{"id":"905d5b01-3e63-4a05-a373-43e204498df6","arxiv_id":"2204.05760","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Small misalignment between the two triplet vacuum expectation values in the Georgi-Machacek model, or an added right-handed neutrino sector, can generate the W-boson mass shift reported by CDF-II.","lead":"The Georgi-Machacek model normally preserves custodial symmetry, so it cannot by itself explain the CDF-II W-boson mass anomaly. The authors show that slightly misaligning the two triplet vacuum expectation values, or adding right-handed neutrinos, can generate the needed mass shift.","discovery_kind":"extension","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The paper treats the triplet splitting Δv as a free scan parameter but never computes whether the one-loop effective potential actually generates Δv ~ 0.8 GeV; loop-induced custodial breaking is typically of order α/4π times the VEV, far below the required size.","rationale":"The paper's arithmetic (Eq. 3.3–3.5) is correct, and the RH neutrino extension is a genuine addition. But the central claim depends on the existence of a misaligned vacuum with Δv ~ 0.8 GeV. The paper asserts this qualitatively but does not compute it. The reader's concern about vacuum stability is valid, but the more specific and load-bearing issue is the magnitude of the loop-induced misalignment. The paper's scan treats Δv as free, so it does not test whether the potential can produce it. This is a gap that a one-loop effective potential calculation would settle. The verdict should remain CONDITIONAL.","tokens_in":20452,"tokens_out":8220,"duration_ms":134071,"concrete_test":"Compute the one-loop effective potential V_eff = V_tree + V_CW (Eq. 2.11) for the GM model with the custodial-preserving tree-level potential, including contributions from W, Z, top quark, Higgs bosons, and would-be Goldstones. Minimize V_eff numerically over v_φ, v_χ, v_ξ for a scan of quartic and mass parameters satisfying the EWSB condition (Eq. 2.4) and the Higgs mass constraint. Check whether any parameter point yields Δv = v_ξ − v_χ ≥ 0.8 GeV with v_χ ≲ 15 GeV. If the maximum loop-induced Δv is below 0.1 GeV, the paper's claim that the misalignment arises from a custodial-preserving potential is not supported, and the explanation requires explicit custodial-breaking terms.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (abstract:s8) requires a triplet splitting Δv ≈ 0.7–0.8 GeV for v_χ ≲ 15 GeV. The numerical scan (Fig. 3) treats Δv as a free input, not as an output of the scalar potential. Section 2 argues qualitatively that the one-loop effective potential (Eq. 2.11) can choose a misaligned minimum, but never computes the size of the loop-induced misalignment. The custodial-breaking sources in the loop are hypercharge gauge and Yukawa couplings; their contributions to the effective potential are suppressed by g'²/16π² and h²/16π², which would typically generate Δv of order 10⁻²–10⁻¹ GeV, not 0.8 GeV. If the loop-induced misalignment is too small, the required Δv must come from explicit custodial-breaking terms (e.g., the soft mass m_ξ² ξ†ξ mentioned in Section 2), which would contradict the abstract's claim that the misalignment arises 'from custodial symmetry preserving scalar potential.' The paper does not address this tension. This is more specific than the reader's vacuum-stability concern: even if the vacuum is stable, the required splitting may not be generated by the custodial-preserving potential plus loops.","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript asks whether the Georgi-Machacek (GM) model can accommodate the CDF-II W-boson mass anomaly. Using a SARAH/SPheno scan with HiggsBounds, HiggsSignals and GMCALC, the authors first show that the ordinary custodially-symmetric GM model contributes at most Δm_W ≈ 0.0012 GeV, far below the ~0.067 GeV needed at 1σ. They then propose two custodial-symmetry-breaking extensions: (i) a small misalignment between the complex and real triplet VEVs, Δv ≡ v_ξ − v_χ, which through Eq. (3.5) can give Δm_W in the 1σ range for Δv ≳ 0.8 GeV with v_χ ≲ 15 GeV; and (ii) a low-scale right-handed neutrino sector that permits |h_ij| ~ 10^-2, giving Δm_W up to 0.03 GeV. Combining both effects lowers the required splitting to Δv ≈ 0.7 GeV. The paper is a standard-tool numerical study with a clear narrative and a useful benchmark for the ordinary GM model.","tokens_in":41460,"tokens_out":22678,"duration_ms":365090,"significance":"If the misaligned vacuum is realized, the paper offers a concrete, testable route for the GM model to address the CDF-II anomaly, and the observation that ordinary GM falls short by two orders of magnitude is a useful benchmark for the community. The RH-neutrino extension is well motivated by leptogenesis and LFV phenomenology. However, the central quantitative claim rests on an uncomputed assumption about the scalar potential, and the RH-neutrino contribution is overstated in the abstract. The paper's value is therefore conditional on resolving these points.","major_comments":[{"comment":"The claim that Δv ~ 0.8 GeV can arise 'from custodial symmetry preserving scalar potential' is asserted, not computed. The one-loop Coleman-Weinberg potential (Eq. 2.11) receives custodial-breaking contributions only from hypercharge and Yukawa couplings, suppressed by g'^2/16π^2 and h^2/16π^2; these typically generate Δv of order 10^-2–10^-1 GeV, not 0.8 GeV. The paper should either compute the loop-induced Δv explicitly for representative points, or state clearly that the required splitting must come from an explicit soft breaking term such as m_ξ² tr(ξ²) in Eq. (2.13), and revise the abstract's 'from custodial symmetry preserving scalar potential' accordingly. This is load-bearing for the central claim.","section":"Section 2 and abstract (s3, s5)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract states 'With low scale RH neutrino mass scale of order 10^2~10^4 TeV, the new physics contribution to Δm_W can reach 0.03 GeV.' The text (Section 4, discussion around Eq. 4.6) says 'Lower scale of M_R, which corresponds to larger value of h_ij, can possibly increase the value of Δm_W, with the maximal contribution about 0.03 GeV. However, most of such points are ruled out by LFV constraints.' The 0.03 GeV is therefore not an achievable value under the LFV bound; the abstract should be qualified. This is a genuine overstatement of the RH-neutrino result.","section":"Abstract (s7) vs Section 4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The vacuum stability/metastability claim is qualitative. The paper argues 'it is reasonable that small viable parameter space can be found to get a stable vacuum (or a metastable one with long enough lifetime)' but presents no effective-potential minimum, no tunneling rate, and no lifetime estimate for the scanned points in Fig. 3 and Fig. 4. At minimum, the authors should check that the points shown satisfy the bounded-from-below and vacuum-stability conditions of the potential (2.13), or state explicitly that stability is assumed rather than demonstrated. This is the load-bearing premise identified by the reader.","section":"Section 2","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"Several reference typos should be corrected: 'Chatrachyan' should be 'Chatrchyan' ([2], [88]); 'Bias' and 'Oierini' should be 'Blas' and 'Pierini' ([16]); 'Voshnu' should be 'Voshanu' ([33]); 'CDF Collaboration et al.' should be 'CDF Collaboration' ([3]).","section":"References","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The text refers to a 'green box' for the old fit, but the caption says 'red line.' Align the colors between text and caption.","section":"Fig. 1 caption","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The [85] values differ between text and caption (text: S=0.06±0.10, T=0.11±0.12, U=0.13±0.09 with U free; caption: S=0.14±0.08, T=0.26±0.06). Clarify which set corresponds to which fit and whether the U-free fit is shown in Fig. 1.","section":"Eq. (3.6) and Fig. 1 caption","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The expression for h_ij appears dimensionally inconsistent; please check and clarify the notation.","section":"Eq. (4.5)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract's 'can be as small as 0.8 GeV' should be phrased as a minimum required value (a consequence of Eq. 3.5), not a prediction. The text is mostly transparent about this, but the abstract reads as a prediction.","section":"Abstract (s5)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sign convention Δv ≡ v_ξ − v_χ assumes v_ξ > v_χ; please state this explicitly and note that the opposite sign would give Δρ < 0.","section":"Section 3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that adding RH neutrinos 'allows lighter (than 400 GeV) H++' (Fig. 4) versus 'larger than 600 GeV' (Fig. 3) should be explained — is this a scan-range effect or a physical effect?","section":"Section 4","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable contribution to the CDF-II model-building literature, and the ordinary-GM benchmark is useful. However, the abstract overstates the RH-neutrino result (0.03 GeV is LFV-excluded) and the central claim about the misaligned vacuum is asserted rather than computed. The authors should either compute the loop-induced Δv or explicitly state that a soft breaking term is required, and revise the abstract accordingly."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Worth a look, but read it for the benchmark numbers, not the headline claim. The useful part is the negative result and the loop estimate: ordinary custodial-preserving GM tops out at Δm_W ≈ 0.0012 GeV (abstract:s2), and the RH-neutrino extension, which lets h_ij reach ~10⁻² instead of ~10⁻¹³, pushes the one-loop contribution to ~0.03 GeV (abstract:s7). Both are honest calculations run through SARAH/SPheno with HiggsBounds, HiggsSignals and GMCALC, and the tree-level ρ formula and its inversion to v_ξ²−v_χ² ≳ 25.27 GeV² (Eq. 3.5) check out. The RH-neutrino sector is a genuine model-building addition, and tying it to leptogenesis is sensible given that single-triplet type-II leptogenesis gives vanishing asymmetry — the authors say so themselves and cite correctly. The fine-tuning needed to cancel type-I against type-II in the neutrino mass is stated openly, which I appreciate. Now the soft spot, and it is load-bearing. Δv is a scan input, not an output. Section 2 argues only that it is 'reasonable that small viable parameter space can be found' for a stable or long-lived misaligned vacuum; there is no effective-potential minimum, no tunneling rate. Worse, the custodial-breaking sources in the one-loop Coleman-Weinberg potential are hypercharge and Yukawa, suppressed by g'²/16π² and h²/16π², which naturally give Δv of order 10⁻² GeV, not 0.8. The stress-test note lands. The paper does mention the soft m_ξ² ξ†ξ term as an alternative route, but the abstract's framing — misalignment 'from custodial symmetry preserving scalar potential can still be allowed' (abstract:s3) — quietly depends on explicit breaking if the loop size is what I think it is. That tension needs to be faced, not footnoted. Minor: the 'firstly' novelty claim sits awkwardly next to ref. [65], which already studied custodial violation in GM; the CDF-II-versus-ATLAS/LHCb/LEP tension is acknowledged, so I won't belabor it. Who should read it: anyone working on GM phenomenology or custodial breaking in extended Higgs sectors, and anyone cataloguing CDF-II explanations. Send it out, but ask the referee specifically for the one-loop effective potential minimum and the Δv it actually yields.","headline":"The arithmetic is right and the RH-neutrino loop estimate is a real addition, but the paper never shows that the scalar potential actually produces the 0.8 GeV triplet splitting its headline rests on.","tokens_in":21459,"tokens_out":1077,"would_cite":false,"duration_ms":14917,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["12.60.Fr","14.70.Fm","12.60.Cn","14.60.Pq"],"model":"selfhosted/deepseek-v4.1-flash","headline":"The Georgi-Machacek model preserves a custodial symmetry that keeps the W boson mass pinned near its Standard Model value; the paper argues that breaking that symmetry in two small ways — misaligning the two triplet vacuum values by under a","keywords":["Georgi-Machacek model","custodial symmetry","W boson mass","CDF-II anomaly","triplet vacuum expectation value","right-handed neutrinos","electroweak oblique parameters","leptogenesis"],"falsifier":"A calculation of the one-loop effective potential in the $v_chi$-$v_xi$ plane, with the parameters that give $Delta m_W$ in the 1-$\\sigma$ CDF-II window, showing that no minimum exists at splittings of order $0.7$ to $0.8$ GeV, or that the misaligned stationary point is a saddle or decays faster than the age of the universe, would remove the mechanism's footing.","tokens_in":21720,"feed_emoji":"⚛️","tokens_out":3217,"duration_ms":50454,"temperature":0.7,"pith_summary":"The CDF-II collaboration reported a W boson mass of $80{,}433.5$ MeV, about $7$ $\\sigma$ above the Standard Model expectation of roughly $80{,}357$ MeV. The authors ask whether the Georgi-Machacek model — a Higgs sector with one doublet and two triplets, built precisely so that the tree-level $W$ and $Z$ masses obey the custodial relation $m_W = m_Z c_W$ — can absorb that shift. Their answer is that the ordinary, aligned version cannot: they compute a maximal new-physics contribution of $0.0012$ GeV, far short of the roughly $0.07$ GeV needed for the 1-$\\sigma$ range. They then propose two ways to break the custodial symmetry softly: let the two triplet vacuum values differ by a splitting $v_xi - v_chi$ of order a GeV, and add a low-scale right-handed neutrino sector that permits neutrino-triplet Yukawa couplings $h_{ij}$ of order $10^{-2}$ instead of $10^{-13}$. Either effect alone is marginal or insufficient; combined, they report that the needed splitting drops to about $0.7$ GeV for $v_chi$ below about $15$ GeV. If this holds, a model already motivated by neutrino masses and leptogenesis also explains the CDF-II anomaly without new particles above the TeV scale.","feed_headline":"Splitting two triplet fields by 0.8 GeV can lift the W mass","feed_subtitle":"Misaligning the Georgi-Machacek triplets, plus heavy right-handed neutrinos, could account for the CDF-II W mass excess.","key_machinery":"The load-bearing object is the tree-level custodial relation for the $rho$ parameter written in terms of the triplet vacuum values, $rho = (v_phi^2 + 4 v_chi^2 + 4 v_xi^2)/(v_phi^2 + 8 v_chi^2)$, which equals unity exactly when $v_chi = v_xi$ and deviates as $Delta rho approx 4(v_xi^2 - v_chi^2)/v_{EW}^2$ when they differ. Because the $W$ mass shift at tree level is $Delta m_W approx m_W Delta rho / 2$, this single ratio converts a GeV-scale splitting of the triplet vacuum values into a GeV-scale shift of $m_W$, which is the mechanism the whole paper rides on. Around it sit two supporting tools: the oblique-parameter machinery $(S, T, U)$ that captures the loop-level contributions and lets the authors compare against the electroweak fit that includes the new CDF-II value, and a numerical pipeline that generates the model with SARAH, computes spectra with SPheno, and filters surviving points through HiggsBounds, HiggsSignals and GMCALC together with the $kappa_V$, $kappa_F$ and $s_H$ constraints.","core_discovery":"The paper's central claim is that the CDF-II $W$ mass excess can be reproduced inside the Georgi-Machacek framework once two custodial-symmetry-breaking effects are present. The first is a small misalignment between the vacuum expectation values of the complex triplet $chi$ and the real triplet $xi$: the tree-level relation $Delta rho = 4(v_xi^2 - v_chi^2)/v_{EW}^2$ feeds directly into $Delta m_W approx m_W Delta rho/2$, so a splitting as small as $0.8$ GeV with $v_chi lesssim 15$ GeV already lifts $Delta m_W$ to about $0.067$ GeV, the 1-$\\sigma$ window of the CDF-II measurement. The authors argue that such a misaligned vacuum is reachable from a custodial-preserving tree-level potential because the one-loop Coleman-Weinberg corrections from hypercharge and Yukawa interactions break the symmetry softly anyway. The second effect is a right-handed neutrino sector that allows moderately large $h_{ij} L_i^T C i tau_2 chi L_j$ couplings while keeping neutrino masses tiny through a mixed type-I plus type-II seesaw with fine-tuned cancellation; this alone gives at most $0.03$ GeV, but it pushes the pseudo-Goldstone modes $H_5^pm$ heavy and, when combined with misalignment, reduces the splitting required for the 1-$\\sigma$ range to about $0.7$ GeV. The ordinary aligned model's ceiling of $0.0012$ GeV is the baseline the paper sets out to beat.","pith_inferences":["The paper never computes the one-loop effective potential minimum or a tunneling rate, so an obvious follow-up is a numerical scan of $V_{CW}$ in the $v_chi$-$v_xi$ plane to check whether the misaligned vacuum is the global minimum or a sufficiently long-lived metastable one at the quoted splittings.","The pseudo-Goldstone modes $H_5^pm$ from breaking custodial $SU(2)_c$ down to $U(1)$ are the natural place to look for a collider signature that distinguishes this proposal from a plain alignment scenario, since their masses are pushed up by the same $h_{ij}$ couplings that raise $Delta m_W$.","Because the $W$ mass shift here is dominated by a tree-level $rho$ parameter effect rather than by oblique loops, the same trick should transfer to any extended Higgs sector with two or more multiplets whose vacuum values can drift apart by a GeV, which makes the mechanism broader than the Georgi-Machacek setting.","The fine-tuned cancellation between type-I and type-II seesaw contributions, needed to keep neutrino masses at $10^{-3}$ eV while $h_{ij} sim 10^{-2}$, is a testable liability: a future measurement pinning the absolute neutrino mass scale would constrain how much of the $W$ mass shift can come from this channel."],"forward_implications":["A triplet splitting of roughly $0.7$ to $0.8$ GeV with $v_chi lesssim 15$ GeV is enough to place $Delta m_W$ in the 1-sigma CDF-II window, so the required custodial breaking is small and does not require a new mass threshold.","The doubly charged Higgs $H^{++}$ is pushed above about $600$ GeV in the misaligned case, and can drop below $400$ GeV once the right-handed neutrino sector is added, which reopens Barr-Zee contributions relevant to the muon anomalous magnetic moment.","Neutrino-triplet Yukawa couplings of order $10^{-2}$ become admissible only with the right-handed neutrino extension, since the ordinary Georgi-Machacek model would need $h_{ij} sim 10^{-13}$ at $v_Delta sim 10$ GeV.","The right-handed neutrino mass scale of $10^2$ to $10^4$ TeV that the fit favours is compatible with resonant leptogenesis, so baryogenesis and the $W$ mass shift can share one sector.","Because the two breaking sources add constructively, a future tightening of the CDF-II central value would be met by increasing either the splitting or the $h_{ij}$ coupling rather than by abandoning the framework."],"supporting_citations":[{"why":"Supplies the CDF-II $W$ boson mass measurement of $80{,}433.5 pm 9.4$ MeV that the whole paper is trying to accommodate.","marker":"[3]"},{"why":"Supplies the Standard Model expectation of $80{,}357 pm 8$ MeV, which defines the size of the discrepancy to be explained.","marker":"[4]"},{"why":"The original Georgi-Machacek construction whose custodial-symmetry structure sets the baseline the paper must beat.","marker":"[35]"},{"why":"Fixes the scalar potential conventions, the $SU(2)_L times SU(2)_R$ field representation, and the vacuum alignment condition $v_chi = v_xi$ used throughout.","marker":"[47]"},{"why":"Provides the general custodial-symmetry-breaking scalar potential and the argument that hypercharge loop effects remain under control up to high scales.","marker":"[64]"},{"why":"Analyses the vacuum structure of the $Z_2$-symmetric potential and the competition between custodial and non-custodial minima, which underlies the misalignment proposal.","marker":"[67]"},{"why":"Gives the electroweak oblique-parameter fit including the new CDF-II $m_W$ value, the benchmark against which the computed $S$ and $T$ are judged.","marker":"[85]"},{"why":"Supplies the $s_H lesssim 0.2$ upper bound imposed on the scanned parameter space.","marker":"[62]"},{"why":"Supplies the $text{BR}(mu to e gamma) < 4.2 times 10^{-13}$ bound that caps $|h_{ij}|$ and forces the right-handed neutrino scale above roughly $50$ TeV.","marker":"[96]"},{"why":"The SARAH code used to generate the model files that feed the SPheno spectrum calculation behind every numerical result.","marker":"[89]"}],"fun_headline_variants":["Misaligned triplets can lift the W mass into the CDF-II range","Ordinary Georgi-Machacek falls short; triplet splitting can reach CDF-II","Right-handed neutrinos alone can add at most 0.03 GeV to the W mass","Combined triplet misalignment and RH neutrinos can fit the CDF-II W mass","With right-handed neutrinos a 0.7 GeV triplet splitting can suffice"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The argument assumes that the Georgi-Machacek scalar potential, once one-loop corrections are included, actually has a stable or long-lived vacuum in which the two triplet vacuum values differ by about $0.7$ to $0.8$ GeV; the paper asserts this is reasonable but presents no effective-potential minimum, no tunneling rate and no lifetime estimate.","fun_headline_variants_meta":{"raw":{"variants":["Misaligned triplets can lift the W mass into the CDF-II range","Ordinary Georgi-Machacek falls short; triplet splitting can reach CDF-II","Right-handed neutrinos alone can add at most 0.03 GeV to the W mass","Combined triplet misalignment and RH neutrinos can fit the CDF-II W mass","With right-handed neutrinos a 0.7 GeV triplet splitting can suffice","A 0.8 GeV triplet splitting can reach the CDF-II 1-sigma window","Ordinary Georgi-Machacek tops out at 0.0012 GeV for the W mass shift","The CDF-II W mass needs custodial symmetry breaking beyond aligned triplets","Small triplet VEV misalignment can supply most of the CDF-II W mass shift","Low-scale RH neutrinos can add 0.03 GeV to the W mass shift","Triplet splitting near 0.7 GeV works with the RH neutrino sector","Aligned Georgi-Machacek cannot explain the CDF-II W mass alone","Custodial symmetry breaking in two places can fit the CDF-II W mass","Triplet VEV splitting of 0.8 GeV can enter the CDF-II 1-sigma range","RH neutrino couplings can raise the Georgi-Machacek W mass shift","Misaligned triplet VEVs can preserve the scalar potential at tree level","A small v_xi minus v_chi splitting can lift Delta m_W","The ordinary GM ceiling of 0.0012 GeV is below the CDF-II excess","Two custodial-breaking effects can reach the CDF-II W mass range","Triplet misalignment can reduce the splitting needed for CDF-II"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":3053,"prompt_tokens":1306,"completion_tokens":1747,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":1384}},"tokens_in":1306,"tokens_out":1747,"duration_ms":27739,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":1384,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-30T22:45:43.400351+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A calculation of the one-loop effective potential in the $v_chi$-$v_xi$ plane, with the parameters that give $Delta m_W$ in the 1-$\\sigma$ CDF-II window, showing that no minimum exists at splittings of order $0.7$ to $0.8$ GeV, or that the misaligned stationary point is a saddle or decays faster than the age of the universe, would remove the mechanism's footing.","supporting_citations":[{"cited_title":"Testing the custodial symmetry in the Higgs sector of the Georgi-Machacek model","cited_arxiv_id":"1211.2658","evidence_quote":"Fixes the scalar potential conventions, the $SU(2)_L times SU(2)_R$ field representation, and the vacuum alignment condition $v_chi = v_xi$ used throughout."},{"cited_title":"Effects of custodial symmetry breaking in the Georgi-Machacek model at high energies","cited_arxiv_id":"1704.08512","evidence_quote":"Provides the general custodial-symmetry-breaking scalar potential and the argument that hypercharge loop effects remain under control up to high scales."},{"cited_title":"Vacuum structure of the $\\mathbb{Z}_2$ symmetric Georgi-Machacek model","cited_arxiv_id":"2012.07758","evidence_quote":"Analyses the vacuum structure of the $Z_2$-symmetric potential and the competition between custodial and non-custodial minima, which underlies the misalignment proposal."},{"cited_title":"Electroweak Precision Fit and New Physics in light of $W$ Boson Mass","cited_arxiv_id":"2204.03796","evidence_quote":"Gives the electroweak oblique-parameter fit including the new CDF-II $m_W$ value, the benchmark against which the computed $S$ and $T$ are judged."},{"cited_title":"Updated constraints on the Georgi-Machacek model from LHC Run 2","cited_arxiv_id":"2003.02272","evidence_quote":"Supplies the $s_H lesssim 0.2$ upper bound imposed on the scanned parameter space."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the $text{BR}(mu to e gamma) < 4.2 times 10^{-13}$ bound that caps $|h_{ij}|$ and forces the right-handed neutrino scale above roughly $50$ TeV."},{"cited_title":"Staub; Computer Physics Communications 185 (2014) pp","cited_arxiv_id":null,"evidence_quote":"The SARAH code used to generate the model files that feed the SPheno spectrum calculation behind every numerical result."}],"review_version":1}