{"id":"6556f3d7-ff56-4af4-8d3c-550a55f6c1dd","arxiv_id":"2412.13130","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"For equal Higgs coupling precision, FCC-ee is estimated to be about six times faster and four to five times less electricity-intensive than CLIC or ILC@CERN.","lead":"This note compares three proposed electron-positron Higgs factories at CERN (FCC-ee, CLIC, and ILC@CERN) for the same physics outcome, a fixed set of Higgs coupling precisions. It concludes that FCC-ee reaches those precisions in 8 years while CLIC and ILC would need roughly half a century, with higher electricity, cost, and carbon footprint.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'half a century' estimate assumes each SMEFT coupling precision scales exactly as L^{-1/2}; in a global fit this exponent can differ, and the abstract's list of couplings is broader than the computed set.","rationale":"The reader's weakest_assumption correctly identifies the sqrt-luminosity scaling in Section 4.1 as the load-bearing premise for the duration comparison. My stress-test agrees with that identification and sharpens it: the issue is not only that the improvement may be slower than 1/sqrt(L) due to HL-LHC or systematics, but that in a multi-parameter SMEFT fit the scaling exponent can also be larger than 0.5 because additional luminosity can resolve correlations and degeneracies. The paper's caveat in Section 6.6 only considers the slower direction, so it does not bound the faster direction that would reduce the required linear-collider durations. I also flag a concrete scope mismatch: the abstract includes H->gg among the decays for which the 'half a century' claim is made, but Section 4.1 excludes gluon couplings from the quantitative analysis. Despite these issues, the qualitative conclusion is robust: FCC-ee's much larger integrated luminosity and four interaction points make it substantially faster and more resource-efficient for the five couplings that are computed. The exact 'half a century' figure should therefore be treated as an estimate with a significant systematic uncertainty, not as a precise prediction. The reader's CONDITIONAL verdict remains appropriate, so no verdict change is recommended.","tokens_in":20490,"tokens_out":10413,"duration_ms":105346,"concrete_test":"Rerun the global SMEFT fit used for Ref. [11] (the same code and inputs that produced Tables 2 and 5) for CLIC380 and ILC250 at integrated luminosities multiplied by 2, 4, 9, and 16, keeping the energy stages and HL-LHC combination fixed. Extract the precision on the b, c, tau, Z, and W couplings at each luminosity and fit sigma_i = a_i L^{-alpha_i} for each coupling and collider. If any alpha_i deviates from 0.5 by more than about 0.1, recompute Tables 4 and 7 using the empirical exponents instead of squared precision ratios, and rescale the headline 'half a century' accordingly. Also re-issue the abstract's list of couplings so that it matches the set actually used in the computation (i.e., remove H->gg unless a dedicated fit including gluon couplings is provided).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central duration numbers in Tables 4 and 7 are obtained by multiplying the default linear-collider integrated luminosity by the square of the precision ratio from Tables 2 and 5, i.e. by assuming sigma_i ~ L^{-1/2} for each of the five selected effective couplings. This scaling is applied over a factor of roughly 4-8 in required luminosity and an extrapolation to 30-50 years of operation. The assumption is not exact for a global SMEFT fit: correlations among observables can break parameter degeneracies faster than 1/sqrt(L), while HL-LHC contamination, theory uncertainties, and experimental systematics can make improvement slower. Section 6.6 only discusses the slower direction and calls it conservative, but the faster direction is not tested. Because every duration in Tables 4 and 7 is proportional to the squared precision ratio, a modest deviation of the true exponent from 0.5 changes the 'half a century' claim by tens of percent. In addition, the abstract lists H->gg among the decays covered, yet Section 4.1 explicitly excludes gluon (and photon) couplings because HL-LHC dominates the fit; the quantitative comparison is therefore over b, c, tau, Z, W only, not over the full list in the headline. Neither issue overturns the qualitative conclusion that FCC-ee is far more luminosity-efficient, but it does mean the headline number is not a parameter-free arithmetic result.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper compares three future e+e- Higgs factory options at CERN — FCC-ee, CLIC, and ILC@CERN — by fixing a common physics outcome: the precision on the Higgs couplings to b, c, tau, Z, and W obtained from SMEFT global fits. Using the sensitivity projections of Ref. [11], the authors rescale the integrated luminosities of the linear colliders by the square of the precision ratios, assuming precision scales as L^{-1/2}, and then translate the required luminosities into operation time, electricity consumption, cost, and carbon footprint. The central finding is that CLIC and ILC@CERN would need about 30 years in their first stage and roughly 46-48 years over two stages to match the precision FCC-ee achieves in 3 or 8 years, respectively, with substantially larger resource consumption. The paper concludes that FCC-ee is vastly superior as a Higgs factory and as the first step toward a 100 TeV hadron collider.","tokens_in":20745,"tokens_out":6333,"duration_ms":57287,"significance":"The question addressed is timely and important for the upcoming European Strategy Update. The paper's arithmetic is transparent: every duration is computed by rescaling published precision projections with a clearly stated scaling law, and the input luminosity scenarios are referenced. The qualitative conclusion — that FCC-ee achieves a given Higgs-coupling precision with much less time and energy than the linear options — is robust and worth stating explicitly. The paper also performs a useful service by including electricity, cost, and carbon estimates for a fixed physics outcome, rather than per facility. However, the quantitative headline is contingent on several assumptions and on a selection of couplings that is narrower than the abstract advertises.","major_comments":[{"comment":"The abstract states that the comparison covers 'already demonstrated Higgs decays (bbar, tau+tau-, gg, ZZ, WW) and H->c cbar', but Section 4.1 explicitly excludes the gluon (and photon) couplings because HL-LHC dominates the combined fit and the L^{-1/2} scaling assumption would be invalid. All quantitative results in Tables 2-7 are therefore for b, c, tau, Z, and W only. The abstract overstates the computed set of couplings and should be corrected, or the gluon coupling must be included via a stand-alone fit as suggested in the text.","section":"Abstract and Section 4.1"},{"comment":"The 'time needed to reach the same precision as FCC-ee' is computed separately for each coupling and then averaged. To reach the FCC-ee precision on all five couplings simultaneously, the required time is the maximum over the couplings (or the time from a combined fit), not the arithmetic mean. For example, Table 7 shows CLIC durations ranging from 26 to 56 years and ILC durations from 41 to 49 years; the reported averages of 48 and 46 years mask the fact that the W and tau couplings require approximately 54-56 years for CLIC. The text's claim that the duration is 'almost independently of the coupling considered' is inconsistent with the spread in the tables. The averaging procedure should be stated explicitly and justified, or the maximum should be used.","section":"Sections 4.1-4.2 and Tables 4, 7"},{"comment":"The central rescaling assumes that each coupling precision improves exactly as L^{-1/2}. Section 6.6 acknowledges that the improvement may be slightly slower because of HL-LHC contamination and argues that this is conservative for the linear colliders, but it does not address the opposite direction: in a global SMEFT fit, correlations among observables can break parameter degeneracies faster than L^{-1/2}. Since every duration in Tables 4 and 7 is proportional to the square of the precision ratio, a modest change in the scaling exponent changes the headline durations by tens of percent. The paper should provide a sensitivity scan over the scaling exponent (e.g., sigma ~ L^{-alpha} with alpha = 0.4-0.6) or otherwise bound the robustness of the 'half a century' claim.","section":"Sections 4.1 and 6.6"},{"comment":"The treatment of outliers is inconsistent. In Table 4, the CLIC c-coupling duration of 77 years is excluded from the average as 'off, probably because of rounding errors', while in Table 7 the CLIC b-coupling duration of 26 years is described with the same caveat but is 'conservatively included in the average'. Both values appear to suffer from the same rounding instability in the input precisions, yet the two tables handle them differently, shifting the reported averages by several years. The authors should either use a robust estimator (median) or propagate the rounding uncertainty (as done later in Section 6.6) consistently across both tables.","section":"Tables 4 and 7"}],"minor_comments":[{"comment":"The captions refer to the 'free-Gamma_H fit' without defining it; a sentence explaining that this is the SMEFT fit with the Higgs width left free would help readers not familiar with Ref. [11].","section":"Table 2 and Table 5"},{"comment":"The phrase 'almost independently of the coupling considered' is an overstatement given the ranges in Table 4 (24 to 36 years for CLIC after excluding the c value, and 28 to 31 years for ILC).","section":"Section 4.1"},{"comment":"The left panel has a stray 'Years 250 GeV' label on the x-axis that appears to be a typo; the axis should simply read 'Years'.","section":"Figure 1"},{"comment":"The systematic bias of +/-10% on the operation times is stated, but the corresponding error bars are not shown in Figures 2 and 5; adding them would make the uncertainty of the headline numbers visible.","section":"Section 6.6"},{"comment":"Ref. [11] is cited as 'Global SMEFT Fits at Future Colliders (2022)' with arXiv number but no version; the version actually used (v5, July 2024) should be cited explicitly, since the paper states that the July 2024 update is used.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is essentially a policy brief for the ESPP, and its conclusions are strongly worded. The core comparison is useful and mostly reproducible, but the abstract is not aligned with the analysis (the gluon coupling is advertised but not computed), and the averaging method over couplings is not the natural metric for 'reaching the same precision'. These are fixable within the manuscript's scope, hence major revision rather than rejection. The authors should also be asked to tone down the phrase 'vastly superior' in the abstract unless the caveats about the excluded couplings and the L^{-1/2} assumption are fully reflected there."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Honest take: this is a policy-facing arithmetic note, not a new physics result. The central qualitative claim—FCC-ee wins decisively on time-to-precision for the five couplings where e+e− data dominate—is well supported. I would not sign the abstract's “half a century” as a statement about all listed Higgs decays, because the quantitative tables cover b, c, tau, Z, W only; gg and photon couplings are explicitly excluded in Section 4.1. That mismatch is the biggest rhetorical flaw, though the direction of the conclusion survives it.\n\nWhat is new: the updated FCC-ee baseline with four interaction points, ILC@CERN-specific running-time rescaling, a “time to fixed precision” metric, and more complete cost and carbon life-cycle numbers than their earlier Ref. [12]. The arithmetic is transparent; you can rebuild Tables 4 and 7 from Tables 2/5 and the design luminosities. No parameters are fitted. They also state in Section 6.6 the rounding bias and the systematic-floor caveat, which is more honesty than this literature usually gets.\n\nSoft spots, in order of importance. First, the precision scaling as L^-1/2 is assumed, not derived, for a global SMEFT fit. Section 6.6 only discusses the slow side; the fast side is not tested. Since every duration is proportional to the squared precision ratio, a modest deviation in the effective exponent moves the headline numbers by tens of percent. Second, the abstract overstates coverage relative to Section 4.1. Third, the per-coupling rows scatter widely—CLIC b at 26 years versus an average of 48—so the headline is an average, not a uniform statement. The authors handle outliers inconsistently, excluding c in Table 4 and including b in Table 7, though they flag both. Fourth, the ILC@CERN cost and electricity numbers are explicitly estimates, and the carbon projection depends on an assumed grid mix. This is minor because those inputs do not drive the ordering.\n\nThe critique of Refs. [13,14] is pointed and probably fair on the concrete omissions (zero carbon after 2040, missing second-stage carbon budgets), though I would not import it uncritically.\n\nVerdict: the central claim holds under its stated assumptions; the quantitative headline needs coupling-by-coupling qualification. This paper is for anyone preparing for the 2026 European Strategy update and for any physicist trying to check the FCC-versus-linear numbers themselves. It deserves a serious referee; the right outcome is publication with the abstract fixed and the L^-1/2 scaling assumption stress-tested. I would cite it as the standard reference for this comparison.","headline":"A transparent, policy-facing arithmetic comparison whose qualitative conclusion (FCC-ee dominates on time-to-precision) likely survives scrutiny, but whose 'half a century' headline overstates what the tables actually compute.","tokens_in":21313,"tokens_out":2113,"would_cite":true,"duration_ms":23379,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"FCC-ee would reach a given Higgs-coupling precision in eight years; CLIC and ILC@CERN would need about half a century for the same precision, with higher electricity, cost, and carbon footprint.","keywords":["Higgs factory","FCC-ee","CLIC","ILC","Higgs couplings","SMEFT fit","sustainability","luminosity scaling"],"falsifier":"Take the first years of data from a linear collider (CLIC 380 or ILC 250 at CERN) and measure the uncertainties on the $b$, $c$, $\\tau$, $Z$, and $W$ Higgs couplings from a SMEFT fit; if those uncertainties do not shrink as $1/\\sqrt{L}$ with increasing integrated luminosity, the 50-year durations calculated here would be wrong. A single measurement of the $H \\to b\\bar{b}$ coupling uncertainty at two different integrated luminosities at ILC250 would show whether the $1/\\sqrt{L}$ scaling holds.","tokens_in":20216,"feed_emoji":"⚛️","tokens_out":5481,"duration_ms":45854,"temperature":0.7,"pith_summary":"This note compares three proposed electron-positron Higgs factories—FCC-ee, CLIC, and ILC operated at CERN—on equal footing by fixing the target: the same precision on the Higgs couplings to b, c, tau, Z, and W bosons. It claims that FCC-ee reaches this precision in about eight years, while CLIC and ILC@CERN would need roughly half a century to accumulate the integrated luminosity required for the same precision, and would consume three to four times more electricity, cost more, and emit more carbon for that outcome. The reason is FCC-ee's much larger luminosity and its four interaction points, which outweigh the longitudinal beam polarisation advantage of linear colliders. If right, this changes the sustainability debate: the meaningful quantity is resources per physics outcome, not per facility.","feed_headline":"FCC-ee hits Higgs precision in 8 years; linear colliders need 50","feed_subtitle":"CLIC and ILC@CERN would need far more time, power, and carbon for the same Higgs precision.","key_machinery":"The comparison is built on a precision-for-precision metric. Higgs coupling uncertainties from a SMEFT global fit (Ref. [11]) are taken as the scientific outcome; for each coupling, the integrated luminosity needed to reach FCC-ee's precision is obtained by scaling the linear collider luminosity by the square of the ratio of precisions (so that the required luminosity grows as $1/\\sigma^2$), and the extra running time is inferred from the design yearly luminosity of each machine. This carries the whole argument: it translates coupling precision directly into operation time, electricity, cost, and carbon, and it is why the paper's conclusions are expressed in years and TWh rather than in percentages.","core_discovery":"The paper's central claim is that the often-repeated statement 'all e+e- Higgs factories have similar reach' is misleading once time and resources are fixed. Using the most recent SMEFT global-fit projections, the authors show that for the five Higgs couplings already dominated by e+e- data—Z, W, b, c, tau—FCC-ee in its planned 240 and 365 GeV runs achieves a precision that CLIC (380+1500 GeV) and ILC@CERN (250+500 GeV) would only match after about 48 and 46 years of running respectively, more than half a century when shutdowns are counted. They further argue that FCC-ee is the only place to attempt the electron Yukawa coupling, that FCC-ee plus FCC-hh is orders of magnitude better for couplings needing billions of Higgs bosons, and that the full FCC programme is out of reach of linear colliders; hence FCC-ee is 'vastly superior' as the first step towards a 100 TeV hadron collider.","pith_inferences":["If the assumed $1/\\sqrt{L}$ scaling is optimistic because systematic uncertainties floor the precision, the linear collider durations would likely be even longer than half a century, not shorter; the paper itself notes this assumption is favourable to the linear colliders.","The comparison could be extended to other Higgs couplings (such as $gg$, $\\gamma\\gamma$, $Z\\gamma$, $\\mu^+\\mu^-$) with a stand-alone SMEFT fit that does not combine with HL-LHC; the paper excludes them because HL-LHC dominates those channels, but a stand-alone fit might change the relative ranking.","The 'half a century' framing implies that a linear collider programme would span an entire professional generation, a sociological and institutional constraint that the paper mentions but does not quantify.","The cost estimates for ILC@CERN are acknowledged as a 'guesstimate' from the Snowmass implementation report; updated official estimates could widen the cost gap with FCC-ee."],"forward_implications":["For the already demonstrated Higgs decays ($b\\bar{b}$, $\\tau^+\\tau^-$, $gg$, $ZZ$, $WW$) and for $H \\to c\\bar{c}$, CLIC and ILC@CERN would need roughly half a century to reach the precision FCC-ee achieves in eight years.","The electricity consumption for the same physics outcome would be three to four times larger for the linear colliders than for FCC-ee.","FCC-ee is claimed to be the only place to attempt the electron Yukawa coupling with sensitivity close to the Standard Model prediction, thanks to running at $\\sqrt{s} = m_H$ with a reduced energy spread.","The combination of FCC-ee and FCC-hh would provide order-of-magnitude better precision on rare Higgs couplings and a few-percent measurement of the Higgs self-coupling, both out of reach of linear colliders.","Even with an aggressive doubling of ILC's instantaneous luminosity at 250 GeV, ILC@CERN would still need about 52 years to match the eight-year FCC-ee precision on Higgs couplings."],"supporting_citations":[{"why":"Supplies the SMEFT global-fit projections of Higgs coupling precisions that define the common physics outcome for all three colliders.","marker":"[11]"},{"why":"Provides the CLIC design parameters, integrated luminosities, and yearly electricity consumption used for the CLIC durations.","marker":"[6]"},{"why":"Provides the ILC design parameters, run plan, and luminosity upgrade assumptions that are rescaled for ILC@CERN.","marker":"[8]"},{"why":"Defines the FCC-ee integrated luminosities and run durations at 240 and 365 GeV used as the reference scenario.","marker":"[15]"},{"why":"Documents the FCC-ee yearly electricity consumption from the Feasibility Study Midterm Report.","marker":"[19]"},{"why":"Earlier comparison of carbon footprints of e+e- Higgs factories that this note extends with cost, carbon projections, and precision-based scaling.","marker":"[12]"}],"fun_headline_variants":["FCC-ee bests linear colliders for Higgs: 8 years vs 50","8 years to match 50: FCC-ee dominates Higgs precision","FCC-ee's 8-year precision: linear colliders need 50 years","Common belief wrong: FCC-ee beats linear colliders for Higgs","All Higgs factories equal? Data says no: FCC-ee wins"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire duration comparison rests on the assumption that Higgs coupling precision improves as $1/\\sqrt{L}$ (the inverse square root of integrated luminosity), applied to the SMEFT fit projections of Ref. [11]; if the true precision improves more slowly—for example due to systematic floors—the required linear collider durations change.","fun_headline_variants_meta":{"raw":{"variants":["FCC-ee bests linear colliders for Higgs: 8 years vs 50","8 years to match 50: FCC-ee dominates Higgs precision","FCC-ee's 8-year precision: linear colliders need 50 years","Common belief wrong: FCC-ee beats linear colliders for Higgs","All Higgs factories equal? Data says no: FCC-ee wins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000831,"raw_usage":{"total_tokens":3686,"prompt_tokens":1059,"completion_tokens":2627,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":675,"completion_tokens_details":{"reasoning_tokens":2527}},"tokens_in":675,"tokens_out":2627,"duration_ms":15472,"temperature":1.0,"reasoning_tokens":2527,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T13:23:42.428265+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the first years of data from a linear collider (CLIC 380 or ILC 250 at CERN) and measure the uncertainties on the $b$, $c$, $\\tau$, $Z$, and $W$ Higgs couplings from a SMEFT fit; if those uncertainties do not shrink as $1/\\sqrt{L}$ with increasing integrated luminosity, the 50-year durations calculated here would be wrong. A single measurement of the $H \\to b\\bar{b}$ coupling uncertainty at two different integrated luminosities at ILC250 would show whether the $1/\\sqrt{L}$ scaling holds.","supporting_citations":[{"cited_title":"Janot, C","cited_arxiv_id":null,"evidence_quote":"Defines the FCC-ee integrated luminosities and run durations at 240 and 365 GeV used as the reference scenario."},{"cited_title":"Auchmann, W","cited_arxiv_id":null,"evidence_quote":"Documents the FCC-ee yearly electricity consumption from the Feasibility Study Midterm Report."},{"cited_title":"The carbon footprint of proposed $\\rm e^+e^-$ Higgs factories","cited_arxiv_id":"2208.10466","evidence_quote":"Earlier comparison of carbon footprints of e+e- Higgs factories that this note extends with cost, carbon projections, and precision-based scaling."}],"review_version":1}