{"id":"554f6770-289b-4d88-ab75-eee73f344e53","arxiv_id":"2603.18799","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.5,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"In the RxSM, singlet-driven SFOEWPTs yield strong LISA GW signals with SM-like Higgs couplings, while doublet-driven ones yield large κ_λ deviations visible at ILC1000 but weak GWs.","lead":"A simple real-singlet extension of the Standard Model can produce a strong first-order electroweak phase transition in two distinct ways. One way leaves the Higgs almost Standard-Model-like and is best seen by LISA gravitational waves; the other distorts the Higgs self-coupling and is best seen at a future e+e- collider.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the wall-velocity sensitivity already flagged by the reader.","rationale":"The strongest claim is a clean phenomenological dichotomy inside a well-studied model, obtained with consistent one-loop methods and public codes. The only assumption that can quantitatively rearrange the “detectable vs. undetectable” boundary is the fixed wall velocity already identified by the reader. Because the paper is transparent about this limitation and the qualitative complementarity (SM-like Higgs + strong GWs versus large κ_λ + collider signals) remains robust under plausible variations of vw, the CONDITIONAL verdict with high confidence is appropriate and needs no further adjustment. The two hand-chosen planes and the lack of public cards are secondary presentation issues that do not undermine the central argument.","tokens_in":16564,"tokens_out":457,"duration_ms":5598,"concrete_test":"Recompute the SNR maps of Figs. 4 (left) and 6 (left) for a continuous scan vw∈[0.4,1.0] (or with a simple friction-based estimate of vw from the latent heat and plasma parameters already available in BSMPT). If the region of BP2 with SNR>10 remains empty or only a thin sliver while BP1 stays largely above threshold, the dichotomy survives; if a sizable fraction of BP2 crosses SNR=10, the “undetectable” half of the claim must be softened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader’s weakest_assumption correctly isolates the only load-bearing soft spot: SNR values (and therefore the “detectable vs. undetectable” dichotomy between BP1 and BP2) rest on a fixed, pessimistic bubble-wall velocity vw=0.95 that is not computed from the model parameters. The paper itself states that vw∼0.6 can raise the SNR by a large factor, so the claimed complementarity is only semi-quantitative. All other elements of the central claim—two disjoint thermal histories, consistent one-loop trilinear couplings, κ_λ ranges, and the qualitative collider/GW split—are internally consistent and supported by the published figures and public tools. No deeper inconsistency or hidden assumption that would overturn the dichotomy was found.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript studies the general real-singlet extension of the SM (RxSM) as a minimal setting that can realise a strong first-order electroweak phase transition (SFOEWPT). Using BSMPT 3.1.1 (with the RxSM newly implemented) the authors map the thermal histories of the scalar potential and identify six distinct patterns, three of which produce SFOEWPTs. Two representative benchmark planes are constructed: BP1 (singlet-driven) and BP2 (doublet-driven). One-loop corrections to the trilinear couplings λ_hhh and λ_hhH are evaluated consistently with anyH3 in a fully on-shell scheme and are fed both into the thermal analysis and into MadGraph predictions for e^{+}e^{-}\to Zhh and e^{+}e^{-}\to\nu\nu hh at ILC1000. The central claim is that the two classes of SFOEWPT yield complementary experimental signatures: BP1 produces LISA SNRs ≳ 10 while κ_λ remains SM-like; BP2 forces 1.35 ≲ κ_λ^{(1)} ≲ 1.7 (and correspondingly large deviations in the di-Higgs rates) while the LISA SNR stays below 10 for almost the entire plane.","tokens_in":16761,"tokens_out":1032,"duration_ms":8530,"significance":"If the reported dichotomy holds, the work supplies a concrete, falsifiable illustration of the complementarity between future e^{+}e^{-} colliders and LISA for reconstructing the shape of the Higgs potential. The consistent inclusion of one-loop trilinear couplings in both the thermal and collider calculations, the public-code implementation of the RxSM in BSMPT, and the explicit differential distributions with experimental cuts and polarisations constitute genuine technical advances over earlier RxSM studies. The two benchmark planes cleanly separate the phenomenological regimes and therefore provide useful targets for both communities.","major_comments":[{"comment":"The SNR values that underpin the claimed “detectable vs. undetectable” split between BP1 and BP2 are computed exclusively with the fixed, pessimistic wall velocity v_w = 0.95 (and three years of LISA observation). The text itself notes (around the discussion of Fig. 4 and Fig. 6) that a lower velocity v_w ∼ 0.6 can raise the SNR by a large factor. Because v_w is not derived from the model parameters, the quantitative complementarity is only semi-quantitative; a short sensitivity scan or an explicit statement of the range of v_w over which the dichotomy survives is needed to make the central claim robust.","section":null},{"comment":"The linear relations that define BP1 (Eq. (1)) and BP2 (Eq. (2)) are chosen so as to maximise either the GW signal or the κ_λ deviation. While the choices are transparent, the paper should demonstrate that the qualitative split (SM-like κ_λ + large SNR versus large κ_λ + small SNR) persists for nearby, less optimised slices of parameter space; otherwise the complementarity could be an artefact of the particular hyperplanes selected.","section":null}],"minor_comments":[{"comment":"Fig. 1 captions and the accompanying text use the labels A–F for thermal histories; it would help the reader if the same letters were printed directly on the panels.","section":null},{"comment":"The units of κ_SH in the right-hand panel of Fig. 6 and in the caption of Fig. 7 are occasionally written as “TeV” while the plotted values are in GeV; a uniform convention would avoid confusion.","section":null},{"comment":"A brief remark on the numerical stability of the one-loop effective potential near the vacuum-trapping boundary (region F of BP2) would reassure the reader that the sharp transition from SFOEWPT to trapping is not a lattice artefact of BSMPT.","section":null},{"comment":"The polarisation choice (−80 %, +30 %) and the integrated luminosity 3200 fb^{-1} for ILC1000 are stated only in the caption of Fig. 7; they should also appear in the main text of Sec. 5.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is a conference-proceedings summary of a longer arXiv paper (2510.12569). The technical content is solid and the complementarity message is clear; the only load-bearing soft spot is the fixed wall velocity, which can be addressed with a short additional paragraph or plot. I see no reason to reject or to demand a major re-analysis."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful takeaway is simple: in the RxSM the parameter space that produces a strong first-order electroweak phase transition splits into two practically disjoint classes. Singlet-driven transitions (their BP1) give LISA SNRs above 10 while the 125 GeV Higgs stays SM-like; doublet-driven ones (BP2) force 1.35–1.7 deviations in the one-loop κ_λ and clear ILC1000 di-Higgs signals, but almost never reach SNR 10. That experimental complementarity is what the paper actually delivers.\n\nWhat is new is the consistent use of the same one-loop, on-shell trilinear couplings (from anyH3) both in the finite-temperature potential (via their BSMPT implementation) and in the MadGraph collider matrix elements. Earlier RxSM phase-transition papers did not close that loop. The thermal-history classification (six cases, three of them SFOEWPT) is cleanly mapped with a public code, the two benchmark planes are explicit, and the ILC1000 distributions include polarisation, cuts and the resonant H contribution. The math and the citation pattern look solid; they cite the relevant prior literature and do not over-claim.\n\nThe soft spot is exactly the one the reader flagged: all SNRs assume vw = 0.95. The paper itself notes that vw ~ 0.6 can raise the signal substantially, so the “detectable vs undetectable” dichotomy is only semi-quantitative. The planes are also hand-chosen linear slices that maximise the effect of interest; that is fine for illustration but means the maps are not a full scan. Neither issue breaks the central claim.\n\nThis is for people working on electroweak baryogenesis, multi-scalar models, or the physics case for LISA + a high-energy e+e- collider. It is not a resolution of the baryon asymmetry, just a clear experimental roadmap inside a simple model. I would send it to a serious referee; the calculation is careful enough to deserve the time. Worth reading and citing if you need a concrete example of collider–GW complementarity.","headline":"Clean, usable map of two disjoint SFOEWPT regimes in the RxSM, with consistent one-loop trilinear couplings; the LISA/collider split is real but only semi-quantitative because of fixed wall velocity.","tokens_in":17385,"tokens_out":545,"would_cite":true,"duration_ms":5653,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Singlet-driven and doublet-driven strong first-order electroweak phase transitions leave opposite experimental footprints: gravitational waves or large Higgs self-coupling deviations.","keywords":["RxSM","strong first-order electroweak phase transition","gravitational waves","LISA","trilinear Higgs coupling","di-Higgs production","ILC1000","electroweak baryogenesis"],"falsifier":"A LISA detection with SNR greater than 10 together with a measured trilinear Higgs coupling still consistent with the Standard Model within a few percent would confirm the singlet-driven class; a measured coupling modifier between 1.35 and 1.7 with no corresponding LISA signal would confirm the doublet-driven class; either opposite combination would falsify the claimed complementarity.","tokens_in":17457,"feed_emoji":"🌌","tokens_out":1115,"duration_ms":10022,"temperature":0.7,"pith_summary":"The paper maps how a strong first-order electroweak phase transition can occur inside the real-singlet extension of the Standard Model and shows that the transition falls into two disjoint classes with opposite experimental signatures. When the transition is driven mainly by the singlet field, the 125 GeV Higgs boson stays essentially Standard-Model-like, so colliders see almost nothing, yet the latent heat and duration of the transition produce a stochastic gravitational-wave background that LISA can detect with signal-to-noise ratio greater than 10. When the transition is instead driven by the electroweak doublet, the same barrier that makes the transition strong forces the trilinear Higgs self-coupling to be 35–70 percent larger than its Standard-Model value; that deviation produces clear excesses or deficits in di-Higgs production at a 1 TeV electron-positron collider, while the gravitational-wave signal remains marginal. Because both calculations consistently include one-loop corrections to the same trilinear couplings, the two probes become complementary: a positive LISA signal with no collider deviation points to the singlet-driven class, while a large measured self-coupling with a weak gravitational-wave signal points to the doublet-driven class. The result therefore supplies a concrete experimental strategy for reconstructing which shape of the Higgs potential was realised in the early Universe.","feed_headline":"Two paths to a strong phase transition leave opposite signals","feed_subtitle":"Singlet-driven cases light up LISA; doublet-driven cases light up e+e- di-Higgs rates","key_machinery":"Two benchmark planes that isolate the two driving directions of the transition, with all relevant trilinear scalar couplings evaluated at full one-loop order both for the finite-temperature effective potential and for the collider cross sections.","core_discovery":"In the RxSM the parameter regions that realise a strong first-order electroweak phase transition split into two disjoint phenomenological classes: singlet-driven transitions produce LISA signal-to-noise ratios above 10 while the one-loop trilinear Higgs coupling modifier stays within a few percent of unity, whereas doublet-driven transitions force that modifier into the range 1.35–1.7 (and correspondingly large deviations in e+e- di-Higgs rates) while the LISA signal-to-noise ratio stays below 10 for almost the entire plane.","pith_inferences":["If future lattice or real-time simulations fix the bubble-wall velocity well below 0.95, the “GW-only” window of the singlet-driven plane may shrink and the two classes could begin to overlap in SNR space.","The same complementarity logic should apply to any multi-scalar model in which the barrier can be generated either by a singlet or by the electroweak doublet itself; the RxSM merely supplies the cleanest laboratory.","A null result at both LISA and ILC1000 would not kill the possibility of a strong first-order transition, but would force it into a narrow intermediate strip where both signals are just below threshold."],"forward_implications":["A positive LISA signal with SM-like Higgs couplings would select the singlet-driven region of the RxSM and rule out a pure doublet-driven barrier.","A measured trilinear coupling modifier of order 1.5 at ILC1000, even without a LISA signal, would select the doublet-driven region and indicate that the electroweak barrier itself drove the transition.","Differential m_hh distributions at a 1 TeV e+e- collider can separately resolve the resonant heavy-Higgs peak and the continuum shift induced by the modified self-coupling, giving two independent handles on the same potential.","Because the same one-loop couplings enter both the phase-transition calculation and the collider rates, a joint measurement would reconstruct which field direction dominated the early-Universe transition."],"fun_headline_variants":["Singlet-driven SFOEWPT lights LISA while hiding from colliders","Doublet-driven transitions boost di-Higgs rates mute GWs","RxSM phase paths split into LISA-only or collider-only signals","Opposite probes for singlet versus doublet electroweak transitions","Strong EWPT in RxSM yields LISA or e+e- footprints not both"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The claimed split between “detectable” and “undetectable” gravitational-wave signals rests on fixing the bubble-wall velocity at the pessimistic value 0.95; a lower velocity would raise the signal-to-noise ratio by a large factor and could erase the dichotomy.","fun_headline_variants_meta":{"raw":{"variants":["Singlet-driven SFOEWPT lights LISA while hiding from colliders","Doublet-driven transitions boost di-Higgs rates mute GWs","RxSM phase paths split into LISA-only or collider-only signals","Opposite probes for singlet versus doublet electroweak transitions","Strong EWPT in RxSM yields LISA or e+e- footprints not both"]},"model":"grok-4.5","effort":"low","cost_usd":0.004806,"raw_usage":{"total_tokens":1485,"prompt_tokens":930,"num_sources_used":0,"completion_tokens":99,"cost_in_usd_ticks":48060000,"prompt_tokens_details":{"text_tokens":930,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":456,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":930,"tokens_out":99,"duration_ms":4575,"temperature":1.0,"reasoning_tokens":456,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-13T22:23:23.202277+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A LISA detection with SNR greater than 10 together with a measured trilinear Higgs coupling still consistent with the Standard Model within a few percent would confirm the singlet-driven class; a measured coupling modifier between 1.35 and 1.7 with no corresponding LISA signal would confirm the doublet-driven class; either opposite combination would falsify the claimed complementarity.","supporting_citations":[],"review_version":1}