{"id":"bad83741-0a46-4fdc-ba0b-3de436947355","arxiv_id":"2204.05085","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Type-I and Type-II two-Higgs-doublet models can accommodate a strong first-order electroweak phase transition and the CDF-II W mass shift in overlapping regions of heavy-Higgs mass splitting, but future lepton colliders would separate them.","lead":"A parameter-space scan of two-Higgs-doublet models asking whether the same region of heavy-Higgs mass splittings can simultaneously produce a strong first-order electroweak phase transition and the W-boson mass shift reported by CDF-II. It matters because it converts a cosmological requirement (electroweak baryogenesis) into a concrete target for future lepton-collider precision measurements.","discovery_kind":"unclear","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The headline green region is the intersection of two 95% CL cuts on quantities that are both functions of the same (S,T,U); the authors acknowledge the missing joint fit in §2.4 but never quantify how far the boundary-hugging green points would move.","rationale":"The reader's weakest_assumption identifies precisely the load-bearing premise: §2.4 treats the Z-pole S,T,U constraint and the CDF-II m_W as independent 95% CL cuts even though both are functions of the same oblique parameters. I agree this is the right target and would only sharpen it in two ways. First, the direction of the bias is not stated and matters: because the green points hug the boundary (§3.3), a proper joint fit could either shrink or eliminate them, and the paper does not say which. Second, there is a possible double-counting risk if the Table 1 S,T,U ranges already incorporate an m_W input, which the text does not clarify. Both are acknowledged in spirit by the authors ('for simplicity we just take them as two separate measurements') but neither is quantified, so the abstract's flat 'can explain ... at same time' (abstract:s1) is stronger than the analysis supports. The qualitative conclusion, that heavy-Higgs mass splitting links SFOEWPT, oblique parameters, and m_W, and that a SM-consistent future lepton collider would exclude the CDF-II explanation, is a reasonable inference from the authors' own figures and is not threatened. The secondary issues the reader raises (the xi_c > 0.9 loosening in Eq. 2.15, scan-density boundaries presented as allowed regions, and the §2.6 flavor bound versus the Type-II Delta m_C range) are real but not load-bearing: the xi_c loosening is modest and cited to uncertainty estimates, and the flavor bound is a projection issue rather than a clean contradiction because the Delta m_C range is marginalized over m_H. None of these change the verdict. The paper is a competent extension of an established program; the appropriate verdict remains CONDITIONAL, with the joint-fit check as the specific step that would settle whether the quantitative claim survives at its stated strength.","tokens_in":17208,"tokens_out":5689,"duration_ms":145805,"concrete_test":"Recompute the green region with a single joint chi-square over (S,T,U) that combines the Table 1 likelihood with the CDF-II m_W likelihood through Eq. 2.12, using the full correlation matrix and stating explicitly whether the Table 1 inputs already contain an m_W measurement. Report the number of SFOEWPT points surviving at 95% CL and whether the quoted Delta m_A/C and tan beta ranges in abstract:s2 shift. If the green region shrinks materially or disappears, the claim weakens from 'can explain at same time' to 'marginally consistent at the 95% boundary.'","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim (abstract:s2, Conclusion item 2) is that both Type-I and Type-II 2HDM can simultaneously satisfy SFOEWPT, Z-pole, Higgs, and CDF-II m_W. The green region of Fig. 3 is defined by conjoining two 95% CL cuts: the Table 1 S,T,U ellipsoid and the CDF-II m_W interval of Eq. 3.3. But m_W is not an independent observable in this framework: Eq. 2.12 makes m_W^2HDM an explicit function of the same S,T,U that Table 1 constrains. The two datasets (LEP/SLD Z-pole and CDF-II) are independent measurements, but the model prediction links them, so the correct procedure is a single joint chi-square over the (S,T,U) plane, not two hard 95% cuts. The authors state this themselves in §2.4 ('a global analysis to recast the S,T,U parameters is needed ... here for simplicity we just take them as two separate measurements'), and §3.3 concedes the green points 'mainly locate around the boundary region.' Because the surviving points sit at the edge of both cuts, the joint fit is exactly where the two treatments diverge most, and the sign of the effect is not stated. A second, related risk: the Table 1 S,T,U ranges are quoted from a fit that may already include an m_W input, in which case imposing the CDF-II m_W again would double-count. The paper does not resolve either point, so the strength of 'can explain at same time' rests on an unquantified approximation. This is the load-bearing soft spot; the qualitative physics (mass splitting controls SFOEWPT, oblique parameters, and m_W) is sound and is not in question.","agreement_with_reader":"agree"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript revisits whether the Type-I and Type-II two-Higgs-doublet models (2HDMs) can simultaneously accommodate a strong first-order electroweak phase transition (SFOEWPT), the LEP/SLD Z-pole oblique-parameter constraints, LHC Higgs-coupling measurements, and the CDF-II W-boson mass. The authors perform a six-parameter random scan (tan beta, cos(beta-alpha), m_A, m_H±, m_12^2, m_H) over roughly 10^9 points, apply vacuum-stability, perturbativity and unitarity constraints, direct-search limits, and the S,T,U windows of Table 1, compute the phase transition with BSMPT using the criterion xi_c = v_c/T_c > 0.9, and compute Delta m_W^{2HDM} from Eq. (2.12). The headline result (Fig. 3, Conclusion item 2) is that a non-empty region survives all of these simultaneously, with Delta m_{A/C} in (-400, 400) GeV and tan beta in (1, 50) for Type-I and Delta m_{A/C} in (-200, 300) GeV and tan beta in (1, 12) for Type-II, and that the CEPC-level Higgs and Z-pole projections would exclude the CDF-II-compatible points while leaving SFOEWPT viable. The physics message — that the same heavy-Higgs mass splittings control the phase transition, the oblique parameters, and m_W, so the scenario is testable at future lepton colliders — is well motivated and clearly presented.","tokens_in":17504,"tokens_out":4182,"duration_ms":106531,"significance":"The paper connects three normally separate threads (EWPT, electroweak precision obliques, and the CDF-II m_W anomaly) through a single set of 2HDM mass splittings, and it makes a falsifiable statement: if the CDF-II-compatible SFOEWPT region is real, CEPC/ILC/FCC-ee should see correlated deviations in Higgs and Z-pole observables, and if those measurements land on the SM the scenario is excluded. That is a useful, checkable target for the field, and the scan is broad enough to be a genuine global survey rather than a benchmark-point study. The result is, however, a statement about the intersection of several 95% CL windows whose statistical combination is not performed, so the quoted allowed ranges should be read as approximate until the points below are addressed.","major_comments":[{"comment":"The green region of Fig. 3 — the paper's headline result — is defined by conjoining two separate 95% CL cuts: the Table 1 S,T,U ellipsoid and the CDF-II window of Eq. (3.3). But Eq. (2.12) makes m_W^{2HDM} an explicit function of the same S,T,U that Table 1 constrains, so the model prediction links the two data sets even though the measurements are independent. The authors acknowledge this in §2.4 ('a global analysis to recast the S,T,U parameters is needed ... here for simplicity we just take them as two separate measurements') and note in §3.3 that the green points 'mainly locate around the boundary region' — precisely where a joint fit and two hard cuts diverge most. The manuscript should either perform the joint chi-square over (S,T,U) including both the Z-pole and CDF-II inputs, or at minimum quantify how the boundary of the green region moves under a joint treatment and state the sign of the effect. A related check is needed: if the S,T,U ranges of Table 1 (from Ref. [78]) were obtained from a fit that already used a measured m_W as input, then imposing the CDF-II m_W again in Eq. (3.2) partially double-counts the same observable. Please state explicitly which m_W value, if any, entered the Table 1 fit and how the double-counting is avoided.","section":"§2.4, Eq. (3.2), Fig. 3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The SFOEWPT criterion is loosened from the standard xi_c > 1 to xi_c > 0.9, justified by 'the uncertainty in xi_c calculation [28, 29]'. This choice is load-bearing: it directly determines which scan points enter the grey region of Fig. 3 and therefore which points can subsequently turn green. The manuscript should show the impact quantitatively — for example, the fraction of the grey and green samples that survive with xi_c > 1, and whether the quoted ranges Delta m_{A/C} in (-400, 400) GeV (Type-I) and (-200, 300) GeV (Type-II) shrink materially. If the allowed ranges are stable under the stricter cut, saying so strengthens the result considerably; if they are not, the abstract and Conclusion item 2 should quote the ranges obtained with the standard criterion.","section":"§2.7, Eq. (2.15)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"§2.6 states that b -> s gamma disfavors m_H± < 580 GeV in Type-II 2HDM, but §3.1 lists 'B-physics' among the constraints applied without specifying which observables and which mass window, and the scan range of Eq. (3.1) allows m_H± down to 10 GeV. Since the Type-II allowed region quoted in the abstract extends to Delta m_C = -200 GeV with m_H as low as 125 GeV, whether the b -> s gamma cut is actually imposed changes the Type-II result. Please state explicitly which flavor observables are applied, with what numerical treatment (hard cut versus chi-square), and whether the 'can be alleviated with contributions from other sectors' caveat of §2.6 means the constraint was switched off in the scan. If it was switched off, the Type-II ranges should be labeled as flavor-independent upper bounds on the allowed parameter space.","section":"§2.6 and §3.1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The claim that future lepton colliders 'can exclude the region for m_W at CDF-II' rests on the red region being disjoint from the green one, which in turn depends on the assumed CEPC uncertainties in Table 1 and on the assumption that the future central values equal the SM predictions. The manuscript should quantify the robustness of this statement: how far must the CEPC central values move, or how much must the S,T,U uncertainties in Table 1 be relaxed, before the red and green regions overlap? It would also help to explain physically why the red points collapse onto Delta m_A = 0 or Delta m_C = Delta m_A, and to state whether this is simply the m_H± ~ m_H or m_H± ~ m_A requirement already noted in §2.4 or an independent effect of the one-loop Higgs-coupling fit.","section":"§3.3, Fig. 3, Table 1","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The abstract states that 'O(100) GeV new scalars in 2HDMs are favored by SFOEWPT', but the quoted allowed regions extend to m_H ~ 900-1000 GeV. The phrasing should be softened to reflect the actual range, or the range should be tightened.","section":"Abstract and §3.2/Conclusion","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The Type-I upper bound on m_H is quoted as 1000 GeV in §3.2 and as 950 GeV in Conclusion item 2. Please reconcile the two numbers.","section":"§3.2 versus Conclusion item 2","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The denominator is written as a sum over sigma_mW^2 without defining the sum; presumably this is the combined experimental uncertainty. Please write it as a single combined variance and state its numerical value.","section":"Eq. (3.2)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Both figures are drawn in the alignment limit cos(beta-alpha) = 0, while the scan of Eq. (3.1) allows |cos(beta-alpha)| < 0.5. Please state how sensitive the S,T,U and Delta m_W maps are to cos(beta-alpha) away from alignment, or note explicitly that the figures are illustrative.","section":"Figs. 1 and 2","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The text says the Higgs precision study 'will deep into one-loop level' but does not describe the one-loop calculation or cite the specific expressions used. Please point to the source of the one-loop Higgs-coupling predictions (presumably Refs. [44, 79]) so the reader can reproduce the treatment.","section":"§3.1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Given roughly 10^9 scan points in six dimensions and about 10^6 surviving, please comment on whether the scan density is sufficient to resolve the boundaries quoted in the abstract, particularly the tan beta = 50 edge for Type-I and the Delta m_{A/C} extrema.","section":"§3.1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"There are numerous typographical errors that should be corrected: 'letpon' in the abstract, 'differnt' in §2.1, 'V acuum stability' in §2.2, 'can not be too heavy than EW scale' in §1, 'a certain mount of splitting' in §3.2, 'is is mainly because' in §3.3, 'than a clear deviation' in §1 (should be 'then'), and 'proprieties' in §3.3.","section":"Throughout","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Ref. [27] (Su, Williams, Zhang) already studied SFOEWPT in the 2HDM against future Z and Higgs factory measurements, and the present work shares two authors with it. The Introduction should state explicitly what is new here relative to that reference — presumably the CDF-II m_W input and the joint SFOEWPT/m_W analysis — so the incremental contribution is clear.","section":"Introduction","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The physics is reasonable and the scan is broad, but the headline 'can explain at same time' is the conjunction of two 95% CL cuts on quantities linked by the model prediction, and the authors themselves flag the missing joint fit. I would want to see either the joint fit or a quantified statement of its impact before acceptance. The xi_c > 0.9 loosening and the ambiguous status of the b -> s gamma constraint in Type-II are the other two items I would check most carefully in revision. The overlap with Ref. [27] is substantial but the new m_W ingredient is a legitimate addition; I would not treat it as a novelty problem provided the delta is stated."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"The pitch is straightforward: take the 2HDM strong-first-order scan the same group published in 2021, add the CDF-II W mass as a constraint, and project onto future lepton-collider Higgs and Z-pole precision. The qualitative link is real and worth stating clearly — heavy-Higgs mass splitting controls the phase transition strength, the oblique parameters, and m_W, so the three are not independent knobs. The conclusion that a future lepton collider consistent with the SM would kill the CDF-II explanation while leaving SFOEWPT alive is a fair reading of their own figures, and it is the useful part of the paper. The scan is large (a billion points), BSMPT is the right tool, and the one-loop treatment of Higgs precision is not hand-waving. Credit where due: this is a clean, honest piece of phenomenology, and the authors are upfront about their simplifications rather than burying them. Section 2.4 says in plain text that a global fit combining Z-pole and m_W is needed and that they instead impose two separate measurements. That is the load-bearing soft spot, and the stress-test note is right about it: m_W in Eq. 2.12 is an explicit function of the same S,T,U that Table 1 constrains, so conjoining two 95% cuts is not the same as a joint chi-square, and the surviving green points sit exactly at the boundary where the two treatments diverge most. The authors flag it; they just don't quantify it. That is a fixable omission, not a fatal one, but the abstract's flat 'can explain at same time' should be softened to match the 'slight tension' language in Sections 1 and 3.3. Two smaller things. The ξ_c > 0.9 threshold in Eq. 2.15 is loosened from the standard >1 with a nod to Refs. [28,29] but no number attached to how much it buys. And Section 2.6 quotes a Type-II bound of m_H± > 580 GeV from b→sγ, while the Type-II allowed region reaches Δm_C = -200 GeV at m_H = 125 GeV; the text never says whether that bound was actually applied in the scan. Worth a referee question. Who should read it: anyone working on 2HDM electroweak baryogenesis or on CDF-II W mass explanations, and people preparing lepton-collider precision projections. It deserves referees — the fixes are within reach and the result is useful if the joint fit confirms it.","headline":"A competent, timely extension of the authors' own 2HDM phase-transition scan to include the CDF-II W mass; the physics story is sound, but the headline green region rests on two 95% cuts that should have been one joint fit.","tokens_in":18252,"tokens_out":1262,"would_cite":true,"duration_ms":40955,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["12.60.Fr","98.80.Cq","14.70.Fm","12.15.Lk"],"model":"selfhosted/deepseek-v4.1-flash","headline":"Under current data, both Type-I and Type-II two-Higgs-doublet models can simultaneously produce a strong first-order electroweak phase transition, satisfy Higgs and Z-pole precision measurements, and account for the CDF-II W boson mass, all","keywords":["two-Higgs-doublet model","electroweak phase transition","electroweak baryogenesis","W boson mass","oblique parameters","Higgs precision measurements","future lepton colliders","heavy Higgs mass splitting"],"falsifier":"A future lepton collider measurement of $S$, $T$ and $U$ at the percent level, together with improved Higgs coupling measurements, that agrees with the Standard-Model predictions would exclude the region this paper identifies; equally, an independent W mass measurement from another experiment that confirms the Standard-Model value rather than the CDF-II value would empty the W-compatible region.","tokens_in":18459,"feed_emoji":"⚛️","tokens_out":3623,"duration_ms":83066,"temperature":0.7,"pith_summary":"The paper asks whether the same new particles can do three jobs at once: make the early-universe electroweak transition strongly first order (the prerequisite for electroweak baryogenesis), stay consistent with the extremely precise Z-pole and Higgs measurements, and produce the heavier W boson reported by the CDF collaboration in 2022. The authors work in the two-Higgs-doublet models (2HDM), where a second Higgs doublet adds a neutral scalar $H$, a pseudoscalar $A$ and a charged scalar $H^+$, all light enough to be present during the transition. Their claim is that in both the Type-I and Type-II versions of the model there is a surviving region of parameter space that satisfies all of these at once, and that the same quantities, the mass splittings $|Delta m_A = m_A - m_H$ and $|Delta m_C = m_{H^+} - m_H$, control the phase transition, the oblique parameters $S,T,U$ and the W mass. If that is right, the W mass anomaly is not an isolated curiosity but a hint of new scalars near the electroweak scale, exactly the kind of spectrum baryogenesis needs. The paper then turns the argument around: because future lepton colliders will measure $S,T,U$ and the Higgs couplings far more precisely, they can either confirm this picture through a visible deviation from the Standard Model or shut it down.","feed_headline":"CDF's heavy W mass fits a first-order electroweak transition","feed_subtitle":"Two-Higgs-doublet models can satisfy Higgs, Z-pole and W data at once, with heavy-Higgs splittings under 400 GeV.","key_machinery":"The load-bearing object is the pair of mass splittings $Delta m_A = m_A - m_H$ and $Delta m_C = m_{H^+} - m_H$. These enter the oblique parameters $S$, $T$ and $U$ through one-loop gauge-boson self-energies, and $T$ carries by far the tightest current bound, so the Z-pole data effectively pin the splitting pattern; the same $S,T,U$ then feed the 2HDM prediction for $m_W$ through the standard relation $m_W^2(1 - m_W^2/m_Z^2) = pi alpha/(sqrt(2) G_F)(1 + Delta r)$, with a small extra term from the modified triple-Higgs coupling. The phase transition side uses the finite-temperature effective potential, tree level plus Coleman-Weinberg plus counterterms plus thermal corrections, and the criterion that the minimum of the potential jump discontinuously as the temperature falls, with $v_c/T_c > 0.9$ to avoid washing out any generated baryon number. The numerical engine is BSMPT, which tracks the minima and reports the critical temperature and the strength of the transition.","core_discovery":"The central claim is a conjunction, established by a large numerical scan rather than by an analytic identity. The authors scan six 2HDM parameters (with $|cos(beta-alpha)| < 0.5$, $m_{A,H^+}$ and $m_H$ up to 1.5 TeV, $tan beta$ from 0.2 to 50), keep points that pass vacuum stability, unitarity, perturbativity, $B$-physics, LEP and LHC direct searches, and current Higgs and Z-pole precision data, and then require a strong first-order transition using the washout criterion $xi_c = v_c/T_c > 0.9$ computed with the public code BSMPT. On top of that they impose the CDF-II W mass at 95% confidence, which in their treatment corresponds to a shift $Delta m_W in (36.3, 103.4)$ MeV. The result is that a non-empty set of points survives all of it in both model types: roughly $m_H$ between 125 and 950 GeV with $tan beta$ from 1 to 50 and splittings $Delta m_{A/C}$ in $(-400, 400)$ GeV for Type-I, and $m_H$ between 125 and 900 GeV with $tan beta$ from 1 to 12 and splittings in $(-200, 300)$ GeV for Type-II. The authors also show the reverse side: if future CEPC-type measurements come out Standard-Model-like, the surviving region shrinks to slices at $Delta m_A = 0$ or $Delta m_C = Delta m_A$ that do not overlap the W-mass-compatible region, so the CDF-II explanation and a Standard-Model-consistent future cannot both hold in this model.","pith_inferences":["Because $m_W$ and the Z-pole observables are generated by the same radiative corrections, a genuine joint fit over both data sets would very likely shrink the region the paper calls allowed; the surviving slivers may partly reflect the choice to impose two separate 95% confidence cuts rather than one combined likelihood.","The paper's own logic makes the scenario fragile in a useful way: if an independent W mass measurement lands on the Standard-Model value, the W-compatible region empties and only the phase-transition-only region remains, which is a clean and near-term test of the whole construction.","The threshold $v_c/T_c > 0.9$ is a perturbative proxy for whether baryons survive the transition; a lattice or higher-order treatment of the 2HDM transition could move that boundary and therefore shift which mass splittings count as viable.","A first-order transition with these splittings would also source gravitational waves from bubble collisions and sound waves, so a stochastic background search offers a channel that is independent of the collider program described here."],"forward_implications":["If the paper is right, new scalars with masses of order 100 GeV to about 1 TeV, split by a few hundred GeV, are compatible with every current precision measurement while still driving a strong first-order electroweak transition.","The W mass, the Z-pole oblique parameters and the phase transition strength are then not independent observables: measuring any one of them constrains the other two through the shared splittings $Delta m_A$ and $Delta m_C$.","A future lepton collider measuring $S,T,U$ at the percent level and improving Higgs coupling precision would either observe a deviation from the Standard Model or exclude the region that explains the CDF-II W mass together with a strong first-order transition.","Conversely, if the CDF-II W mass is real and the 2HDM is the correct description, a deviation from Standard-Model predictions must appear at those future machines with high confidence."],"supporting_citations":[{"why":"Supplies the CDF-II W boson mass measurement and its uncertainty, which sets the target shift the scan must reproduce.","marker":"[3]"},{"why":"Provides BSMPT, the public code used to compute the finite-temperature effective potential and identify the critical temperature and transition strength.","marker":"[85]"},{"why":"Supplies the $S,T,U$ central values, uncertainties and correlation matrices used as the Z-pole constraint, and the Type-II Higgs precision treatment.","marker":"[78]"},{"why":"Supplies the Higgs coupling precision measurements adopted for the Type-I analysis and for the future-collider projections.","marker":"[79]"},{"why":"Establishes the earlier 2HDM strong-first-order phase transition analysis and the LHC recasting that this work extends with W mass and future-collider data.","marker":"[27]"},{"why":"Provides the relation between $m_W$, $m_Z$, $G_F$, $alpha$ and the radiative correction $Delta r$ used to convert oblique parameters into a W mass prediction.","marker":"[80]"},{"why":"Supplies the one-loop $Delta r$ calculation in the two-Higgs-doublet model that underlies the $m_W$ formula.","marker":"[35]"},{"why":"Supplies the flavour-physics bounds on the charged Higgs mass and $tan beta$ applied as a cut on the scan.","marker":"[83]"}],"fun_headline_variants":["2HDM scan finds points fitting CDF W mass and strong EW transition","Type-I and Type-II 2HDM survive Higgs, Z-pole and CDF W checks","CDF W shift and first-order EW transition share 2HDM parameter space","Future SM-like Higgs data would close the 2HDM CDF W window","Heavy-Higgs splittings under 400 GeV in W-compatible 2HDM points"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The Z-pole oblique-parameter constraint and the CDF-II W mass are imposed as two separate 95% confidence cuts, which the authors themselves flag in Section 2.4 as a simplification standing in for a proper joint fit over correlated observables.","fun_headline_variants_meta":{"raw":{"variants":["2HDM scan finds points fitting CDF W mass and strong EW transition","Type-I and Type-II 2HDM survive Higgs, Z-pole and CDF W checks","CDF W shift and first-order EW transition share 2HDM parameter space","Future SM-like Higgs data would close the 2HDM CDF W window","Heavy-Higgs splittings under 400 GeV in W-compatible 2HDM points"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":2916,"prompt_tokens":1148,"completion_tokens":1768,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":1668}},"tokens_in":1148,"tokens_out":1768,"duration_ms":35848,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":1668,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-30T22:45:53.942084+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A future lepton collider measurement of $S$, $T$ and $U$ at the percent level, together with improved Higgs coupling measurements, that agrees with the Standard-Model predictions would exclude the region this paper identifies; equally, an independent W mass measurement from another experiment that confirms the Standard-Model value rather than the CDF-II value would empty the W-compatible region.","supporting_citations":[{"cited_title":"BSMPT - Beyond the Standard Model Phase Transitions -A Tool for the Electroweak Phase Transition in Extended Higgs Sectors","cited_arxiv_id":"1803.02846","evidence_quote":"Provides BSMPT, the public code used to compute the finite-temperature effective potential and identify the critical temperature and transition strength."},{"cited_title":"Type-II 2HDM under the Precision Measurements at the $Z$-pole and a Higgs Factory","cited_arxiv_id":"1808.02037","evidence_quote":"Supplies the $S,T,U$ central values, uncertainties and correlation matrices used as the Z-pole constraint, and the Type-II Higgs precision treatment."},{"cited_title":"Type-I 2HDM under the Higgs and Electroweak Precision Measurements","cited_arxiv_id":"1912.01431","evidence_quote":"Supplies the Higgs coupling precision measurements adopted for the Type-I analysis and for the future-collider projections."},{"cited_title":"Strong first order electroweak phase transition in 2HDM confronting future Z & Higgs factories","cited_arxiv_id":"2011.04540","evidence_quote":"Establishes the earlier 2HDM strong-first-order phase transition analysis and the LHC recasting that this work extends with W mass and future-collider data."},{"cited_title":"Radiative Corrections in Precision Electroweak Physics: a Historical Perspective","cited_arxiv_id":"1210.5296","evidence_quote":"Provides the relation between $m_W$, $m_Z$, $G_F$, $alpha$ and the radiative correction $Delta r$ used to convert oblique parameters into a W mass prediction."},{"cited_title":"Delta r in the Two-Higgs-Doublet Model at full one loop level -- and beyond","cited_arxiv_id":"1211.0311","evidence_quote":"Supplies the one-loop $Delta r$ calculation in the two-Higgs-doublet model that underlies the $m_W$ formula."},{"cited_title":"Status of the Charged Higgs Boson in Two Higgs Doublet Models","cited_arxiv_id":"1706.07414","evidence_quote":"Supplies the flavour-physics bounds on the charged Higgs mass and $tan beta$ applied as a cut on the scan."}],"review_version":1}