{"id":"dde755bd-991a-461a-b353-be479adfe799","arxiv_id":"1908.11847","paper_version":3,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"In the NMSSM, strong first-order electroweak phase transitions occur in four distinct phase-structure patterns, but only the simultaneous Higgs-singlet transition and the singlet-first-keeping-sign transition are likely to complete.","lead":"This paper maps the ways the early universe could undergo a strong first-order phase transition in a supersymmetric model called the NMSSM. It finds four distinct patterns, and shows which ones can actually complete to produce the matter-antimatter asymmetry or gravitational waves.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Gauge dependence of the one-loop potential could reorder the 'strongest' transition or restore nucleation in the Type-Only-H / Type-Only-S(flip) benchmarks; the published Landau-gauge check is qualitative only.","rationale":"The paper is internally coherent and unusually candid: scan-level transitions are explicitly labelled 'possible', benchmark points are cross-checked with CosmoTransitions, and the gauge dependence of the one-loop potential is acknowledged in Sec. 4. The central classification is therefore not an overclaim relative to what is computed. The remaining soft spot is that the benchmark-level 'fail to nucleate' conclusions for Type-Only-H and Type-Only-S(flip) are precisely the kind of quantitative statements most sensitive to the one-loop gauge ambiguity. A moderate shift in gamma_EW can reorder which transition is 'strongest' and thereby change the maintain/flip sub-classification, while a moderate shift in the bounce action can change whether a prior transition completes. The reader's weakest assumption already identifies the same root cause, namely that the one-loop Feynman-gauge potential is assumed to determine the order and strength of every transition. I therefore do not see a reason to change the CONDITIONAL verdict, but a concrete gauge-invariant recalculation of the four benchmarks would either retire this concern or force a revision of the categorical dead-end statements.","tokens_in":29567,"tokens_out":7879,"duration_ms":77373,"concrete_test":"Apply a dimensionally reduced 3d effective field theory (or, at minimum, the xi = 0 Landau-gauge potential with the same daisy resummation) to the four benchmark points in Table 2. Recompute the full PhaseTracer phase history, gamma_EW of every first-order transition via Eq. (33), and CosmoTransitions SE/TN for every transition required to reach the observed vacuum via Eq. (34). If the Type-Only-H or Type-Only-S(flip) benchmarks acquire SE/TN < 140, or if the strongest-FOPT label changes, the categorical conclusions in Sec. 6 need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The categorical statements about which NMSSM phase histories can support electroweak baryogenesis are decided by the one-loop, daisy-resummed, Feynman-gauge effective potential. Section 4 states explicitly that, at this truncation, the critical temperature is gauge dependent and that gamma_EW in Eq. (33) always depends on the gauge parameter xi. That dependence is load-bearing in two places. First, the classification into Type-Only-S(maintain) versus Type-Only-S(flip) is defined by which transition has the largest gamma_EW; a moderate xi-shift in gamma_EW can swap the 'strongest' label and move a sample between categories. Second, the no-nucleation verdicts for Type-Only-H and Type-Only-S(flip) use Eq. (34), SE/TN ~ 140, computed with the same gauge-dependent potential; a gauge-invariant or higher-order calculation could change a bounce action by an O(1) factor and turn a 'cannot complete' benchmark into a completing one. The Landau-gauge check reported in Sec. 5.3 is described only as 'typically mild' and is not tabulated per transition for all four benchmarks, so the benchmark-level viability claims are not yet demonstrated to be gauge-independent.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies the thermal phase structure of the Z3-symmetric NMSSM matched to a THDMS effective field theory, with all superpartners integrated out. Using a one-loop effective potential with daisy resummation in Feynman gauge, the authors trace the temperature dependence of the minima with their new code PhaseTracer, cross-checked against CosmoTransitions for benchmarks. From a MultiNest scan over eight NMSSM parameters, subject to LHC Higgs constraints, LEP chargino bounds, and a sampling penalty that targets gamma_EW ~ 1, they classify the phase histories into Type-H-and-S, Type-Only-H, and Type-Only-S(maintain/flip). They report that Type-H-and-S and Type-Only-S(maintain) benchmarks can contain completing strong first-order electroweak phase transitions ending in the observed vacuum, whereas their Type-Only-H and Type-Only-S(flip) benchmarks fail to nucleate. They also characterize the associated parameter regions, including lambda ~ 0.6, kappa ~ 0.2, small tan beta, and the frequent occurrence of the SM-like Higgs as the second-lightest CP-even state.","tokens_in":29800,"tokens_out":6481,"duration_ms":64423,"significance":"If the results hold, this is a useful step beyond earlier NMSSM phase-transition studies: it maps multi-phase histories rather than assuming a single transition between the symmetric and broken minima, shows that not every candidate transition actually completes, and identifies which phase histories can in principle support electroweak baryogenesis or gravitational-wave signals. The paper ships model files and uses public spectrum and sampling tools, and the benchmark results are independently cross-checked with CosmoTransitions. The quantitative predictions for lambda, kappa, tan beta, and the Higgs mass ordering are falsifiable by future collider and gravitational-wave observations. The main limitation is that the central classification and viability verdicts rest on a one-loop, daisy-resummed effective potential whose gauge dependence is acknowledged but only qualitatively checked; this is the key risk to the strength of the conclusions.","major_comments":[{"comment":"The gauge dependence of the one-loop potential is load-bearing, not a side remark. The authors state in Sec. 4 that at this truncation the critical temperature is gauge dependent and that the order parameter gamma_EW defined in Eq. (33) always depends on the gauge parameter xi. The distinction between Type-Only-S(maintain) and Type-Only-S(flip) is defined by which transition has the largest gamma_EW, so a moderate xi-shift can move a sample between categories. Likewise, the no-nucleation verdicts for the Type-Only-H and Type-Only-S(flip) benchmarks are based on bounce actions computed from the same gauge-dependent potential, so an O(1) change in SE/TN in Eq. (34) could turn a 'cannot complete' benchmark into a completing one. The Landau-gauge check reported in Sec. 5.3 is described only as 'typically mild' and is not tabulated per transition. Please provide a quantitative xi = 1 versus xi = 0 comparison of TC, gamma_EW, and SE/TN for all four benchmark points, and show explicitly that the strongest-transition label and the completion outcomes are unchanged. Without this, the benchmark-level viability conclusions are not yet demonstrated to be gauge independent.","section":"Sec. 4 and Sec. 5.3"},{"comment":"The paper describes the work as a 'comprehensive survey' and uses the scan to make statements about relative rarity, such as Type-Only-H being by far the rarest scenario and the absence of negative-mu samples in some categories. However, the final paragraph of Sec. 5.5 concedes that the sampling coverage at large m_h3 is inadequate and that large masses 'may just be rare with our sampling strategy.' Since MultiNest is an importance-sampling algorithm with a targeted penalty chi2_SFOPT of Eq. (37), the raw number of saved points does not by itself quantify coverage of the eight-dimensional parameter space. Please provide a coverage or convergence diagnostic per category, or rephrase the frequency and absence claims as upper limits. This does not invalidate the four benchmark analyses, but it is needed to support the 'comprehensive' and 'whole parameter space' claims in the abstract and Sec. 5.2.","section":"Sec. 5.5"},{"comment":"The classification labels each sample by its 'strongest FOPT' even when that transition is not on the realized cosmological history, as in Type-Only-H and in the samples where the strongest FOPT does not end in the SM vacuum. The text explains this in Sec. 5.2, but the scatter plots in Figs. 3, 5, 6, 8, 11, and 12 do not distinguish points whose strongest transition is part of a completing history from those for which it is not. Since the paper's headline conclusion is about which scenarios could in principle help provide a viable theory of electroweak baryogenesis, please mark in the figures which samples pass the nucleation check, or clearly state in the figure captions and conclusions that the displayed samples are only candidate transitions pending nucleation calculations.","section":"Secs. 5.2 and 5.4"}],"minor_comments":[{"comment":"The sentence 'The Nielsen identities in (20) imply that the critical temperature is gauge independent' is potentially misleading in its immediate context, because the next paragraph explains that the one-loop truncation makes the critical temperature gauge dependent. Please rephrase to make explicit that gauge independence holds for the full effective potential at exact extrema, not for the truncated one-loop result used here.","section":"Sec. 4"},{"comment":"The entry 'N/A' for the first transition in the Type-Only-H column is unclear: the text says this transition is second order, but the table label '2nd at T = 155' is ambiguous. Please state explicitly that the first EW-breaking transition is a crossover and therefore has no critical temperature or nucleation temperature.","section":"Table 2"},{"comment":"The table lists ranges for |kappa|, |A_lambda|, |A_kappa|, |A_t|, and |v_S|, while the text says both positive and negative values are considered. Please clarify in the table caption that the scan covers both signs with the stated magnitude ranges, or change the table entries to signed ranges.","section":"Table 1"},{"comment":"The abstract and conclusions state that the paper 'checked which scenarios could in principle help provide a viable theory of EW baryogenesis.' Given that only four benchmark points receive nucleation checks and the scan samples are not all checked for completion, I suggest adding a qualifier such as 'for benchmark points' to these summary statements, so that the scope is not overstated.","section":"Abstract and Sec. 6"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid and useful contribution, but its categorical conclusions about which NMSSM phase histories can support electroweak baryogenesis are stronger than the gauge-dependence validation supports. The requested quantitative Landau-gauge comparison and coverage diagnostics are feasible within the paper's existing framework and would substantially raise confidence. I do not see a basis for rejection; the issues are load-bearing but fixable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nThe short version: this is a solid, comprehensive survey of NMSSM phase structures, with a new tool (PhaseTracer) and a new classification (Type-Only-H and Type-Only-S(flip)) that earlier work missed. It deserves a careful read. The benchmark points are checked against CosmoTransitions, the model files and code are available, and the authors are unusually honest about the limitations of their one-loop effective potential.\n\nWhat is actually new: PhaseTracer traces multiple minima and finds phase histories rather than a single transition. The four-way classification, and the observation that Type-Only-H and Type-Only-S(flip) fail to nucleate in the benchmarks, directly shape what model-builders should look for in electroweak baryogenesis and gravitational wave searches. The scan is large and the parameter-space plots give a useful lay of the land. The finding that the SM-like Higgs is often not the lightest is a concrete, testable consequence.\n\nSoft spots: the gauge dependence of the finite-temperature potential is the main one. The authors state it plainly in Sec. 4, and they do a Landau-gauge check, but only qualitatively and not per transition. Since the classification of Type-Only-S(maintain) vs Type-Only-S(flip) is defined by which transition has the largest gamma_EW, and the no-nucleation verdicts come from Eq. (34) with the same gauge-dependent potential, a moderate shift could reorder the strongest transition or change a bounce action around threshold. That doesn't sink the paper—the language is properly hedged ('may be possible', 'might not help')—but it means the categorical claims are not yet gauge-robust. A per-benchmark gauge comparison tabulated would be the obvious fix. The scan-level SFOPT counts also lack nucleation checks, as the authors acknowledge.\n\nBottom line: this is a paper for anyone working on phase transitions in the NMSSM or singlet extensions. It is a genuine step forward and the limitations are disclosed rather than hidden. I would send it to a serious referee, asking for the gauge dependence to be quantified or the claims softened.\n\nBest,\n[Your name]","headline":"A comprehensive, honestly hedged NMSSM phase-structure survey with a new tool and classification; the main caveat is gauge dependence that could shift some categorical claims.","tokens_in":30388,"tokens_out":2838,"would_cite":true,"duration_ms":25990,"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":"The NMSSM can host strong first-order electroweak phase transitions in two of its four phase histories.","keywords":["NMSSM","electroweak phase transition","first-order phase transition","electroweak baryogenesis","gravitational waves","singlet extension","Higgs sector","finite-temperature effective potential"],"falsifier":"Recompute the paper's benchmark points using a gauge-invariant effective potential, such as a full two-loop or dimensionally reduced calculation: if any Type-H-and-S or Type-Only-S(maintain) point loses its first-order character or drops below γ_EW = 1, or if any Type-Only-H or Type-Only-S(flip) point nucleates successfully, the central viability dichotomy would fail.","tokens_in":29332,"feed_emoji":"🌌","tokens_out":4098,"duration_ms":37128,"temperature":0.7,"pith_summary":"This paper asks which symmetry-breaking histories in the NMSSM can produce the strongly first-order electroweak phase transition needed for electroweak baryogenesis. By tracing the minima of the finite-temperature effective potential over a scan of millions of parameter points, it identifies four distinct phase histories and shows that only two of them, Type-H-and-S and Type-Only-S(maintain), can yield completing strong transitions with strength above one that end in the observed vacuum. The other two histories, Type-Only-H and Type-Only-S(flip), contain strong-looking transitions that fail to nucleate. If the classification is right, it narrows the viable NMSSM parameter space and sharpens predictions for Higgs searches and gravitational wave experiments.","feed_headline":"NMSSM scan finds two viable paths to strong electroweak transition","feed_subtitle":"Only histories where the singlet gets a VEV before or with the Higgs complete with strength above one; the others fail to nucleate.","key_machinery":"The machinery is the temperature-traced minima of the one-loop finite-temperature effective potential, including daisy resummation, for the NMSSM matched to a two-Higgs-doublet-plus-singlet effective theory. The central object is the order parameter γ_EW, the jump in the Higgs-field combination divided by the critical temperature; the paper uses phase tracing to identify which pairs of minima become degenerate, then checks bubble nucleation for benchmark points to decide whether a transition actually completes in the early Universe.","core_discovery":"The central claim is that the NMSSM's electroweak phase structure is classified by the first symmetry-breaking transition: Type-H-and-S, where Higgs and singlet VEVs appear together; Type-Only-H, where only Higgs VEVs appear first; and Type-Only-S, where the singlet gets a VEV first and during the strongest transition either maintains its sign or flips it. Across the scanned parameter space, only Type-H-and-S and Type-Only-S(maintain) contain strong first-order transitions with γ_EW > 1 that complete and end in the observed electroweak vacuum. The Type-Only-H histories require an intermediate transition that temporarily restores electroweak symmetry, and that transition never nucleates; the Type-Only-S(flip) histories have a strongest transition whose tunneling action is too large to complete. The scan also produces sharp phenomenological predictions: quartic couplings near λ ≈ 0.6 and κ ≈ 0.2, small tan β, an effective μ parameter below about 300 GeV, and the 125 GeV Higgs often being the second-lightest CP-even scalar rather than the lightest.","pith_inferences":["The same four-way classification logic likely applies to any singlet-extended Higgs model, and the paper's THDMS matching means its results carry over to a subspace of non-supersymmetric models.","Earlier scans that located only the strongest transition may have overcounted viable baryogenesis points, since the paper shows that a strong transition can be unreachable in the actual cosmological history.","The preference for the 125 GeV Higgs being the second-lightest state gives a concrete target for searches for an additional light CP-even scalar with suppressed couplings.","A gauge-invariant or higher-order calculation could shift individual benchmarks between the categories, so the viability boundary should be rechecked with such methods before relying on the precise parameter limits."],"forward_implications":["Only Type-H-and-S and Type-Only-S(maintain) histories can support electroweak baryogenesis among the scanned NMSSM points.","Type-Only-H and Type-Only-S(flip) histories should not be counted as baryogenesis candidates, because their necessary transitions fail to nucleate.","Viable strong transitions concentrate in a narrow parameter window: λ ≈ 0.6, κ ≈ 0.2, small tan β, and light higgsino mass parameter.","The 125 GeV Higgs is usually the second-lightest CP-even Higgs, not the lightest, in samples that pass collider constraints.","Type-Only-S(maintain) histories can provide two-step transitions that may yield observable gravitational wave signatures."],"supporting_citations":[{"why":"Supplies the prior NMSSM phase-transition study and the two-Higgs-doublet-plus-singlet conventions used throughout.","marker":"[15]"},{"why":"Establishes the singlet-catalyzed electroweak phase transition mechanism that motivates the NMSSM scenario.","marker":"[16]"},{"why":"Shows that the baryon yield depends on whether the singlet VEV appears before or during the electroweak transition.","marker":"[58]"},{"why":"Provides earlier NMSSM electroweak phase transition results that the paper extends by mapping all possible histories.","marker":"[60]"},{"why":"Documents the gauge dependence of the one-loop effective potential, supporting the paper's stated caveat about critical temperature and order parameter.","marker":"[84]"},{"why":"Supplies the Arnold-Espinosa daisy resummation method used for the finite-temperature potential.","marker":"[90]"},{"why":"Provides the phase-tracing and bubble-nucleation algorithm that the paper adapts to map multiple transitions and check completion.","marker":"[96]"}],"fun_headline_variants":["NMSSM electroweak transition: only two histories succeed","Strong EW phase transitions limited to two NMSSM histories","NMSSM survey: strong first-order transition needs singlet VEV early","Only NMSSM histories with singlet VEV before or with Higgs work","Two NMSSM paths yield strong first-order electroweak transition"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The classification assumes that the one-loop finite-temperature effective potential with daisy resummation reliably decides the order, strength, and completion of every transition, despite the authors' own note that the critical temperature and order parameter are gauge dependent at this truncation.","fun_headline_variants_meta":{"raw":{"variants":["NMSSM electroweak transition: only two histories succeed","Strong EW phase transitions limited to two NMSSM histories","NMSSM survey: strong first-order transition needs singlet VEV early","Only NMSSM histories with singlet VEV before or with Higgs work","Two NMSSM paths yield strong first-order electroweak transition"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000681,"raw_usage":{"total_tokens":3089,"prompt_tokens":940,"completion_tokens":2149,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":556,"completion_tokens_details":{"reasoning_tokens":2059}},"tokens_in":556,"tokens_out":2149,"duration_ms":13920,"temperature":1.0,"reasoning_tokens":2059,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:07:07.251931+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the paper's benchmark points using a gauge-invariant effective potential, such as a full two-loop or dimensionally reduced calculation: if any Type-H-and-S or Type-Only-S(maintain) point loses its first-order character or drops below γ_EW = 1, or if any Type-Only-H or Type-Only-S(flip) point nucleates successfully, the central viability dichotomy would fail.","supporting_citations":[{"cited_title":"Baryogenesis, dark matter and inflation in the Next-to-Minimal Supersymmetric Standard Model","cited_arxiv_id":"1309.5091","evidence_quote":"Shows that the baryon yield depends on whether the singlet VEV appears before or during the electroweak transition."}],"review_version":1}