{"id":"3c73b34a-b0d1-4148-b4fd-c79bf03dc2f8","arxiv_id":"2506.03260","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In the inverted Type-I 2HDM, one-step and two-step strong first-order electroweak phase transitions live in largely separate parameter regions, and LISA-detectable gravitational wave signals come predominantly from the two-step paths.","lead":"This paper maps where a strong first-order electroweak phase transition can happen in the inverted Type-I two-Higgs-doublet model, and finds that one-step and two-step transition paths occupy partially non-overlapping regions of the parameter space. It also predicts that two-step transitions dominate the gravitational wave signals LISA could detect, and proposes two Higgs decay channels through which a 1.5 TeV CLIC collider could discover the new Higgs bosons.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Scan-derived exclusion ranges in Eq. (28) are not coverage-complete; the claimed one-step/two-step separation needs a scan-density and vacuum-tracer robustness check.","rationale":"The reader's weakest-assumption identification matches the most load-bearing vulnerability in the paper. The headline separation of one-step and two-step SFOEWPT parameter spaces is the basis for the abstract's quantitative ranges and for the collider-discrimination argument, but it is derived from a finite random scan whose coverage is not demonstrated. The authors explicitly flag algorithm dependence of the BSMPT minimum tracer, which is an honest limitation but still means the classification itself could shift with the tracing method. Other uncertainties, such as the assumed bubble-wall velocity in GW SNR calculations and the estimated rather than simulated SM backgrounds, are real but secondary: the phase-space separation is the central claim that the collider and GW analyses build upon. My concern therefore supports the reader's CONDITIONAL verdict rather than changing it. The concrete test proposed would settle whether the seemingly sharp boundaries in Eq. (28) are physical or artifacts of sampling and tracing.","tokens_in":840,"tokens_out":982,"duration_ms":44462,"concrete_test":"Rescan the full Eq. (22) ranges with at least 10x the density, or with a deterministic quasi-Monte Carlo / adaptive grid, and recompute the extrema in Eq. (28). In parallel, rerun the vacuum-phase tracing on the same inputs with BSMPT's alternative minimum-tracer modes and cross-check with an independent tracer such as PhaseTracer or CosmoTransitions. If the one-step mHpm lower bound drops below roughly 295 GeV, the two-step upper bound rises above roughly 351 GeV, or a nontrivial fraction of points changes transition classification between tracers, the separation claim must be weakened. Releasing scan data and scripts would make this check reproducible.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative separation in Eq. (28) and Sec. IV.B is inferred from the extrema of a random scan over the ranges in Eq. (22), not from a coverage-complete scan. With only 5,343 one-step and 4,486 two-step SFOEWPT points out of 2.36e6 physical points, the statement that one-step transitions are confined to mHpm in [295,441] GeV and tan(beta) in [4.2,8.8], while two-step transitions occupy mHpm in [100,350] GeV and tan(beta) in [2.5,45.4], is effectively an under-occupancy claim: the absence of found points outside these intervals is treated as exclusion. Random scanning can miss narrow or low-density regions, especially near the overlap window and at large tan(beta). The paper itself notes in Sec. IV.A that the SFOEWPT counts depend on BSMPT's default minimum-tracing algorithm, so both sampling density and vacuum-branch tracing affect which intervals are populated. If a denser or differently-traced scan finds one-step points below 295 GeV or two-step points above 351 GeV, the 'partial but significant separation' is weaker than presented, and the claimed collider discrimination based on mHpm and tan(beta) loses some force. This concern does not invalidate the existence of SFOEWPT regions, but it does undermine the precise exclusion ranges and the stronger reading of the separation as a robust discriminator.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates the electroweak phase transition (EWPT) in the inverted Type-I 2HDM, where the observed 125 GeV Higgs boson is identified as the heavier CP-even scalar H. Using public codes (2HDMC, ScannerS, HiggsTools, BSMPT) a random scan over the parameter ranges in Eq. (22) yields 2.36e6 physical parameter points, of which 5343 support a one-step SFOEWPT and 4486 support a two-step SFOEWPT via the second step; three-step cases are rare. The central quantitative claims are that the one-step and two-step SFOEWPT parameter spaces are partially yet significantly separated (Eq. 28: one-step mH± in [295,441] GeV, tanβ in [4.2,8.8]; two-step mH± in [100,350] GeV, tanβ in [2.5,45.4]), that negative sin(β−α) occurs almost exclusively in one-step scenarios, that LISA-detectable GW signals (SNR>10) come predominantly from two-step transitions (114 points vs 1, Eq. 29), and that the ∆F0–ξc correlation persists for one-step but breaks down for multi-step transitions. A collider analysis at the 1.5 TeV CLIC identifies e+e− → H+H− → W+W−hh as a promising channel, with two complementary final states motivated by enhanced h→γγ for negative sin(β−α).","tokens_in":42731,"tokens_out":8251,"duration_ms":89055,"significance":"If the quantitative separation in Eq. (28) and the GW counts in Eq. (29) are robust, the paper establishes a striking cosmology–collider complementarity: measuring mH± and tanβ at a future collider could discriminate one-step from multi-step EWPT histories, and a LISA detection would favor two-step transitions. The analysis uses standard public codes and provides reproducible numerics, benchmark points, and explicit transition-step classifications, which are strengths. The observation that the vacuum-uplifting measure ∆F0 correlates with ξc in one-step transitions but fails in multi-step cases is a useful caution for the community, since it shows that a zero-temperature proxy cannot replace a full finite-temperature computation when intermediate vacua are present. The claimed overlap structure between one-step and two-step regions is the central new result; however, as detailed below, the finite-scan derivation of exclusion intervals and the fixed bubble-wall-velocity assumption currently leave the quantitative claims insufficiently supported. The paper is therefore of moderate-to-high significance contingent on the robustness checks requested.","major_comments":[{"comment":"The statement 'if an observation yielded mH± < 295 GeV, only a two-step transition could have facilitated the SFOEWPT' is not supported by the paper's own samples. The three-step SFOEWPT benchmark BP3-step in Eq. (23) has mH± = 184.3 GeV, and the targeted scan in Section IV.B produced PT(3-step)_3 SFOEWPT points with mH± in [160,240] GeV. Thus a charged Higgs below 295 GeV can be associated with a three-step SFOEWPT, not only a two-step one. The authors should either report the ranges for all transition classes (including PT(2-step)_1 and PT(3-step)_3) in Eq. (28), or explicitly restrict the claim to 'the two dominant transition types' and avoid the unconditional wording. This is load-bearing because the abstract and introduction advertise the one-step/two-step separation as the key discriminator.","section":"Section IV.B (paragraph after Fig. 2)"},{"comment":"The exclusion intervals in Eq. (28) are the extrema of a finite random scan over the ranges in Eq. (22), with no convergence or coverage test to demonstrate that 'no points found' outside these intervals implies exclusion. The footnote attached to Eq. (27) explicitly states that the SFOEWPT counts depend on the BSMPT default minimum-tracing algorithm. Since the 'partial but significant separation' is an under-occupancy claim, the authors should (i) repeat the scan with at least two different sample sizes (e.g., 10^6 and 10^7 physical points) and show that the intervals stabilize; (ii) perform targeted scans in the boundary windows near mH± = 295 GeV and mH± = 351 GeV and at large tanβ, where sparse occupation is visible in Figures 3–5; and (iii) test the classification with an alternative minima-tracing setting (e.g., a different BSMPT mode or PhaseTracer). Without these, the precise boundaries in Eq. (28) cannot be interpreted as robust exclusion ranges, and the stronger reading of the separation as a reliable collider discriminator is not justified.","section":"Section IV.A and Eq. (28)"},{"comment":"The GW SNR values and the central statement that detectable LISA signals (SNR > 10) arise predominantly from two-step transitions (114 points vs 1) assume a fixed bubble wall velocity vw = 0.95. The paper correctly notes in Section III.D that vw is an input parameter not predicted from first principles. Since the sound-wave peak amplitude in Eq. (20) scales with max(vw, cs) (squared in one regime), a change in vw can shift points across the SNR > 10 threshold by an order-one factor. The authors should repeat the SNR calculation for at least two other plausible values (e.g., vw = 0.5 and vw = 1.0) and show how the counts in Eq. (29) change. If the strong dominance of two-step transitions persists, the qualitative conclusion is robust; otherwise the claim should be softened.","section":"Section IV.D, Eq. (29) and Figs. 8–10"}],"minor_comments":[{"comment":"The assertion that the SM backgrounds for W+W−bbτ+τ− and W+W−bbγγ are 'well below 1 ab' is based on an extrapolation from simplified parton-level processes, not on a full background computation; the authors should either provide a conservative quantitative upper bound from Monte Carlo tools or explicitly state that the background estimate is an expectation, not a simulated result.","section":"Section V.B, Eq. (33)"},{"comment":"The claims of a 'clear positive correlation' between ξc and ∆F0 for one-step transitions and its absence for multi-step transitions are made from visual inspection; reporting Spearman or Pearson correlation coefficients and p-values would make the comparison quantitative and more persuasive.","section":"Section IV.C, Fig. 7"},{"comment":"The footnote stating that the SFOEWPT counts depend on the BSMPT default minimum-tracing algorithm is important and should be elevated to the main text, since it directly qualifies the central quantitative results.","section":"Section IV.A, footnote to Eq. (27)"},{"comment":"The two-step charged-Higgs range is quoted as mH± ∈ [102.7, 351.4] GeV in Eq. (28) but as [100,350] GeV in the abstract and Section IV.B; the rounding should be made consistent.","section":"Eq. (28) and abstract"},{"comment":"When the expected background is zero, the Poisson significance in Eq. (34) is ill-defined; the decision to quote only signal event counts is reasonable, but the paper should make clear that discovery claims in the Nbg ≈ 0 regime rely on the background estimate and Poisson statistics, not on a quoted significance value.","section":"Section V.B, Eq. (34)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a solid application of standard tools to a moderately studied scenario, and the central qualitative claims about multi-step transitions are plausible. However, the key quantitative deliverables—the exclusion ranges in Eq. (28), the GW-detectability counts in Eq. (29), and the collider-based discrimination statement—need the robustness checks described in the major comments. The authors have the codes and the scan infrastructure to perform these checks, so I expect the issues to be addressable within a revision. No concerns about novelty disclosure or citation practices."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a useful, mostly sound phenomenological study. The genuinely new piece is the first systematic mapping of one-, two-, and three-step SFOEWPT regions in the inverted Type-I 2HDM, together with two non-obvious findings: LISA-detectable GW points (SNR > 10) are dominated by two-step transitions (114 vs 1), and the DeltaF0–xi_c correlation that holds for one-step transitions breaks down in multi-step cases. The collider chapter, with the h->gamma-gamma enhancement for negative sin(beta-alpha) and the proposed bb tau tau and bb gamma gamma channels, is a reasonable addition rather than a headline result. The authors use standard public tools (BSMPT, 2HDMC, ScannerS, HiggsTools) and are upfront about several of the limitations. No fitted input drives the target results, so circularity is not a concern.\n\nThe weak spot is exactly where the stress test lands. The exclusion intervals in Eq. (28) are inferred from the extrema of a finite random scan: 5,343 one-step and 4,486 two-step SFOEWPT points out of 2.36e6 physical points. The statement that one-step transitions are confined to mHpm in [295,441] GeV and tan(beta) in [4.2,8.8] is effectively an under-occupancy claim. The paper even notes in Sec. IV.A that the counts depend on BSMPT's default minimum-tracing algorithm, so both sampling density and vacuum-branch tracing can move the boundaries. I agree with the conditional verdict: the qualitative separation may well survive, but the precise ranges should not be quoted as hard exclusions until the authors release scan data, demonstrate coverage, and check robustness against the tracer algorithm. This is a moderate, not fatal, issue.\n\nTwo smaller soft spots: the GW SNR uses a fixed bubble wall velocity v_w = 0.95 throughout, which is standard practice but not defended for this model, and the collider background estimates are scaled from simpler parton-level processes rather than full high-multiplicity simulations. The \"negligible background\" claim is plausible but not proven; a real background study, or at least a convincing scaling argument, would strengthen the discovery claim.\n\nWho gets value from this? Anyone working on 2HDM phase transitions, LISA forecasts, or CLIC physics. It deserves referee time: the central question is important, the tools are appropriate, and the shortcomings are fixable. My recommendation is to send it to peer review, with the requirement that the authors release the scan data and add a coverage/vacuum-tracer robustness check before the quantitative ranges are accepted at face value.","headline":"First systematic map of one- vs two-step SFOEWPT parameter space in the inverted Type-I 2HDM, with a genuinely interesting LISA preference for two-step transitions; the quantitative separation ranges in Eq. (28) are scan-dependent and should be softened until coverage is shown.","tokens_in":43390,"tokens_out":1552,"would_cite":true,"duration_ms":21239,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that in the inverted Type-I two-Higgs-doublet model, the parameter regions for one-step and two-step strong first-order electroweak phase transitions are significantly separated, so a few collider measurements could…","keywords":["Electroweak Phase Transition","Two-Higgs-Doublet Model","Inverted Higgs scenario","First-order phase transition","Gravitational waves","LISA","CLIC","Higgs vacuum uplifting"],"falsifier":"Run a substantially denser scan or an analytic boundary tracker over $m_{H^\\pm}\\in[280,360]$ GeV, $\\tan\\beta\\in[4,9]$, $m_h\\in[60,120]$ GeV and count SFOEWPT points by transition type; one-step points below $m_{H^\\pm}=295$ GeV or two-step points above 351 GeV in appreciable numbers would refute the claimed separation. A direct collider measurement of $m_{H^\\pm}<295$ GeV in a universe where a strong electroweak transition occurred would also falsify the one-step window.","tokens_in":42253,"feed_emoji":"🌌","tokens_out":14773,"duration_ms":147308,"temperature":0.7,"pith_summary":"The paper tries to establish that the history of the electroweak phase transition can be read off from two measurable quantities in the inverted Type-I two-Higgs-doublet model, where the observed 125 GeV boson is the heavier scalar $H$. Scanning 2.36 million parameter points, it finds that a one-step strong first-order transition ($\\xi_c>1.3$) requires a charged Higgs mass $m_{H^\\pm}$ between 295 and 441 GeV and $\\tan\\beta$ between 4.2 and 8.8, while a two-step transition allows $m_{H^\\pm}$ between about 100 and 350 GeV and $\\tan\\beta$ between 2.5 and 45.4. The two sets overlap only in a narrow window, so measuring $m_{H^\\pm}$ and $\\tan\\beta$ could tell whether the early Universe went through an intermediate vacuum before settling into the current one. The same separation predicts that LISA-detectable gravitational-wave signals come almost entirely from two-step histories, and that a strongly enhanced $h\\to\\gamma\\gamma$ rate would point to the one-step path.","feed_headline":"Charged Higgs mass tells one-step from two-step early Universe","feed_subtitle":"One-step and two-step strong transitions occupy different mass and tan-beta ranges, so colliders could identify the cosmic path.","key_machinery":"The mechanism that carries the argument is the one-loop finite-temperature effective potential $V_{\\mathrm{eff}}(w_1,w_2,w_3,T)$ of the inverted Type-I 2HDM, with its temperature-dependent local minima traced to classify each transition step $PT_i^{(n\\text{-}step)}$. For a general step, the critical temperature $T_c$ is where two neighbouring minima become degenerate, and the order parameter is the magnitude of the VEV jump between the two minima divided by $T_c$, with $\\xi_c>1.3$ defining a strong transition. The separation of one-step and two-step regions emerges because a direct transition from the symmetric vacuum to the electroweak vacuum imposes different barriers and curvature conditions on the scalar potential than a path that first passes through an intermediate metastable minimum, and these conditions translate into different allowed ranges for $m_{H^\\pm}$ and $\\tan\\beta$ after all theoretical and experimental constraints are imposed.","core_discovery":"The central claim is a partial but significant separation between the parameter regions supporting a strong first-order electroweak phase transition (SFOEWPT) in one step and those supporting it in two steps, within the inverted Type-I 2HDM with $m_H=125$ GeV. With the SFOEWPT criterion $\\xi_c>1.3$, one-step transitions confine the charged Higgs to $m_{H^\\pm}\\in[295,441]$ GeV and $\\tan\\beta\\in[4.2,8.8]$, whereas the second step of a two-step transition permits $m_{H^\\pm}\\in[100,350]$ GeV and $\\tan\\beta\\in[2.5,45.4]$; the overlap is only near $m_{H^\\pm}\\in[295,351]$ GeV. Negative $\\sin(\\beta-\\alpha)$ arises almost exclusively in one-step scenarios, so its measured sign would favour the one-step reading. The paper also reports that LISA-detectable gravitational-wave signals ($\\mathrm{SNR}>10$) come predominantly from two-step transitions (114 scan points versus 1) even though one-step SFOEWPT points are more numerous (5343 versus 4486), that the $\\Delta F_0$--$\\xi_c$ correlation known from one-step transitions breaks down in multi-step histories, and that $e^+e^-\\to H^+H^-\\to W^+W^-hh$ with the final states $W^+W^-b\\bar b\\tau^+\\tau^-$ and $W^+W^-b\\bar b\\gamma\\gamma$ offers the strongest collider test at the 1.5 TeV CLIC.","pith_inferences":["If the claimed boundary is real, denser scans should sharpen it into a sharp frontier; a dedicated scan of $m_{H^\\pm}\\in[280,360]$ GeV that populates the supposedly empty regions would force the dichotomy to be recast as a preference rather than an exclusion.","The near absence of negative $\\sin(\\beta-\\alpha)$ in two-step points suggests a direct test: a future Higgs-factory measurement of the sign of the light-Higgs coupling deviations would, within this model, select one cosmological history over another, a link the paper does not state explicitly.","Because the LISA-detectable points are almost all two-step while one-step points are numerically dominant, future LISA upper limits could be reinterpreted as weak evidence for a one-step history, directing searches toward the lighter-charged-Higgs region and the $h\\to\\gamma\\gamma$ final state.","The near-background-free CLIC estimates imply that even a handful of events in the $W^+W^-b\\bar b\\gamma\\gamma$ channel would be informative; a natural follow-up would be a full detector-level background study including tau fakes and photon conversions to test how much of the discovery power survives."],"forward_implications":["If the paper is right, a charged Higgs discovered with $m_{H^\\pm}>351$ GeV would imply that any associated strong electroweak transition must have been one-step, whereas $m_{H^\\pm}<295$ GeV would force a two-step or higher history.","A measured negative $\\sin(\\beta-\\alpha)$ would favour the one-step scenario, since multi-step SFOEWPT points are almost exclusively positive in this quantity.","A LISA detection with SNR above 10 would most naturally be the gravitational-wave echo of a two-step transition, and every such detectable point in the scan has $\\xi_c>2$; a LISA null would therefore not exclude a strong one-step transition.","At the 1.5 TeV CLIC, charged-Higgs pair production followed by $H^\\pm\\to W^\\pm h$ would yield tens of signal events in at least one of the two golden final states $W^+W^-b\\bar b\\tau^+\\tau^-$ and $W^+W^-b\\bar b\\gamma\\gamma$, with Standard Model backgrounds below roughly one event.","The breakdown of the $\\Delta F_0$--$\\xi_c$ correlation in multi-step histories means a full finite-temperature calculation is required to certify transition strength whenever intermediate vacua are present."],"supporting_citations":[{"why":"Supplies the one-loop finite-temperature effective potential, counterterms, and SFOEWPT machinery used to compute transition strengths.","marker":"[74]"},{"why":"Gives the upper bound on BSM Higgs masses for SFOEWPTs that motivates the inverted scenario's viable parameter window.","marker":"[90]"},{"why":"Provides the earlier 2HDM collider and gravitational-wave complementarity that the paper extends to multi-step transitions.","marker":"[96]"},{"why":"Defines the vacuum-uplifting measure and the one-step correlation whose breakdown in multi-step cases is central to the paper.","marker":"[106]"},{"why":"Supplies the multi-step phase-transition code that classifies one-, two-, and three-step histories and computes critical temperatures and gravitational-wave spectra.","marker":"[127]"},{"why":"Defines the LISA mission and the nominal sensitivity curve used to compute the SNR>10 detectability thresholds.","marker":"[12]"},{"why":"Supplies the 1.5 TeV CLIC design and detector card used for the collider signal study.","marker":"[181]"}],"fun_headline_variants":["Charged Higgs mass picks one-step or two-step cosmic transition","Two-step phase transitions dominate LISA gravitational wave signals","Negative sin(beta-alpha) flags one-step cosmic phase transition","Two-step cosmic path yields louder gravitational waves for LISA","Rare three-step transitions also succeed in inverted 2HDM"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper's exclusion intervals rest on a finite random scan over the ranges in Eq. (22), so 'no point found' is treated as 'region excluded' without a proof that the scan is dense, and the transition classification depends on the specific minimum-tracing algorithm chosen.","fun_headline_variants_meta":{"raw":{"variants":["Charged Higgs mass picks one-step or two-step cosmic transition","Two-step phase transitions dominate LISA gravitational wave signals","Negative sin(beta-alpha) flags one-step cosmic phase transition","Two-step cosmic path yields louder gravitational waves for LISA","Rare three-step transitions also succeed in inverted 2HDM"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000648,"raw_usage":{"total_tokens":3174,"prompt_tokens":1345,"completion_tokens":1829,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":961,"completion_tokens_details":{"reasoning_tokens":1744}},"tokens_in":961,"tokens_out":1829,"duration_ms":15572,"temperature":1.0,"reasoning_tokens":1744,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:08:01.688012+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a substantially denser scan or an analytic boundary tracker over $m_{H^\\pm}\\in[280,360]$ GeV, $\\tan\\beta\\in[4,9]$, $m_h\\in[60,120]$ GeV and count SFOEWPT points by transition type; one-step points below $m_{H^\\pm}=295$ GeV or two-step points above 351 GeV in appreciable numbers would refute the claimed separation. A direct collider measurement of $m_{H^\\pm}<295$ GeV in a universe where a strong electroweak transition occurred would also falsify the one-step window.","supporting_citations":[],"review_version":1}