Descoped and Upscoped FCC-ee Running Scenarios in the SMEFT

Elie Hammou; Eugenia Celada; Jaco ter Hoeve; Marion O.A. Thomas

REVIEW 3 major objections 5 minor 34 references

Descoped and Upscoped FCC-ee Running Scenarios in the SMEFT

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A staged top-quark run, not raw luminosity, is what preserves the FCC-ee's new-physics reach.

desk verdict Read it before the next ESPPU26 scoping meeting: the top-run result is new and holds up, but its quantitative size rests on an admitted systematics rescaling rule. read the letter →

arxiv 2608.05874 v1 pith:CUDIIN6Q submitted 2026-08-06 hep-ph

Eugenia Celada , Elie Hammou , Jaco ter Hoeve , Marion O.A. Thomas This is my paper · ORCID

classification hep-ph

keywords FCC-eeSMEFTtop-quarkrundescopedcolliderscenariosHL-LHCcomplementarityHiggsself-couplingluminosityscalingFisherinformation

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

This paper asks how a cheaper or more expensive FCC-ee programme would change the machine's sensitivity to new physics, using the Standard Model Effective Field Theory (SMEFT, the model-independent framework in which new heavy physics appears through higher-dimension operators) to quantify the reach. The central finding is that the run at 365 GeV near the top-pair threshold, not the total integrated luminosity, carries most of the programme's power: in a global fit where all new-physics parameters vary together, every variant without that run performs about as well as LEP3, a lower-luminosity version of the old LEP design. A staged top-quark run at a fraction of the baseline luminosity restores most of the reach even when the machine collects only 36.5% of the baseline data. Adding luminosity, either across all energies or only at the top run, changes the bounds very little, because the global fit is limited by HL-LHC systematic uncertainties rather than by FCC-ee statistics. These results matter for deciding whether the descoped alternative to the full FCC-ee can still deliver a meaningful physics programme.

What carries the argument

The load-bearing object is a global SMEFT fit to 61 independent dimension-six Wilson coefficients in the Warsaw basis, with one-loop renormalisation-group running from a 10 TeV initial scale down to the observables. To locate the source of the scenario differences, the paper decomposes the Fisher information matrix $F_{ii'}=\sum_{j,j'}\kappa_{i,j}\Sigma^{-1}_{j,j'}\kappa_{i',j'}$ into dataset groups and diagonalises it, so that each eigenmode of the coefficient space is assigned a fractional contribution from LEP, LHC, HL-LHC, and each FCC-ee energy point. This decomposition shows that the first roughly 40 eigenmodes are FCC-ee-dominated while the remaining directions need HL-LHC data, and that the top-quark run works through two channels: new observables that lift correlations, and a sharper top mass that reduces parametric uncertainties on the Z-pole observables. Luminosity changes enter only through rescaling statistical and statistically-driven systematics by $\sqrt{L_{\rm baseline}/L_{\rm scenario}}$, with all other systematics kept fixed.

What would settle it

Run the same global SMEFT fit with a dedicated detector-level simulation of the 2-IP, 30 MW FCC-ee that recomputes the systematic uncertainties on the Z-pole asymmetries and Higgs measurements as functions of integrated luminosity instead of the assumed $\sqrt{L}$ rescaling; if those systematics scale more steeply with luminosity, the descoped scenarios would degrade relative to baseline and the top-run-versus-luminosity contrast would shrink.

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Extended reading notes

Core claim

The paper's central claim is that a substantial fraction of the FCC-ee physics potential depends on the top-quark run at $\sqrt{s}=365$ GeV, and that the combination of a staged top run with LHC/HL-LHC data is what separates any FCC-ee variant from LEP3. In individual fits, where each of the 61 Wilson coefficients is constrained one at a time, the top run improves the mass reach by typically less than 10%; in the marginalised fit, where all coefficients vary simultaneously, the same run produces improvements of order 100% or more, moving for example $c_{t\ell}$ from about 1.5 TeV to 4 TeV at the baseline. The mechanism is twofold: the top run adds observables with new operator dependencies that break flat directions and correlations in the 61-dimensional parameter space, and it pins down the top-quark mass to roughly 10 MeV, reducing parametric uncertainties that would otherwise limit the Z-pole observables. The paper shows that an FCC-ee dataset alone has Fisher-information rank 52 out of 61, so the HL-LHC is required to lift the remaining flat directions, which is why luminosity upscoping and descoping matter so little. The same pattern controls the Higgs self-coupling: without the top run all scenarios return the LEP3-level bound $\delta\kappa_3=0.280$, while a staged top run gives 0.164 (baseline), 0.183 (4-IP descope), and 0.203 (2-IP descope).

Load-bearing premise

That the descoped and upscoped projections can be modelled by rescaling statistical and statistically-driven systematic uncertainties by the square root of the luminosity ratio while keeping all other systematics fixed, an approximation the paper states needs dedicated simulations that are not yet available.

Editorial extensions

If this is right

A descoped FCC-ee running nine years at two IPs and 30 MW collects 36.5% of baseline luminosity; without a top run its global marginalised bounds sit at LEP3 level, and running 23 years to recover the luminosity does not recover the lost reach.
Restoring a staged top-quark run at 36.5% (two-IP) or 60% (four-IP) of the baseline 365 GeV luminosity recovers most of the baseline constraints, making the staged top run the minimum ingredient for a meaningful descoped programme.
Upscoping luminosity by 20% at all energies or by 50% on the top run alone improves the global bounds only marginally, so the exact luminosity of the top run is comparatively unimportant once it is present.
In the global marginalised fit, HL-LHC systematic uncertainties are the dominant limitation; the FCC-ee alone constrains 52 of the 61 directions, so the LHC and FCC-ee are complementary programmes rather than substitutes.
On the Higgs self-coupling, the top run tightens $\delta\kappa_3$ from 0.280 without a top run (equal to LEP3) to 0.164 at the baseline, 0.183 at the four-IP descope, and 0.203 at the two-IP descope.

Reading between the lines

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

If a dedicated simulation showed that a larger share of FCC-ee systematics scale with luminosity than the $\sqrt{L}$ rescaling assumed here, the descoped scenarios would degrade and the upscoped ones would improve, shrinking the apparent gap between the top-run effect and the luminosity effect.
The conclusion that luminosity matters little once a top run is present suggests that preserving even a reduced 365 GeV run is a better use of resources than building four IPs or running at 50 MW, a cost-benefit judgement the paper does not itself make.
The flat-directions diagnosis makes the FCC-ee projections hostage to HL-LHC assumptions: improved HL-LHC systematics would tighten all FCC-ee variants together and could make the luminosity ranking more visible, while degraded HL-LHC performance would weaken every FCC-ee scenario.
The paper's linear-versus-quadratic comparison is illustrative; a full $\mathcal{O}(\Lambda^{-4})$ global fit across all 61 operators would test whether the top-run dominance persists when quadratic corrections reshape the correlations.

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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

Read it before the next ESPPU26 scoping meeting. The headline result—that the 365 GeV top run, not total luminosity, drives most of the FCC-ee SMEFT reach—is new and follows from the stated inputs. The quantitative size of that result, however, rests on a systematics rescaling rule the authors admit is untested.

The paper does something genuinely useful: it takes the ESPPU26 descope options—fewer IPs, lower beam power, no top run, staged top run—and evaluates them in the same 61-operator SMEFiT global fit used for the baseline. The staged top run as a recovery scenario is a practical benchmark, and the Fisher-eigenmode decomposition showing that HL-LHC systematics are the global-fit bottleneck is informative. The ranking table (61/61, 52/61, 38/61 constrained directions) neatly summarizes the complementarity argument. The authors also propagate the loss of top-mass precision through parametric uncertainties, which is the right thing to do.

The soft spot is exactly where the stress-test puts it. In Sec. 3, statistical uncertainties are rescaled by 1/sqrt(L), and then for observables whose dominant systematic is statistically driven, that systematic is rescaled the same way; everything else is held fixed. The authors explicitly say a proper assessment requires dedicated simulations that are not available. That binary rule is load-bearing for the claims that descoping and upscoping luminosity matter little and that a staged top run suffices. If more of the FCC-ee systematics scale with luminosity than assumed, the descoped scenarios look worse, the upscoped top-only case looks better, and the headline contrast between top-run importance and luminosity unimportance shrinks. There is also no per-observable list of which systematics were rescaled, so the numbers are not fully reproducible from the paper alone. These are real limitations, but they do not invalidate the core insight: the top run is essential, and the mechanism—breaking flat directions and reducing the top-mass parametric uncertainty that feeds the Z-pole—is physically sound.

This paper is a projection built on Ref. [14]'s inputs, so it inherits those assumptions, but that is normal for this line of work. The authors have flagged the main caveats themselves. I would send it to referees, with a request that the systematics rescaling be justified more carefully or at least quantified with a sensitivity scan, and that the exact fit configurations be released. Conditional accept, but the top-run conclusion will survive even if the luminosity conclusions shift.

Referee Report

3 major / 5 minor

Summary. The manuscript uses the SMEFiT global fit framework to project the SMEFT reach of several FCC-ee running scenarios relative to the baseline FCC-ee programme and to LEP3. The scenarios are a 2-IP descoped FCC-ee with reduced synchrotron-radiation power, a 4-IP descoped variant, both optionally supplemented by a staged top-quark run, and two upscoped variants (a uniform 20% luminosity increase and a 50% increase of the top-quark run only). The analysis is carried out in a 61-operator dimension-six SMEFT with U(2)^3 flavour symmetry, at linear and quadratic order in the EFT expansion, and with aggressive or ideal theory-uncertainty assumptions. The main findings are that the top-quark run at 365 GeV is essential to outperform LEP3 in the marginalised fit, that luminosity variations have comparatively modest effects once a (staged) top run is present, and that systematic uncertainties of the HL-LHC projections constitute the dominant limitation of the global fit. The paper argues that the LHC and FCC-ee should be viewed as complementary programmes.

Significance. If correct, the analysis provides timely quantitative input for the ESPPU26 discussion of descoped FCC-ee options, and it offers useful comparative benchmarks for future collider physics assessments. The manuscript builds on the public SMEFiT code and database, and it presents the results of a genuinely global 61-parameter fit, including Fisher-information decompositions, rank analyses, quadratic EFT corrections, and a dedicated treatment of parametric top-mass uncertainties. These are concrete strengths. The central limitation is acknowledged by the authors themselves: the modelling of FCC-ee systematic uncertainties in non-baseline scenarios rests on a binary luminosity-rescaling rule that is explicitly stated to await dedicated simulations. Since that rule directly controls the quantitative conclusions about descoping, upscoping, and the role of luminosity, the headline claims should be regarded as conditional on this assumption until it is validated or bracketed by a sensitivity study.

major comments (3)

[Sec. 3, "Experimental projections"] The systematics rescaling rule is load-bearing and not fully specified. The text states that, for descoped and upscoped scenarios, statistically driven systematics are rescaled by the square root of the luminosity ratio while all other systematics are held fixed, but it does not provide a per-observable list of which systematics fall into which class, so the results are not fully reproducible. More importantly, this binary rule directly determines the conclusions in Secs. 4.1 and 4.2 that luminosity variations have limited impact and that descoped scenarios with a staged top run retain most of the baseline reach. The authors should provide the full classification and a robustness scan over alternative rescaling choices -- for example, scaling all systematics with sqrt(L), or scaling none -- and show how the bounds in Figs. 4.6, 4.8, and 4.12, as well as the delta_kappa_3 values in Sec. 4.4, change under these alternatives.
[Sec. 4.3, Table 4.1] The claim that the HL-LHC systematics are the dominant limitation of the global fit is supported by Fig. 4.9 and the Fisher-mode decomposition, but two pieces of information are missing. First, the notion of "constrained directions" in Table 4.1 (52/61, 38/61, 61/61) is not defined: the rank of a Fisher matrix is a mathematical statement only up to an eigenvalue threshold, and no threshold is stated. Second, the flat-direction structure and the perceived HL-LHC bottleneck are computed with the covariance matrix built using the Sec. 3 rescaling rule; under an equally plausible alternative rule, the number of FCC-ee-only constrained directions and the size of the HL-LHC contribution could change. The paper should state the eigenvalue threshold used to define rank and should present at least one alternative-rule version of Fig. 4.9 or Table 4.1 to show the stability of the bottleneck claim.
[Sec. 4.1, Fig. 4.6, and Sec. 5] The conclusion that "a staged top-quark run should be favoured over attempting to match the target luminosity of the baseline FCC-ee" is presented as a physics-reach statement but is then phrased as a recommendation that goes beyond physics: no cost model or funding schedule is included, although the scenarios are motivated by cost considerations. In addition, the manuscript attributes much of the top-run benefit to the improved top-quark mass measurement and the resulting reduction of parametric uncertainties, yet it never reports the assumed top-quark mass precision in the baseline and staged-top-run scenarios. Given that the abstract and Sec. 3 place weight on this parametric-uncertainty propagation, the paper should state the m_t uncertainty inputs (e.g., the values from Ref. [7]) for the baseline and staged scenarios and show how they enter the quoted bounds.

minor comments (5)

[Table 2.1 caption] The caption contains a formatting typo: "T able 2.1" should be "Table 2.1", and the header "LUminosity" should be "Luminosity".
[Sec. 4.1] The text says "Even a factor of three difference in luminosity" when comparing the baseline (100%) with the 2-IP descoped (36.5%) scenarios; the actual ratio is 205/74.8 = 2.74 for the Z-pole run. Please use the exact ratio or write "almost a factor of three".
[Fig. 4.4] The table inside Fig. 4.4 is labeled as showing "diagonal entries of the Fisher Information Matrix," but the displayed numbers appear to be relative contributions (percentages) of each dataset group to the diagonal element; please clarify the normalization and units in the caption.
[Sec. 4.3, footnote 1] The footnote beginning "We observe that the 55th Fisher mode..." appears without a footnote marker in the main text; please add the appropriate marker and ensure the footnote is properly anchored.
[Sec. 4.1, Eq. (4.1)] The sentence "V_post increases by 8% once the top-quark run is excluded" is ambiguous because an increase of the posterior volume corresponds to weaker constraints; please rephrase to say explicitly that the volume increases, i.e., the constraints degrade, and that this confirms the constraining power of the top run.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the scenario comparisons are outputs of a transparent SMEFiT fit, while the Sec. 3 systematics rescaling is an acknowledged assumption rather than a fitted prediction.

full rationale

The paper is a projection exercise built on a fixed SMEFiT likelihood; its main claims (top-run importance, mild luminosity sensitivity, and HL-LHC systematics as the global-fit bottleneck) are outputs of the 61-parameter fit, not quantities inserted as inputs. The only potentially load-bearing modeling choice is the Sec. 3 rule that statistical uncertainties and statistically-driven systematics rescale as sqrt(L_baseline/L_scenario) while other systematics are held fixed; the paper explicitly states that this 'requires dedicated simulations that are currently not available.' That is a transparent, externally checkable assumption about the future experiments, not a circular reduction: no equation is defined in terms of the conclusions it supports, and no fitted parameter is relabeled as a prediction. The SMEFiT framework and Ref. [14] are same-group citations, but they supply the computational machinery and baseline projections; the present paper computes the scenario comparisons itself, and the conclusions do not reduce to a self-citation. No uniqueness theorem or ansatz is smuggled in via citation. The acknowledged absence of dedicated systematic studies in Sec. 3 is the main limitation and should be weighed as a robustness/correctness concern, not as circularity.

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

The paper's conclusions rest on three adjustable modeling choices: the size of the (aggressive) theory uncertainties adopted from Ref. [31], the rule for rescaling systematics with luminosity in Sec. 3, and the assumed loss of top-mass precision without the 365 GeV run from Refs. [7] and [32]. In addition, every scenario inherits the projected (HL-)LHC and FCC-ee input databases of Refs. [14] and [23]. No new entities are postulated, and no target number is fitted to produce a conclusion; the Wilson coefficients are the fitted objects of the analysis, not free parameters of the paper's claim.

free parameters (3)

Aggressive theory uncertainty scenario = sizes from ESPPU26 Briefing Book (Ref. [31])
Chosen as the baseline for all main results; the ideal scenario serves only as a sensitivity check.
Systematic luminosity rescaling rule = 1/sqrt(L_baseline/L_scenario) for statistically driven systematics; fixed otherwise
Ad hoc modeling choice in Sec. 3, admitted to require dedicated simulations; it controls how much the scenarios differ from baseline.
Top-quark mass parametric uncertainty = about 10 MeV with top run; degraded without
External input from Refs. [7], [32]; the assumed loss without the 365 GeV run is a key driver of the top-run conclusion.

assumptions (5)

domain assumption Only CP-even dimension-six Warsaw-basis operators with a U(2)^3 flavor symmetry are retained, giving 61 operators
Sec. 3. This defines the SMEFT space being probed; CP-odd operators, other flavor structures, and dimension-eight terms are excluded and would modify the reach numbers.
domain assumption Linear EFT expansion at O(Lambda^-2) is the default, with quadratic corrections as a cross-check
Sec. 4.1 and Fig. 4.3. Most quoted bounds are linear; quadratic corrections change four-fermion reaches by up to a factor of two, so the linear choice affects the numbers.
standard math One-loop RGE running of Wilson coefficients from mu0 = 10 TeV down to observable scales
Sec. 3, implemented via Ref. [24]. Standard SMEFT running; several four-quark operators reach the Z-pole observables only through these RG effects.
domain assumption Projected (HL-)LHC and FCC-ee input datasets from Refs. [14] and [23] are accepted as given
Sec. 3. Every scenario inherits these projections, including the HL-LHC systematic uncertainty model that later becomes the claimed global-fit bottleneck.
domain assumption Parametric uncertainties are propagated with the code of Ref. [32], with top-mass precision depending on whether the 365 GeV run exists
Sec. 3. The assumed degradation of top-mass precision without the top run is an external input (Refs. [7], [32]) and drives the central conclusion about the top run.

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Cite this review

Pith. "Pith review of Descoped and Upscoped FCC-ee Running Scenarios in the SMEFT." pith.science (2026). https://pith.science/paper/CUDIIN6Q

@misc{pith2026260805874,
  author       = {Pith},
  title        = {Pith review of: Descoped and Upscoped FCC-ee Running Scenarios in the SMEFT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CUDIIN6Q}},
  note         = {Machine review of arXiv:2608.05874}
}

read the original abstract

We present projections for the sensitivity to new physics of descoped and upscoped FCC-ee scenarios in the framework of the Standard Model Effective Field Theory (SMEFT). Starting from the baseline FCC-ee programme, we analyse the subsequent impact of, first, removing the top-quark run, then reducing the beam power from 50 MW to 30 MW, and finally removing two interaction points (IPs), in all cases propagating the resulting loss in top-quark mass precision through increased parametric uncertainties. We also analyse the possibility of a staged top-quark run, where the top-quark run is partially restored in case funding becomes available only at a later stage. Motivated by the trade-off between beam power and operational costs, we also consider two upscoped scenarios, either through a uniform increase in luminosity across all energy runs, or through a luminosity enhancement targeting exclusively the top-quark run. We explore the sensitivity and limitations of each scenario and highlight in particular the complementarity between the FCC-ee projections and the (HL)-LHC measurements. By comparing the physics impact of the different running scenarios with the FCC-ee baseline, we show explicitly the importance of the top-quark run, indicating that a substantial fraction of the FCC-ee physics potential depends on it.

Figures

Figures reproduced from arXiv: 2608.05874 by the authors.

**Figure 4.1.** The 95% C.I. on the mass reach of the top operators (top panel) and of the Higgs and electroweak operators (bottom panel) for the various descoping scenarios considered in this work. The results are obtained from individual fits at linear level in the EFT expansion. The dotted bars indicate the impact of the (staged) top-quark run. Aggressive theory uncertainties are adopted. Impact of reduced luminosity We first fo… view at source ↗

**Figure 4.2.** Same as [PITH_FULL_IMAGE:figures/full_fig_p010_4_2.png] view at source ↗

**Figure 4.3.** Same as [PITH_FULL_IMAGE:figures/full_fig_p011_4_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.4.** Figure 4.4: Comparison of diagonal entries of the Fisher Information Matrix for a selected subset of operators in the absence (left) and in the presence (right) of a top-quark run in the baseline FCC-ee scenario. The top-quark run drastically reduces the parametric uncertainties…

**Figure 4.5.** Figure 4.5: 95 % C.I. for the subset of operators c 1 tt, c 8 QQ, cφ□, cφD and cφt entering the 61- dimensional linear global SMEFT fit. We compare the outcome of fits to the baseline FCC-ee scenario with and without a top-quark run, while always including aggressive theory unce…

**Figure 4.6.** Figure 4.6: shows that the luminosity reduction does not substantially affect the constraints, leading only to modest changes in the sizes of the ellipses. Even a factor of three difference in luminosity has a considerably smaller impact than the inclusion or omission of the top…

**Figure 4.7.** Figure 4.7: The 95% C.I. on the mass reach of the top (top panel) and Higgs and electroweak operators (bottom panel) in the individual fit for the various descoping scenarios considered in this work. The dotted bars indicate the impact of the (staged) top-quark run. The ideal th…

**Figure 4.8.** Figure 4.8: The 95% C.I. on the mass reach for the FCC-ee upscoped scenarios in the global marginalised fit for top operators (upper panel) and Higgs and electroweak operators (bottom panel) at the linear level in the EFT expansion. We display the 120% upscoped scenario where th…

**Figure 4.9.** Figure 4.9: 95 % C.I. for the subset of operators c 1 tt, c 8 QQ, cφ□, cφD and cφt entering the global linear SMEFT fit. Starting from the baseline FCC-ee, we compare the impact of removing the LHC systematics or the HL-LHC ones. To visualise this, we show in [PITH_FULL_IMAGE:f…

**Figure 4.10.** Figure 4.10: also helps explain why the bounds obtained for the upscoped and descoped 1We observe that the 55th Fisher mode is mostly constrained by the LHC rather than by the HL-LHC. The reason for this is that the main source of constraint for this direction is a mix of a ttγ¯…

**Figure 4.11.** Figure 4.11: Comparison of the uncertainty budgets for the 95% C.I. bounds in the case of individual fits to the baseline FCC-ee at linear order in the EFT expansion for top operators (upper panel) and Higgs and electroweak operators (lower panel). For each operator, we indicate…

**Figure 4.12.** Figure 4.12: The 68% C.I. on the Higgs self-coupling modifier δκ3 at the linear level in the EFT expansion and at a reference scale µ0 = 250 GeV. We display bounds for both individual and marginalised fits, and separately show the improvement expected from the (staged) top-quark…

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