Fingerprinting New Physics with Effective Field Theories

Jaco ter Hoeve

REVIEW 3 major objections 5 minor 300 references

Fingerprinting New Physics with Effective Field Theories

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A global fit of 445 collider measurements constrains 50 new-physics parameters and converts them into bounds on explicit BSM models.

desk verdict Solid, clearly-written thesis that openly compiles three already-published JHEP papers; the global SMEFT fit and methodology are state-of-the-art, but there is no new research result here. read the letter →

arxiv 2501.08818 v1 pith:6LI77NRY submitted 2025-01-15 hep-ph

Jaco ter Hoeve This is my paper · ORCID

classification hep-ph

keywords SMEFTglobalfitWilsoncoefficientselectroweakprecisionobservablesUV-completemodelsmachinelearningunbinnedlikelihoodfuturecolliders

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The thesis argues that since the LHC has not produced direct evidence of new particles, the most informative way to search for physics beyond the Standard Model is indirect: assume any heavy new physics can be written as the Standard Model Effective Field Theory (SMEFT), and fit its Wilson coefficients to every precision measurement available. It presents SMEFiT3.0, a global fit of 445 LEP, SLD and LHC Run II data points that constrains 45 (linear) or 50 (quadratic) dimension-six coefficients, including a new exact treatment of the electroweak precision observables inside the fit. It then shows that the same likelihood can be re-expressed directly in terms of the masses and couplings of explicit ultraviolet-complete models through automated matching, so that bounds on Wilson coefficients become bounds on concrete new particles. It also develops ML4EFT, a machine-learning framework that builds unbinned multivariate likelihoods which it argues extract substantially more sensitivity from the data than binned analyses, and projects how the HL-LHC, FCC-ee and CEPC would shrink the allowed parameter space. A sympathetic reader would care because the result is a reusable map of what current and near-future colliders can say about new physics without committing to any one model.

What carries the argument

The load-bearing objects are: (i) the SMEFT Lagrangian, the Standard Model plus Warsaw-basis dimension-six operators with coefficients $c_i/\Lambda^2$, which turns every observable into $\sigma_m(c) = \sigma^{\rm SM}_m + \sum_i \sigma^{\rm EFT}_{m,i} c_i + \sum_{i,j\geq i} \sigma^{\rm EFT}_{m,ij} c_i c_j$; (ii) SMEFiT, the fitting framework combining Gaussian likelihoods, a theory covariance matrix, Nested Sampling for the quadratic fits and the Fisher information matrix for decorrelation; (iii) the matching maps $c = f(g, \mu)$ computed by MATCHMAKER EFT at tree level and one loop, translated by the MATCH2FIT interface into run cards so the fit can sample UV couplings directly, with UV invariants defined as the combinations of couplings one-to-one with the fitted coefficients; (iv) ML4EFT, which trains neural networks to parametrise the per-event likelihood ratio $r_\sigma(x, c)$ entering the extended unbinned likelihood, avoiding the exponential cost of Monte Carlo density estimation; and (v) the pseudo-data projection module that rescales Run II measurements to HL-LHC conditions and generates forecasts for FCC-ee and CEPC.

What would settle it

Generate pseudo-data from a model with a sizeable dimension-eight operator and fit them with the dimension-six-only likelihood used here: if the dimension-six coefficients shift to absorb the effect with no significant loss of fit quality, the truncation assumption on which every bound in the thesis rests is falsified in practice.

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Extended reading notes

Core claim

The central claim is that the dimension-six SMEFT, combined with a global likelihood, is a practical and sufficiently general way to search for new physics. Concretely, SMEFiT3.0 fits 50 Wilson coefficients (45 at linear order) against 445 measurements spanning the top, Higgs, diboson and electroweak sectors, with all 16 operators that shift the Z- and W-boson couplings entering as independent degrees of freedom rather than being fixed by the earlier approximate implementation. The fit finds the data consistent with the Standard Model overall ($\chi^2/{\rm ndat} = 0.992$ at linear order versus 1.087 for the SM alone), with the notable pulls confined to specific coefficients and datasets that the thesis traces to correlations and experimental tensions rather than to new physics; quadratic corrections are shown to be indispensable for bounding the four-heavy-quark operators, which are unconstrained at linear order. The same likelihood can be reparametrised through matching relations $c = f(g)$ so that fits run directly on UV couplings and masses, with UV invariants identifying which combinations of model parameters the data can actually see. Finally, the thesis claims that unbinned neural-network likelihoods (ML4EFT) give a significant sensitivity gain over binned observables, and that FCC-ee and CEPC would have an unprecedented impact on the SMEFT parameter space compared with the HL-LHC.

Load-bearing premise

The load-bearing premise is that all new physics is heavy, weakly coupled and fully captured by dimension-six SMEFT operators with the assumed flavour symmetry $U(2)_q \times U(2)_u \times U(3)_d \times [U(1)_\ell \times U(1)_e]^3$ and no renormalisation-group running; if dimension-eight effects are numerically important, the new particles are light or strongly coupled, or the flavour structure differs, the extracted bounds and the model limits built from them would be systematically shifted.

Editorial extensions

If this is right

Any user-defined, weakly-coupled UV model with heavy particles can be confronted with the full LEP, SLD and LHC dataset by matching and fitting, without recomputing predictions for every observable.
Quadratic EFT corrections become a required ingredient of global fits: without them the four-heavy-quark operator directions are flat and several two-light-two-heavy degeneracies persist.
EWPO data must be implemented exactly, with all 16 operator directions free, because the approximate implementation is sometimes too aggressive and artificially narrows posteriors (for example for $c_{\varphi\ell_3}$ and $c_{\varphi d}$).
Unbinned ML observables allow EFT fits to use the full multivariate phase space of each event, so future analyses need not project onto a few binned kinematic variables.
The FCC-ee and CEPC projections give quantitative input to the European Strategy for Particle Physics Update, indicating a step change in SMEFT coverage relative to the HL-LHC.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the fit's pull pattern is a reliable diagnostic, then a genuine new-physics signal would be expected to survive in one-parameter fits and across complementary experiments; the present pulls ($c_{tG}$, $c_{\varphi d}$, $c^{(3)}_{\varphi q}$) fail that test, since they come from specific datasets and inter-coefficient correlations, a screening rule future global fits could apply automatically.
The UV-invariant presentation points to a natural extension: repackaging the same 445-point likelihood as exclusion maps in the mass-coupling planes of a large library of single- and multi-particle models, effectively turning the global fit into an atlas of model constraints.
The ML4EFT claim is testable immediately on statistically-limited measurements, but its advantage may shrink once correlated systematic uncertainties dominate; applying the unbinned likelihood to a systematics-dominated channel would reveal how general the gain actually is.
Because RG running is neglected and the input scheme is fixed, the reported bounds are defined at a single scale; rerunning the exact-EWPO fit with running included would show whether the bounds shift by more than their quoted uncertainties, which would matter for comparing coefficients extracted at different collision energies.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: judge this as a PhD thesis, not as a new research paper. The preface and list of publications are explicit that the science comes from Refs [19], [22], and [23], all JHEP papers, and the core chapters reproduce them. The introductory chapters are pedagogical and written for the thesis. So if the question is whether it contains new results, the answer is no. That is disclosed honestly, not hidden, but it means a research journal should desk reject it as a compilation.

What the thesis does well: it gives a clear, self-contained map of SMEFiT3.0. The global fit is the most comprehensive SMEFT interpretation currently available—445 data points, 45/50 Wilson coefficients, NLO QCD, exact EWPO treatment. The exact EWPO implementation is a genuine improvement over the approximate treatment in earlier SMEFiT versions. The UV-matching automation and the ML4EFT unbinned likelihoods are real methodological contributions, with open code and documented run cards. The ML likelihoods are trained on Monte Carlo theory predictions, not on the fitted data, so there is no circularity there. The literature survey in Chapter 1 is honest and useful.

Soft spots, in proportion. The four CMS Higgs points removed in Table 3.2 are flagged in a footnote but never analysed. The stress-test's stronger framing—that the dataset is biased—goes beyond what the text shows. What is true is that a fit including those points, or a measure of their pull, would settle the question, and its absence is a legitimate robustness gap. I would call it minor rather than fatal: 4 of 445 points, and the removal is disclosed. The future-collider projections use simplified rescaling factors and SM pseudo-data, so the abstract's 'unprecedented impact' language is stronger than those assumptions support. The dim-6 truncation, no RG running, and the specific flavour symmetry are standard and stated; they frame the interpretation rather than invalidate it.

Who should read it: a graduate student entering SMEFT global fits, or a phenomenologist who wants SMEFiT3.0, UV matching, and ML4EFT collected in one place with full derivations. I would cite the original JHEP papers, not the thesis. For a research journal, desk reject as a compilation—the underlying science already passed peer review.

Referee Report

3 major / 5 minor

Summary. The thesis presents a comprehensive SMEFT program built around three published analyses: (i) SMEFiT3.0, a global fit of top, Higgs, diboson and electroweak-precision data from LEP, SLD and LHC Run II, constraining 45 (50) Wilson coefficients in linear (quadratic) fits of 445 data points; (ii) an automated pipeline, based on MatchmakerEFT and the new MATCH2FIT interface, that maps global SMEFT constraints onto the masses and couplings of UV-complete models, including tree-level and one-loop matching and the notion of UV invariants; and (iii) ML4EFT, a machine-learning framework for unbinned multivariate likelihoods aimed at improving EFT sensitivity over binned analyses. The same framework is used to project the impact of HL-LHC, FCC-ee and CEPC data on the SMEFT parameter space. The manuscript is written as a PhD thesis and explicitly identifies the author's contributions and the underlying JHEP publications.

Significance. If the claimed bounds are robust, the thesis provides a valuable, openly documented global SMEFT analysis with several methodological advances: an exact implementation of the EWPOs, a flexible automated UV-matching pipeline, the UV-invariant representation of model parameters, and publicly released code (SMEFiT, ML4EFT, MATCH2FIT). The core fits build on peer-reviewed publications and the reproducibility of the code is a genuine strength. The HL-LHC and FCC-ee/CEPC projections are also timely input for the European Strategy process. However, the central 'state-of-the-art' claim rests on a dataset-selection step that is not yet defended, and on explicitly stated assumptions (dim-6 truncation, the SMEFiT flavour symmetry, and neglect of RG running) whose numerical impact is not quantified. These issues do not invalidate the framework, but they need to be addressed before the strongest claims in the abstract can be fully supported.

major comments (3)

[Table 3.2 (footnote)] The footnote in Table 3.2 states that four CMS Run II Higgs signal-strength points were removed because they 'cannot be described by a multi-Gaussian distribution.' This is a post-hoc selection step in the construction of the 445-point baseline dataset, and the manuscript reports no fit that retains those points, no identification of the points, and no quantitative assessment of their tension with the SM or with the SMEFT. Since the Higgs sector is one of the four pillars of the claimed state-of-the-art interpretation, the central result is directly exposed to this selection. Please add a robustness study: include the four points under a Poisson likelihood or the published CMS likelihood, report the resulting shifts in the 45/50 Wilson-coefficient constraints (in particular the Higgs-sector operators ctφ, cφG, cφ□ and the two-fermion operators entering Higgs decays), and state whether the removal changes any conclusion. If the points are non-Gaussian, deleting them rather than modeling the correct likelihood is not justified; if they are in tension, that tension should be reported explicitly.
[Sec. 1.3.2 and Sec. 1.4] The thesis combines observables at the Z-pole (Q ~ mZ) with LHC observables at scales up to about 1 TeV in a single SMEFT parameter space while explicitly neglecting RG running; in Sec. 1.4 the matching scale is chosen equal to the heavy mass so that matching-scale logarithms vanish. The extracted 95% intervals are therefore interpretable only at a loosely specified scale, and the UV-model limits in Chapter 4 inherit this ambiguity. As a concrete test, please provide a quantitative estimate of the impact of one-loop SMEFT RG running on the most scale-sensitive coefficients, for example using public codes such as wilson or DsixTools, or alternatively specify the common scale at which all 445-point results and all UV-invariant bounds are quoted. This is a correctness-risk concern rather than a claim of internal inconsistency, but it is load-bearing for the 'state-of-the-art' statement.
[Sec. 3.1.3 and Table 3.1] The text states that the information provided by αEW and by Bhabha scattering is 'equivalent from the point of view of constraining the SMEFT parameter space' and that both datasets are included 'for completeness' to increase precision. If these two inputs constrain the same linear combination of Wilson coefficients through independent measurements, their combination is legitimate; however, if they are derived from the same underlying LEP measurement, including both without modeling their correlation could artificially sharpen the EWPO constraints. Please clarify the independence of the αEW and Bhabha inputs and, ideally, show that the main EWPO-driven bounds are unchanged when either one is removed.

minor comments (5)

[Sec. 1.3.1] In the sentence introducing the SMEFT, the gauge group is written as SU(3)c × U(2)L × U(1)Y; the second factor should be SU(2)L.
[Table 3.3 and Sec. 3.2.1] The text says the CMS WZ pTZ measurement consists of ndat = 11 data points, while Table 3.3 reports 10; please reconcile these numbers.
[Sec. 2.3, first paragraph] The word 'unbinnend' should be 'unbinned'.
[Eq. (3.23) and surrounding text] The symbol 'aEW' in the sentence immediately after Eq. (3.23) should be αEW, and the numerical conversion factor 0.007127 would benefit from an explicit citation in that equation block.
[Sec. 2.2.5] The HL-LHC projection method assumes a global systematic reduction factor fred = 1/2 for all datasets and ftot = 1/3 where no breakdown is available; this is a stated assumption, but the sensitivity of the Chapter 6 conclusions to these optimistic factors should be mentioned in the outlook.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the SMEFiT3.0 constraints are external-data fits, the UV limits are post-fit mappings, and the ML4EFT sensitivities are likelihood-ratio constructions rather than fits renamed as predictions.

full rationale

The paper's derivation chain is self-contained against external data and open tools. The Wilson-coefficient bounds in Chapter 3 are obtained by minimising a chi-square that compares measured LEP/SLD/LHC cross-sections to SMEFT predictions; no fitted coefficient is used to define the target of a claimed prediction. The UV-complete-model constraints in Chapter 4 are explicitly a post-fit reinterpretation: the global SMEFT fit 'encapsulates, for a well-defined set of assumptions, the information provided by available experimental observables, while the matching relations determine how this information relates to the masses and couplings of the UV-complete model.' This is a legitimate mapping, not circular reasoning. The ML4EFT unbinned observables in Chapter 5 are trained on Monte Carlo theory predictions, not on the experimental data being fitted, and the unbinned likelihood reduces to the exact likelihood in the zero-bin-width limit, so the claimed gain over binned analyses is an information-theoretic consequence rather than a result whose input equals its output. Future-collider projections in Chapter 6 are labelled pseudo-data generated from extrapolated Run II measurements, an acknowledged projection methodology, not a fitted value used as a prediction. The thesis does contain one disclosed data-handling caveat, the removal of four CMS Run II Higgs points because they 'cannot be described by a multi-Gaussian distribution' (Table 3.2 footnote); this is a potential robustness concern about dataset selection, but it is not a circular step because the remaining data are still external and the removed points are not used to define the fitted parameters. Self-citations to Refs. [13,14,19-23] provide methodological continuity, but the methods are described in the thesis, the code is public, and comparisons with independent fitting groups (Fitmaker, SFITTER, HEPfit) are included, so the self-citations are not load-bearing for the central claims. Overall, no equation or fitted parameter is shown to be equivalent by construction to a claimed prediction, and the appropriate circularity score is essentially zero; the score of 1 reflects only the minor, non-circular data-selection caveat.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central constraints rest on standard SMEFT assumptions: a local operator expansion at dimension six, a specific flavour symmetry, and Gaussian likelihoods. No genuinely new entities, such as particles, forces, or dimensions, are introduced. The only hand-picked numbers are the future-collider projection factors and the fitted parameters themselves.

free parameters (3)

50 dimension-six Wilson coefficients (Warsaw basis, SMEFiT flavour assumptions) = 95% credible intervals in Tables 3.6 and 3.7
The central output of the global fit; their posterior distributions are inferred from 445 data points.
UV couplings and masses of benchmark heavy-particle models (e.g., heavy scalar doublet couplings y_u_phi and lambda_phi) = 95% HDI bounds in Chapter 4 and Ref [22]
Chapter 4 maps the EFT fit onto UV model parameters via matching; these parameters are fitted directly in the UV space.
HL-LHC systematic reduction factors f_red and f_tot = f_red = 1/2, f_tot ~ 1/3
Sec 2.2.5: adopted from the optimistic HL-LHC projection scenario; chosen by hand, not derived from data, and directly affect projected constraints.

assumptions (5)

domain assumption All BSM physics is heavy enough to be integrated out into local higher-dimensional operators (local SMEFT expansion).
Invoked in Sec 1.2.1 (Eq. 1.8) and throughout; if new physics is light or strongly coupled, the SMEFT description breaks down.
domain assumption The EFT expansion is truncated at dimension six; dimension-eight operators and RG running are neglected.
Stated in Sec 1.3.2 as justified mostly on practical grounds; affects the interpretation of all bounds if dim-8 or running effects are sizeable.
domain assumption Flavour symmetry U(2)q x U(2)u x U(3)d x [U(1)l x U(1)e]^3.
Adopted in Sec 1.3.3 to reduce the operator basis to 50 coefficients; restricts which new physics models are covered.
standard math Electroweak symmetry breaking is linearly realized and the Warsaw basis is complete for dim-6 operators.
Standard SMEFT framework used throughout (Sec 1.3.1, Ref [9]).
domain assumption The experimental likelihoods are approximated as Gaussian when only covariance matrices are public.
Sec 2.2.1; the authors argue this is a good approximation, but it is an assumption about the data.

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Cite this review

Pith. "Pith review of Fingerprinting New Physics with Effective Field Theories." pith.science (2026). https://pith.science/paper/6LI77NRY

@misc{pith2026250108818,
  author       = {Pith},
  title        = {Pith review of: Fingerprinting New Physics with Effective Field Theories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6LI77NRY}},
  note         = {Machine review of arXiv:2501.08818}
}

read the original abstract

Given the absence of direct evidence for new resonances beyond the Standard Model (BSM) at the Large Hadron Collider (LHC) so far, a complementary strategy to search for new physics in an indirect way is provided by the Standard Model Effective Field Theory (SMEFT). As the low-energy limit of a generic ultraviolet (UV) completion of the SM, the SMEFT provides a powerful theoretical framework to correlate deviations from the SM between different processes, offering experimental sensitivity to a plethora of SM extensions. This thesis presents a state-of-the-art SMEFT interpretation of the top, Higgs, diboson and electroweak sectors, taking into account data collected at the Large Electron-Positron Collider (LEP), the SLAC Large Detector (SLD) and the LHC. We also include the effect of the upcoming High-Luminosity LHC (HL-LHC) upgrade and demonstrate the unprecedented impact on the SMEFT parameter space of two proposed electron-positron colliders: the electron-positron Future Circular Collider (FCC-ee) and the Circular Electron Positron Collider (CEPC). We present constraints both in terms of Wilson coefficients, and couplings and masses of a wide range of UV-complete models through a newly developed automatised limit-setting procedure. We further present novel methodological advances through the development of unbinned multivariate likelihoods specialised to the SMEFT that provide maximal sensitivity to new physics using classification and regression techniques from Machine Learning. Our results provide an extensive characterisation of the SMEFT parameter space as probed both by current and future colliders, providing timely input to the upcoming European Strategy for Particle Physics Update.

Figures

Figures reproduced from arXiv: 2501.08818 by the authors.

**Figure 2.1.** Likelihood contours at Li in parameter space (left) are sorted by their enclosed prior mass Xi (right). Figure taken from [126]. where the weight wi belonging to point i may be set according to the trapezium rule wi = (Xi−1 − Xi+1) /2. In practice, we adopt MC methods to estimate L(Xi). This follows an iterative procedure that starts with drawing Nlive points from the full prior π(c) at iteration i = 0 with X0 = 1. … view at source ↗

**Figure 3.** are then tabulated in Table 3.5 at the level of the groups of processes entering [PITH_FULL_IMAGE:figures/full_fig_p075_3.png] view at source ↗

**Figure 3.1.** The values of the χ 2 /ndat for the datasets entering the SMEFIT3.0 analysis. We compare the results based on the SM prediction with the outcome of the SMEFT fits, both at linear and quadratic order in the EFT expansion. See also [PITH_FULL_IMAGE:figures/full_fig_p076_3_1.png] view at source ↗

Figures from the paper (49 more)

**Figure 3.2.** Figure 3.2: The length of the 95% CI, expressed in units of 1/TeV2 , for the neft = 50 coefficients entering the fit, both for linear and for quadratic (marginalised) analyses. From top to bottom we display the four-heavy quark (except for the linear fit), two-light-two-heavy qu…

**Figure 3.3.** Figure 3.3: The coefficients ci/Λ 2 for the same fits as shown in [PITH_FULL_IMAGE:figures/full_fig_p080_3_3.png]

**Figure 3.** Figure 3: , confirm that in general there is a good agreement between the EFT fit results [PITH_FULL_IMAGE:figures/full_fig_p081_3.png]

**Figure 3.4.** Figure 3.4: The residuals between the fit results and the SM expectations defined as in Eq. (3.24), for the operators entering [PITH_FULL_IMAGE:figures/full_fig_p082_3_4.png]

**Figure 3.5.** Figure 3.5: The correlation matrix for the neff = 45 coefficients associated to the linear SMEFIT3.0 baseline analysis. To facilitate visualisation, the EFT coefficients whose correlation with all other coefficients is < 0.2 are removed from the plot. the correlation matrix, ρij…

**Figure 3.6.** Figure 3.6: Posterior distributions associated to the neft = 50 Wilson coefficients constrained in the SMEFIT3.0 global analysis, carried out at O [PITH_FULL_IMAGE:figures/full_fig_p087_3_6.png]

**Figure 3.** Figure 3: displays the same comparison of the results of the global analysis based [PITH_FULL_IMAGE:figures/full_fig_p088_3.png]

**Figure 3.7.** Figure 3.7: Same as [PITH_FULL_IMAGE:figures/full_fig_p089_3_7.png]

**Figure 4.** Figure 4: shows the resulting marginalised posterior distributions in the space [PITH_FULL_IMAGE:figures/full_fig_p094_4.png]

**Figure 4.1.** Figure 4.1: Left: marginalised posterior distributions in the space U of UV parameters y u ϕ 33, λϕ in the heavy scalar doublet model given by Eq. (1.33) from Chapter 1 fitted to the data according to the procedure of Sect. 4.2. Right: the same results represented in the spa…

**Figure 4.2.** Figure 4.2: Schematic representation of the pipeline adopted in this work to map the parameter space of UV-complete models using the SMEFT as a bridge to the data. The starting point is a UV-Lagrangian containing a number of free parameters g such as its masses and coupling cons…

**Figure 4.3.** Figure 4.3: Posterior distributions associated to the UV invariants in the one-particle heavy scalar models listed in the upper part of [PITH_FULL_IMAGE:figures/full_fig_p106_4_3.png]

**Figure 4.4.** Figure 4.4: Same as [PITH_FULL_IMAGE:figures/full_fig_p107_4_4.png]

**Figure 4.5.** Figure 4.5: Marginalised posterior distributions of the two UV invariants associated to the heavy scalar model ϕ, comparing the impact of linear and quadratic EFT corrections after matching at tree-level (upper panel) and at one-loop level (lower panel). The rightmost panels ill…

**Figure 4.6.** Figure 4.6: Same as [PITH_FULL_IMAGE:figures/full_fig_p109_4_6.png]

**Figure 4.7.** Figure 4.7: Same as [PITH_FULL_IMAGE:figures/full_fig_p110_4_7.png]

**Figure 4.8.** Figure 4.8: The posterior distributions of the UV invariants in the three-particle model consisting of two heavy fermions Q1, Q7 and a heavy vector boson W, see also see [PITH_FULL_IMAGE:figures/full_fig_p113_4_8.png]

**Figure 4.9.** Figure 4.9: Pair-wise marginalised 95% contours for the UV couplings associated to the threeparticle model consisting of two heavy fermions, Q1 and Q7, and the heavy vector boson W, see also [PITH_FULL_IMAGE:figures/full_fig_p114_4_9.png]

**Figure 4.10.** Figure 4.10: Posterior distributions associated to the UV invariants in the one-particle heavy fermion models T1 and T2, comparing the effect of tree and one-loop level matching. In both cases, we display results based on quadratic corrections in the EFT expansion and at NLO QCD…

**Figure 5.1.** Figure 5.1: Validation of the Machine Learning parametrisation of the EFT cross-section ratios when applied to the case of parton-level top quark pair production. The results shown here correspond to the training of the quadratic neural network NN(j,j) (mtt¯, ytt¯) in Eq.(5.19) …

**Figure 5.** Figure 5: presents an overview of representative validation checks of our procedure [PITH_FULL_IMAGE:figures/full_fig_p135_5.png]

**Figure 5.** Figure 5: displays the differential distributions in the kinematic features used to [PITH_FULL_IMAGE:figures/full_fig_p140_5.png]

**Figure 5.2.** Figure 5.2: Differential distributions in the nk = 18 kinematic features used to parametrise the likelihood ratio in the tt¯→ b ¯bℓ+ℓ −νℓν¯ℓ process. We compare the SM predictions with those obtained in the SMEFT when individual operators are activated for coefficient values use…

**Figure 5.3.** Figure 5.3: Pair-wise 95% CL contours for the Wilson coefficients entering top quark pair production in the dilepton final state, see Sect. 5.2.2 for more details. These contours are obtained by marginalising over the full posterior distribution provided by Nested Sampling. We c…

**Figure 5.** Figure 5: displays the pair-wise 95% CL intervals for the [PITH_FULL_IMAGE:figures/full_fig_p147_5.png]

**Figure 5.4.** Figure 5.4: Same as [PITH_FULL_IMAGE:figures/full_fig_p148_5_4.png]

**Figure 5.5.** Figure 5.5: Same as [PITH_FULL_IMAGE:figures/full_fig_p149_5_5.png]

**Figure 5.6.** Figure 5.6: Same as [PITH_FULL_IMAGE:figures/full_fig_p151_5_6.png]

**Figure 5.** Figure 5: displays the bounds in the parameter space obtained from the unbinned [PITH_FULL_IMAGE:figures/full_fig_p153_5.png]

**Figure 5.7.** Figure 5.7: Same as [PITH_FULL_IMAGE:figures/full_fig_p154_5_7.png]

**Figure 6.1.** Figure 6.1: The ratio of uncertainties Rδci , defined in Eq. (6.1), for the neft = 45 coefficients entering the linear EFT fit, quantifying the impact of the HL-LHC projections when added on top of the SMEFIT3.0 baseline. We display both the results of one-parameter fits and tho…

**Figure 6.** Figure 6: displays the ratio of uncertainties [PITH_FULL_IMAGE:figures/full_fig_p165_6.png]

**Figure 6.2.** Figure 6.2: Same as [PITH_FULL_IMAGE:figures/full_fig_p167_6_2.png]

**Figure 6.3.** Figure 6.3: The marginalised 95% CI in the c (3) φq , c (−) φq plane from linear EFT fits to different datasets. We compare the result of a LEP-only fit (blue) with those adding either the LHC Run II diboson data (orange) or the HL-LHC diboson projections (green). The three …

**Figure 6.** Figure 6: presents the same comparison as that in Fig. 6.1 now with the quadratic [PITH_FULL_IMAGE:figures/full_fig_p168_6.png]

**Figure 6.** Figure 6: (6.6) displays, in the same format as that of Fig. 6.1, the marginalised [PITH_FULL_IMAGE:figures/full_fig_p174_6.png]

**Figure 6.6.** Figure 6.6: This is due to the fact that no FCC-ee observables included in the fit are [PITH_FULL_IMAGE:figures/full_fig_p174_6_6.png]

**Figure 6.4.** Figure 6.4: Same as [PITH_FULL_IMAGE:figures/full_fig_p175_6_4.png]

**Figure 6.5.** Figure 6.5: Diagonal entries of the Fisher information matrix evaluated at O [PITH_FULL_IMAGE:figures/full_fig_p177_6_5.png]

**Figure 6.** Figure 6: reveals that the bulk of the constraints on the SMEFT parameter space [PITH_FULL_IMAGE:figures/full_fig_p179_6.png]

**Figure 6.** Figure 6: illustrates the sequential impact of the datasets collected at different values [PITH_FULL_IMAGE:figures/full_fig_p181_6.png]

**Figure 6.7.** Figure 6.7: Same as [PITH_FULL_IMAGE:figures/full_fig_p182_6_7.png]

**Figure 6.** Figure 6: displays the ratio defined in Eq. (6.5), evaluated separately for the observ [PITH_FULL_IMAGE:figures/full_fig_p183_6.png]

**Figure 6.8.** Figure 6.8: Same as [PITH_FULL_IMAGE:figures/full_fig_p184_6_8.png]

**Figure 6.9.** Figure 6.9: The ratio of the entries of the Fisher information matrix between the FCC-ee and the CEPC, Eq. (6.5), evaluated separately for the observables entering the four centre of mass energies √ s considered. Since projections for both colliders share theory predictions, thi…

**Figure 6.10.** Figure 6.10: The 95% CI lower bounds on the heavy particle mass MUV for the one-particle UV-completions of the SM considered in this work, matched to the SMEFT using tree-level relations. In all cases we include corrections up to quadratic order in the EFT expansion. From top to…

**Figure 6.** Figure 6: , now matched onto the SMEFT at the one-loop level. This one-loop matching [PITH_FULL_IMAGE:figures/full_fig_p189_6.png]

**Figure 6.11.** Figure 6.11: The 95% CI upper bounds on the UV-invariant couplings of representative models obtained from the SMEFIT3.0 dataset (blue) and from its extension with the HL-LHC (orange) and with both the HL-LHC and FCC-ee (green) projections. We consider a 3-particle model, (Q1, Q7…

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