023 −0.0026 0.00078 0.00022 −0.0032 −0.0038 0.025 0.013 −0.0014 −0.00027 0.0011 1 −0.0013 −0.0024 −0.0018 0.15 −0.11 0.018 0.0062 0.0033 0.0042 0.00041 −0.0017 0.0013 −0.0023 −0.0028 0.0023 −0.00067 −0.0013 1 0.24 0.0056 −0.0032 0.0012 0.0032 0.0092 0.00065 0.0038 0.00096 0.0034 −0.0013 0.00059 −0.00056 −0.0017 0.0032 −0.0024 0.24 1 0.0013 −0.015 0.0074 −0.0092 −0.0064 0.003 −0.0042 0.01 −0.0021 0.0029 −0.003 0 0.00039 0.0019 −0.0018 0.0056 0.0013 1 0.00079 −0.00045 0.00088 −0.00068 0.0036 0.00031 −0.00053 0.0096 0.016 0.039 0.0018 −0.0012 −0.00022 0.15 −0.0032 −0.015 0.00079 1 −0.38 0.045 −0.021 0.013 −0.001 −0.0016 −0.0038 0.015 0.015 −0.0027 0.0022 −0.0014 −0.11 0.0012 0.0074 −0.00045 −0.38 1 0.083 0.0027 −0.04 −0.0022 0.00048 0.0046 0.0044 0.008 0.0023 −0.00084 −0.0023 0.018 0.0032 −0.0092 0.00088 0.045 0.083 1 0.61 0.00097 −0.0012 −0.0026 0.0055 −0.0048 −0.0016 0.0018 −0.0023 −0.0026 0.0062 0.0092 −0.0064 −0.00068 −0.021 0.0027 0.61 1 0.0052 −0.0033 −0.0021 −0.00077 −0.0037 0.0022 −0.001 −0.00098 0.00078 0.0033 0.00065 0.003 0.0036 0.013 −0.04 0.00097 0.0052 1 −0.0035 0.0052 0.0045 −0.0037 0.0035 −0.00013 0.00042 0.00022 0.0042 0.0038 −0.0042 0.00031 −0.001 −0.0022 −0.0012 −0.0033 −0.0035 1 −0.18 −0.0018 0.0019 0.0023 −0.00083 0.00036 −0.0032 0.00041 0.00096 0.01 −0.00053 −0.0016 0.00048 −0.0026 −0.0021 0.0052 −0.18 1                                           (C.7) Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] ATLAS collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC,Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE]. [2] CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC,Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE]. [3] F. Richard, Present and future constraints on top EW couplings,arXiv:1403.2893 [INSPIRE]. [4] G. Durieux and O. Matsedonskyi, The top-quark window on compositeness at future lepton colliders,JHEP 01 (2019) 072 [arXiv:1807.10273] [INSPIRE]. [5] C. Englert and M. Russell, Top quark electroweak couplings at future lepton colliders,Eur. Phys. J. C 77 (2017) 535 [arXiv:1704.01782] [INSPIRE]. [6] G. Durieux, M. Perell´o, M. Vos and C. Zhang, Global and optimal probes for the top-quark effective field theory at future lepton colliders,JHEP 10 (2018) 168 [arXiv:1807.02121] [INSPIRE]. [7] https://github.com/silvest/HEPfit/blob/master/NewPhysics/src/ NPSMEFT6dtopquark.cpp [8] J. de Blas et al., Electroweak precision observables and Higgs-boson signal strengths in the Standard Model and beyond: present and future,JHEP 12 (2016) 135 [arXiv:1608.01509] [INSPIRE]. [9] A. Caldwell, D. Kollar and K. Kroninger, BAT: the Bayesian Analysis Toolkit,Comput. Phys. Commun. 180 (2009) 2197 [arXiv:0808.2552] [INSPIRE]. – 36 – JHEP12(2019)098 [10] G. Apollinari et al., High-Luminosity Large Hadron Collider (HL-LHC),CYRM-2017-004 (2017). [11] P. Bambade et al., The International Linear Collider: a global project,arXiv:1903.01629 [INSPIRE]. [12] CLICdp, CLIC collaboration, The Compact Linear Collider (CLIC) — 2018 summary report,CYRM-2018-002 (2018) [arXiv:1812.06018] [INSPIRE]. [13] FCC collaboration, FCC-ee: the lepton collider,Eur. Phys. J. ST 228 (2019) 261. [14] CEPC Study Group collaboration, CEPC conceptual design report: volume 1 — Accelerator,arXiv:1809.00285 [INSPIRE]. [15] S. Bilokin, R. P¨oschl and F. Richard, Measurement of bquark EW couplings at ILC, arXiv:1709.04289 [INSPIRE]. [16] CLICdp collaboration, Top-quark physics at the CLIC electron-positron linear collider, JHEP 11 (2019) 003 [arXiv:1807.02441] [INSPIRE]. [17] M.S. Amjad et al., A precise characterisation of the top quark electro-weak vertices at the ILC,Eur. Phys. J. C 75 (2015) 512 [arXiv:1505.06020] [INSPIRE]. [18] A. Buckley et al., Global fit of top quark effective theory to data,Phys. Rev. D 92 (2015) 091501 [arXiv:1506.08845] [INSPIRE]. [19] M. de Beurs, E. Laenen, M. Vreeswijk and E. Vryonidou, Effective operators in t-channel single top production and decay,Eur. Phys. J. C 78 (2018) 919 [arXiv:1807.03576] [INSPIRE]. [20] N.P. Hartland et al., A Monte Carlo global analysis of the Standard Model Effective Field Theory: the top quark sector,JHEP 04 (2019) 100 [arXiv:1901.05965] [INSPIRE]. [21] D. Barducci et al., Interpreting top-quark LHC measurements in the standard-model effective field theory,arXiv:1802.07237 [INSPIRE]. [22] R. Contino et al., On the validity of the effective field theory approach to SM precision tests, JHEP 07 (2016) 144 [arXiv:1604.06444] [INSPIRE]. [23] J.L. Birman et al., New limits on anomalous contributions to the Wtb vertex,Phys. Rev. D 93 (2016) 113021 [arXiv:1605.02679] [INSPIRE]. [24] W. Bernreuther et al., CP-violating top quark couplings at future linear e+e−colliders,Eur. Phys. J. C 78 (2018) 155 [arXiv:1710.06737] [INSPIRE]. [25] V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti, Is there room for CP-violation in the top-Higgs sector?,Phys. Rev. D 94 (2016) 016002 [arXiv:1603.03049] [INSPIRE]. [26] B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the standard model Lagrangian,JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE]. [27] J.A. Aguilar-Saavedra, A minimal set of top anomalous couplings,Nucl. Phys. B 812 (2009) 181 [arXiv:0811.3842] [INSPIRE]. [28] C. Zhang and S. Willenbrock, Effective-Field-Theory Approach to Top-Quark Production and Decay,Phys. Rev. D 83 (2011) 034006 [arXiv:1008.3869] [INSPIRE]. [29] N. Cabibbo, Unitary symmetry and leptonic decays,Phys. Rev. Lett. 10 (1963) 531 [INSPIRE]. [30] M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction,Prog. Theor. Phys. 49 (1973) 652 [INSPIRE]. – 37 – JHEP12(2019)098 [31] J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations,JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE]. [32] O. Bessidskaia Bylund et al., Probing top quark neutral couplings in the Standard Model Effective Field Theory at NLO in QCD,JHEP 05 (2016) 052 [arXiv:1601.08193] [INSPIRE]. [33] I. Brivio, Y. Jiang and M. Trott, The SMEFTsim package, theory and tools,JHEP 12 (2017) 070 [arXiv:1709.06492] [INSPIRE]. [34] J. De Blas et al., HEPfit: a code for the combination of indirect and direct constraints on high energy physics models,arXiv:1910.14012 [INSPIRE]. [35] HEPfit collaboration, HEPfit, a tool to combine indirect and direct constraints on high-energy physics,http://hepfit.roma1.infn.it. [36] O. Eberhardt, A. Pe˜nuelas and A. Pich, Global fits in the aligned two-Higgs-doublet model, in preparation. [37] O. Eberhardt, V. Miralles and A. Pich, Global fits in the coloured scalar model, in preparation. [38] J. de Blas, O. Eberhardt and C. Krause, Current and future constraints on Higgs couplings in the nonlinear effective theory,JHEP 07 (2018) 048 [arXiv:1803.00939] [INSPIRE]. [39] M. Ciuchini et al., New physics in b→s`+`−confronts new data on lepton universality, Eur. Phys. J. C 79 (2019) 719 [arXiv:1903.09632] [INSPIRE]. [40] F. James and M. Winkler, MINUIT User’s Guide, avilable online. [41] ATLAS collaboration, Observation of Higgs boson production in association with a top quark pair at the LHC with the ATLAS detector,Phys. Lett. B 784 (2018) 173 [arXiv:1806.00425] [INSPIRE]. [42] CMS collaboration, Observation of ttH production,Phys. Rev. Lett. 120 (2018) 231801 [arXiv:1804.02610] [INSPIRE]. [43] ATLAS collaboration, Measurement of the t¯ tZ and t¯ tW cross sections in proton-proton collisions at √s= 13 TeV with the ATLAS detector,Phys. Rev. D 99 (2019) 072009 [arXiv:1901.03584] [INSPIRE]. [44] CMS collaboration, Measurement of the cross section for top quark pair production in association with a Wor Zboson in proton-proton collisions at √s= 13 TeV,JHEP 08 (2018) 011 [arXiv:1711.02547] [INSPIRE]. [45] CMS collaboration, Measurement of top quark pair production in association with a Z boson in proton-proton collisions at √s= 13 TeV,CMS-PAS-TOP-18-009 (2018). [46] ATLAS collaboration, Measurements of inclusive and differential fiducial cross-sections of t¯ tγ production in leptonic final states at √s= 13 TeV in ATLAS,Eur. Phys. J. C 79 (2019) 382 [arXiv:1812.01697] [INSPIRE]. [47] CMS collaboration, Observation of single top quark production in association with a Z boson in proton-proton collisions at √s= 13 TeV,Phys. Rev. Lett. 122 (2019) 132003 [arXiv:1812.05900] [INSPIRE]. [48] ATLAS collaboration, Measurement of the production cross-section of a single top quark in association with a Z boson in proton–proton collisions at 13 TeV with the ATLAS detector, Phys. Lett. B 780 (2018) 557 [arXiv:1710.03659] [INSPIRE]. – 38 – JHEP12(2019)098 [49] A. Czarnecki, J.G. Korner and J.H. Piclum, Helicity fractions of Wbosons from top quark decays at NNLO in QCD,Phys. Rev. D 81 (2010) 111503 [arXiv:1005.2625] [INSPIRE]. [50] ATLAS collaboration, Measurement of the Wboson polarisation in t¯ tevents from pp collisions at √s= 8 TeV in the lepton + jets channel with ATLAS,Eur. Phys. J. C 77 (2017) 264 [Erratum ibid. C 79 (2019) 19] [arXiv:1612.02577] [INSPIRE]. [51] CMS collaboration, Measurement of the W boson helicity fractions in the decays of top quark pairs to lepton +jets final states produced in pp collisions at √s= 8 TeV,Phys. Lett. B 762 (2016) 512 [arXiv:1605.09047] [INSPIRE]. [52] CMS collaboration, Measurement of the W-boson helicity in top-quark decays from t¯ t production in lepton + jets events in pp collisions at √s= 7 TeV,JHEP 10 (2013) 167 [arXiv:1308.3879] [INSPIRE]. [53] ATLAS collaboration, Measurement of the Wboson polarization in top quark decays with the ATLAS detector,JHEP 06 (2012) 088 [arXiv:1205.2484] [INSPIRE]. [54] CMS collaboration, Measurement of the single top quark and antiquark production cross sections in the tchannel and their ratio in proton-proton collisions at √s= 13 TeV, arXiv:1812.10514 [INSPIRE]. [55] ATLAS collaboration, Measurement of the inclusive cross-sections of single top-quark and top-antiquark t-channel production in pp collisions at √s= 13 TeV with the ATLAS detector,JHEP 04 (2017) 086 [arXiv:1609.03920] [INSPIRE]. [56] CMS collaboration, Measurement of the production cross section for single top quarks in association with Wbosons in proton-proton collisions at √s= 13 TeV,JHEP 10 (2018) 117 [arXiv:1805.07399] [INSPIRE]. [57] ATLAS collaboration, Measurement of the cross-section for producing a Wboson in association with a single top quark in pp collisions at √s= 13 TeV with ATLAS,JHEP 01 (2018) 063 [arXiv:1612.07231] [INSPIRE]. [58] ATLAS collaboration, Analysis of the Wtb vertex from the measurement of triple-differential angular decay rates of single top quarks produced in the t-channel at √s= 8 TeV with the ATLAS detector,JHEP 12 (2017) 017 [arXiv:1707.05393] [INSPIRE]. [59] ATLAS collaboration, Probing the Wtb vertex structure in t-channel single-top-quark production and decay in pp collisions at √s= 8 TeV with the ATLAS detector,JHEP 04 (2017) 124 [arXiv:1702.08309] [INSPIRE]. [60] CMS collaboration, Measurement of the Wboson helicity in events with a single reconstructed top quark in pp collisions at √s= 8 TeV,JHEP 01 (2015) 053 [arXiv:1410.1154] [INSPIRE]. [61] ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group collaboration, Precision electroweak measurements on the Zresonance,Phys. Rept. 427 (2006) 257 [hep-ex/0509008] [INSPIRE]. [62] ATLAS collaboration, Measurement of differential production cross-sections for a Zboson in association with b-jets in 7TeV proton-proton collisions with the ATLAS detector,JHEP 10 (2014) 141 [arXiv:1407.3643] [INSPIRE]. [63] CMS collaboration, Measurement of the Z/γ ∗+b-jet cross section in pp collisions at √s= 7 TeV,JHEP 06 (2012) 126 [arXiv:1204.1643] [INSPIRE]. – 39 –