{"id":"3300641d-e55d-4c7d-8b32-a9efdcb2f2d8","arxiv_id":"1908.06186","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In QCH models the large enhancement expected in gg to ZZ cancels once the correct i epsilon branch is used, while gg to HZ develops an order-of-magnitude excess at high invariant mass.","lead":"The authors simulate how a 'quantum critical' Higgs, one that lives inside a strongly interacting conformal sector, would show up at the LHC and at a future 100 TeV collider. They find that the most promising channel is gg to HZ, which shows a large enhancement, while the usually studied gg to ZZ channel looks almost Standard Model-like because the modified propagator and vertex cancel.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"HZ enhancement rests on identifying the 5D vertex with the flat-profile Mandelstam form factor; no direct check against Eq. (3.37) is given, so the central LHC signature is not yet established.","rationale":"The reader's weakest_assumption is exactly this: the HZ prediction assumes the minimal-coupling form factor (5.3) rather than a direct computation of the vertex in the full 5D model. I agree that this is the load-bearing assumption. The ZZ cancellation is comparatively robust because Ward identities tie the form factor to the inverse propagator, and the paper verifies its ZZ implementation against an independent code. The HZ case has no analogous cross-check, and the predicted effect is large, so even moderate form-factor differences at high q^2 can change the conclusion. The paper is honest about the simplifying assumption of SM gauge bosons and high gauge thresholds, but it does not demonstrate that the simplification is harmless in the kinematic region plotted. The concern is not fatal: a high gauge threshold is a legitimate benchmark, and the calculation is coherent within that benchmark. The appropriate status is therefore CONDITIONAL, which is what the reader already assigned; no verdict change is needed, but the concrete test should be run before the HZ signature is used as a model prediction.","tokens_in":19192,"tokens_out":13204,"duration_ms":142997,"concrete_test":"Evaluate Eq. (3.37) in the Sec. 4 model with the gauge profile a(q,z) obtained by solving Eq. (3.30) for a finite gauge threshold mu_g (e.g. 5 and 10 TeV), and compare the resulting f_alpha_beta(p,q1,q2) with Eq. (5.3) over q^2 from threshold to (2 TeV)^2, at mu = 300 GeV and Delta = 1.5. Then re-run the gg -> HZ simulation of Fig. 18 using the direct form factor (and, if different, the longitudinal propagator (4.6)); if the high-m_HZ excess is reduced by more than the statistical spread of the figure, the paper's LHC conclusion is conditional on the flat-profile limit rather than a robust 5D prediction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline LHC signature is the enhanced gg->HZ tail (Figs. 18-20). What actually enters the simulation is not the 5D HZZ vertex but the Mandelstam/minimal-coupling form factor (5.3), which follows from the nonlocal Higgs kinetic term only when the electroweak gauge fields are treated as flat profiles with thresholds above the energies probed. The paper states this in Sec. 4 ('we will work with SM gauge bosons') and Sec. 5.3 ('transverse components ... threshold far larger than the Higgs'). Yet the HZ process samples one Z leg at q^2=m_HZ^2 up to roughly (2 TeV)^2, where the profile a(q,z) from Eq. (3.30) and the longitudinal-sector mixing can no longer be assumed flat. The only defence is the sentence that deviations from (4.7) are small where the warp factor suppresses the integrand; no numerical comparison between the bulk integral (3.37) and (4.7)/(5.3) is shown for this kinematic range. If the true vertex falls differently in p^2, the advertised HZ excess in Fig. 18 is not a prediction of the 5D model. The same caveat applies to the longitudinal gauge propagator (4.6), which is not obviously included in the MG implementation for the off-shell Z*. This is the load-bearing step: the new, experimentally actionable result rests on an unverified identification of two different vertices, not on an internal inconsistency.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies Quantum Critical Higgs (QCH) models, in which the Higgs is part of a strongly coupled conformal sector broken by a threshold scale, and uses AdS/CFT duals with soft walls to compute Higgs propagators and form factors. Two five-dimensional models are presented: a soft-wall model and a more minimal model with analytic form factors. The authors implement the minimal model in MadGraph5 and study gg→H→ZZ, gg→H→γγ, and gg→Z→HZ at the LHC and a 100 TeV collider. The main positive claim is that gg→HZ has a large enhancement in the high-invariant-mass tail, while the apparent enhancement in gg→ZZ is cancelled by the combination of the Higgs propagator and the HZZ form factor once the correct iε prescription is used. The paper also provides details of the MadGraph implementation and compares the ZZ channel against the GGZZ code.","tokens_in":19541,"tokens_out":4180,"duration_ms":44297,"significance":"If the central HZ prediction holds, the paper identifies an experimentally actionable LHC signature for QCH models and corrects an earlier claim of a large enhancement in gg→ZZ. The ZZ cancellation is explained as a consequence of gauge invariance and is properly credited to Ref. [55]; the iε/branch-cut discussion is a useful clarification. The paper also ships a MadGraph implementation and validates it against GGZZ, which is a strength. The work is phenomenological and parameter-dependent, with benchmark choices for Δ and μ, but it does not fit any data, so the predictions are falsifiable. The main limitation is that the advertised HZ signature is computed from the Mandelstam form factor rather than from a direct evaluation of the 5D bulk vertex, leaving the new cross-section prediction not fully tied to the 5D construction.","major_comments":[{"comment":"The HZ enhancement shown in Figs. 18–20 is computed with the Mandelstam form factor (5.3), which follows from the non-local Higgs kinetic term after treating the electroweak gauge profiles as flat and assuming the transverse gauge threshold is far above the energies probed. In the HZ process the off-shell Z leg carries q^2=m_HZ^2 up to roughly (1.4 TeV)^2, a range in which the gauge profile a(q,z) from Eq. (3.30) and the longitudinal-sector mixing (4.6) are not demonstrated to be flat. The paper asserts in §4 that deviations from (4.7) are small because the warp factor suppresses the integrand, but no numerical comparison between the bulk integral (3.37) and the flat-profile expressions (4.7)/(5.3) is shown for this kinematic range. If the true 5D vertex falls differently in p^2, the advertised gg→HZ excess is not a prediction of the 5D model; this is the load-bearing step for the main LHC signature.","section":"§4, Eq. (4.7) and §5.3, Eq. (5.3)"},{"comment":"The MadGraph implementation is described in Appendix C, but it is not stated whether the off-shell Z* propagator in gg→Z→HZ is the SM propagator or the modified longitudinal propagator (4.6). The production amplitude depends on this choice, and the longitudinal-sector continuum is one of the places where QCH effects could appear. The authors should specify exactly which propagator is used for the Z* line in the HZ calculation and, ideally, compare results with and without the longitudinal modification.","section":"§5.3 and Appendix C"},{"comment":"The claim that the backreacted metric of the minimal model still yields an effective continuum relies on tuning the AdS radius R such that the would-be KK mass splitting is below the Higgs width. The appendix gives zs but does not provide the numerical values of R/M5 needed to achieve Δm_KK≤Γ_H, nor does it demonstrate that this tuning leaves the computed spectral densities and form factors unaffected. Since the continuum interpretation underpins the propagators used in the collider analysis, this point should be quantified or explicitly stated as a parameter choice rather than left as an implicit tunable assumption.","section":"Appendix B"}],"minor_comments":[{"comment":"There is a typo: 'hierarcy' should be 'hierarchy'.","section":"Page 3, footnote 1"},{"comment":"The sentence 'there is no new form factor for Hγγ interactions' is imprecise; the vertex has no QCH form factor in the model, but the energy dependence in the gg→γγ channel comes from the modified Higgs propagator, so the phrase could be clarified.","section":"§5.2"},{"comment":"The normalization constants after the field redefinitions are dimensionful; please specify the mass dimension of h_QCH and state explicitly how the normalization is fixed in the MadGraph implementation so that the reported cross sections are reproducible.","section":"Eqs. (3.22), (4.4)"},{"comment":"The vertical axes appear to show negative event counts on a logarithmic scale, which is not meaningful as printed; please check the figure rendering and clarify whether the plotted quantity is the event count or the difference from the Standard Model.","section":"Figs. 15 and 16"}],"recommendation":"major_revision","confidential_remarks":"The paper is well within the scope of a phenomenological hep-ph journal. The main issue is not internal inconsistency but the unverified identification of the flat-profile Mandelstam form factor with the full 5D vertex in the kinematic range relevant for HZ production. This is fixable by adding a numerical comparison of Eq. (3.37) with Eq. (5.3) and by clarifying the Z* propagator used in the simulation. The paper is honest about its assumptions and about the earlier discrepancy in the ZZ channel, which is a positive feature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: This paper does something useful and honest: it corrects the same program's earlier prediction that QCH gives a large gg->ZZ enhancement. With the correct i epsilon branch on (mu^2-p^2)^nu, the enhancement dies, and the cancellation between the Higgs propagator and the HZZ form factor is exactly what gauge invariance plus the oblique-Higgs result in [55] require. The authors validate their MadGraph implementation against GGZZ, which is genuine checking. The new positive candidate is gg->HZ: an enhanced high-m_HZ tail that could be seen at the LHC or a 100 TeV machine. I think the ZZ part is on solid ground. The HZ part is a real finding, but it is softer than the conclusions advertise.\n\nThe load-bearing assumption is in Sec. 5.3. What enters the simulation is not the 5D vertex integral (3.37); it is the flat-profile Mandelstam form factor (5.3), valid when gauge zero-mode profiles are flat and the gauge threshold is far above the energies probed. The HZ process samples one Z leg at q^2 = m_HZ^2 up to roughly (2 TeV)^2. In that range, \"threshold far above the Higgs\" is doing a lot of work. The paper says deviations from (4.7) are small because the warp factor suppresses the integrand, but it never shows a numerical comparison between (3.37) and (4.7)/(5.3) in the HZ kinematic region. If the true vertex falls differently with p^2, the advertised excess in Figs. 18-20 is not a prediction of the 5D model. The stress-test note is right to flag this, and it should be the main thing a referee asks for. Similarly, the longitudinal gauge propagator (4.6) is not obviously what MG uses for off-shell Z*; a short check there would remove another ambiguity.\n\nMinor points: the gamma gamma plots have an unexplained sign convention, most likely a plotting artifact; and Appendix B needs a tuned R to keep the would-be KK splitting below the Higgs width. Neither breaks the paper's qualitative conclusions, but they make the model less self-contained than it first appears.\n\nWho benefits: BSM phenomenologists working on continuum/unparticle Higgs models and people designing LHC or FCC searches. It deserves a serious referee. My recommendation: accept it into the review process, and require the authors to either compute the full 5D HZZ vertex in the HZ regime or state plainly that the HZ prediction is an approximation that has not been checked there. As it stands, the paper's advertised search channel is not yet pinned to the 5D model.","headline":"A careful, self-correcting paper that kills the old gg->ZZ QCH signal and points to gg->HZ instead, but the new search channel rests on a flat-profile vertex that has not been checked against the 5D integral in the HZ regime.","tokens_in":20094,"tokens_out":4161,"would_cite":true,"duration_ms":39335,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.60.Fr","12.60.Rc","11.25.Tq"],"model":"deepseek-v4-flash","headline":"This paper shows that in Quantum Critical Higgs models, gg→ZZ stays Standard-Model-like while gg→HZ is the promising discovery channel.","keywords":["Quantum Critical Higgs","AdS/CFT correspondence","soft-wall model","Higgs compositeness","Higgs form factor","gluon fusion","associated Higgs production","off-shell Higgs"],"falsifier":"A measurement of the $gg\\to HZ$ invariant-mass spectrum at a 13 TeV hadron collider: the paper predicts a clear excess over the Standard Model at $m_{HZ}$ values above roughly $\\mu$ when $\\mu \\approx 300$ GeV and $\\Delta \\approx 1.5$; the absence of such an excess would falsify the central claim.","tokens_in":18935,"feed_emoji":"⚛️","tokens_out":13154,"duration_ms":109208,"temperature":0.7,"pith_summary":"The paper examines how Quantum Critical Higgs (QCH) models, in which the Higgs is a composite of a nearly conformal sector, would appear at colliders. It constructs two five-dimensional AdS/CFT duals with a soft breaking of conformality and computes the Higgs propagator and its coupling to gauge bosons. The central result is that in gluon-fusion production of Z pairs the anomalous momentum dependence of the Higgs propagator is cancelled by the momentum dependence of the HZZ vertex, so the rate stays close to the Standard Model. In contrast, the associated production of a Higgs with a Z boson, $gg\\to HZ$, is predicted to show large enhancements at high invariant mass. The authors argue this makes $gg\\to HZ$ the most promising channel for discovering a QCH at the LHC.","feed_headline":"Gauge invariance masks the critical Higgs in ZZ, exposes it in HZ","feed_subtitle":"The Higgs propagator and Z-pair vertex cancel, so the discovery channel is high-mass HZ.","key_machinery":"The load-bearing object is the momentum-dependent function $K(p)=(\\mu^2-p^2)^\\nu$ (with $\\nu=2-\\Delta$) that appears in the Higgs inverse propagator and, through gauge invariance, in the Higgs coupling to gauge bosons. In the simpler 5D model the bulk-to-boundary propagator is a modified Bessel function and the holographic reduction yields the quadratic term $\\Sigma(p^2) = -(\\mu^2-p^2)^\\nu + (\\mu^2-m_h^2)^\\nu$. Gauge invariance forces the $HZZ$ form factor to be a combination of differences of $K$ evaluated at the external momenta, so that the product of the propagator and the vertex has the same high-energy falloff as the Standard Model. The choice of the $i\\epsilon$ branch at the threshold $p^2=\\mu^2$ is the detail that converts the originally claimed constructive interference in $gg\\to ZZ$ into the Standard-Model-like destructive interference.","core_discovery":"The core claim is a quantitative prediction for QCH collider signatures. In the minimal 5D model, the holographic Higgs inverse propagator takes the form $\\Sigma(p^2) = -(\\mu^2-p^2)^\\nu + (\\mu^2-m_h^2)^\\nu$, producing a continuum spectral density above the threshold $\\mu$. Gauge invariance, implemented by gauging the non-local kinetic term, fixes the $HZZ$ vertex in terms of the same function $K(p)=(\\mu^2-p^2)^\\nu$. Consequently, at high $p^2$ the propagator (falling as $1/p^{2\\nu}$) and the vertex (falling as $1/p^{2-2\\nu}$) multiply to reproduce Standard Model behaviour once the correct $i\\epsilon$ branch is chosen, so the previously claimed large $gg\\to ZZ$ enhancement was an artefact of the wrong branch. The $HZ$ production amplitude, however, involves the vertex in a different combination and is predicted to show relative growth, with clear excesses in the $m_{HZ}$ and transverse-momentum distributions.","pith_inferences":["We infer that the same cancellation mechanism should make off-shell $gg\\to W^+W^-$ Standard-Model-like when the longitudinal $W$ threshold is high, so diboson tails are a less promising probe than the $HZ$ channel.","The analytic-continuation subtlety implies that other unparticle-like models with fractional-power propagators should be audited: advertised enhancements that depend on the branch choice of a non-integer power may be artefacts.","A future high-energy $e^+e^-$ collider could measure the $HZ$ form factor directly in $e^+e^- \\to HZ$ with an off-shell Higgs, testing the minimal-coupling vertex assumed here in a cleaner environment than gluon fusion."],"forward_implications":["The off-shell $gg\\to ZZ$ cross section in QCH models closely tracks the Standard Model once the $i\\epsilon$ branch is chosen correctly, so earlier claims of a large enhancement in this channel are not viable.","The $gg\\to HZ$ channel offers a clean, observable QCH signal at the LHC: for a threshold around 300 GeV and scaling dimension around 1.5, the $m_{HZ}$ distribution shows a large excess over the Standard Model even with 30 fb$^{-1}$.","The $gg\\to \\gamma\\gamma$ channel probes the Higgs propagator directly and would show an energy-growing excess, but the rate at the 13 TeV LHC is too small to explain observed events; a 100 TeV collider would make it visible.","Because the cancellation in $gg\\to ZZ$ is enforced by gauge invariance, searches for QCH should focus on associated Higgs production and di-photon tails rather than on off-shell four-lepton final states.","The model requires the would-be Kaluza-Klein mass splitting to be below the Higgs width, a tuning of the AdS curvature radius, for the continuum description to hold."],"supporting_citations":[{"why":"The original QCH proposal whose predicted gg→ZZ enhancement this paper traces to a missing iε.","marker":"[2]"},{"why":"The soft-wall model used for the complete 5D QCH construction.","marker":"[39]"},{"why":"The simpler 5D model that yields the analytic propagator and form factors used in the collider analysis.","marker":"[40]"},{"why":"The method of gauging a non-local action used to derive the minimal-coupling form factor.","marker":"[46]"},{"why":"The same gauging procedure as applied to general non-local Lagrangians.","marker":"[48]"},{"why":"The previous application of this gauging to the Unhiggs, providing the HZZ vertex form.","marker":"[50]"},{"why":"The oblique-Higgs analysis showing that propagator and vertex modifications cancel, which supports the paper's cancellation claim.","marker":"[55]"},{"why":"The Standard Model gg→ZZ amplitude used to benchmark the interference and the SM baseline.","marker":"[56]"}],"fun_headline_variants":["Critical Higgs: ZZ is noise, HZ is signal","Holographic Higgs: ZZ stays SM, HZ shows criticality","Critical Higgs hides in ZZ, appears in HZ","AdS/CFT predicts critical Higgs: ZZ null, HZ excess"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predicted HZ enhancement assumes that the Higgs–Z vertex takes the minimal-coupling form derived from the non-local Higgs kinetic term, a formula the paper does not derive directly from its full 5D model with realistic non-flat gauge profiles.","fun_headline_variants_meta":{"raw":{"variants":["Critical Higgs: ZZ is noise, HZ is signal","Holographic Higgs: ZZ stays SM, HZ shows criticality","Critical Higgs hides in ZZ, appears in HZ","AdS/CFT predicts critical Higgs: ZZ null, HZ excess"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000561,"raw_usage":{"total_tokens":2643,"prompt_tokens":899,"completion_tokens":1744,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":515,"completion_tokens_details":{"reasoning_tokens":1671}},"tokens_in":515,"tokens_out":1744,"duration_ms":12145,"temperature":1.0,"reasoning_tokens":1671,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:55:22.342852+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A measurement of the $gg\\to HZ$ invariant-mass spectrum at a 13 TeV hadron collider: the paper predicts a clear excess over the Standard Model at $m_{HZ}$ values above roughly $\\mu$ when $\\mu \\approx 300$ GeV and $\\Delta \\approx 1.5$; the absence of such an excess would falsify the central claim.","supporting_citations":[{"cited_title":"The Soft-Wall Standard Model","cited_arxiv_id":"0808.3977","evidence_quote":"The soft-wall model used for the complete 5D QCH construction."},{"cited_title":"Quantum Electrodynamics Without Potentials,","cited_arxiv_id":null,"evidence_quote":"The method of gauging a non-local action used to derive the minimal-coupling form factor."},{"cited_title":"Gauging nonlocal Lagrangians,","cited_arxiv_id":null,"evidence_quote":"The same gauging procedure as applied to general non-local Lagrangians."},{"cited_title":"The Unhiggs: electroweak symmetry breaking via an unparticle,","cited_arxiv_id":null,"evidence_quote":"The previous application of this gauging to the Unhiggs, providing the HZZ vertex form."},{"cited_title":"Z Boson Pair Production Via Gluon Fusion,","cited_arxiv_id":null,"evidence_quote":"The Standard Model gg→ZZ amplitude used to benchmark the interference and the SM baseline."}],"review_version":1}