{"id":"24651f8c-e653-44bd-967c-ddb4a5a57032","arxiv_id":"2506.02743","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Loop corrections from inverse-seesaw neutrinos and sneutrinos can change the SM-like Higgs self-coupling by up to 10.5% and the SM-like Higgs mass by up to 4.5% in the NMSSM with inverse seesaw.","lead":"Physicists have computed the full one-loop corrections to the three-Higgs coupling in a supersymmetric model that also explains tiny neutrino masses through the inverse seesaw mechanism, adding two-loop top corrections on top. The extra neutrino and sneutrino particles can shift the effective Higgs self-coupling by up to about 10 percent and the 125 GeV Higgs mass by up to 4.5 percent, which matters for future Higgs pair measurements.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Two-loop (s)neutrino corrections are omitted while the one-loop (s)neutrino contribution is the entire source of the quoted 10% effect.","rationale":"The paper is technically careful and the one-loop calculation with full momentum dependence and the OS-DR scheme is plausible; the scan and external constraints are a real strength. The reader's weakest assumption identifies precisely the only structural weakness: the two-loop NMSSM terms are imported from the vanilla NMSSM and do not contain the ISS sector, while the ISS effect is exactly the quantity the paper claims to predict. This is not an ad hominem or a disagreement with consensus; it is a completeness/consistency concern about the stated precision. Since the one-loop ISS contribution is the entire origin of the claimed 10.5%, and the new fields have O(1) Yukawas, the omission of ISS-dependent two-loop corrections cannot be argued away by generic smallness; it needs a quantitative estimate. My concrete test is the minimal check (an effective-potential estimate of the dominant y_nu^4 two-loop term) that would settle the concern. If the estimate is small, the central claim stands and the verdict would be ACCEPT for the main numerical conclusion; as written, the appropriate verdict remains CONDITIONAL because the preprint does not provide that estimate. I do not agree that the omissions of code or of coupling formulas are the most load-bearing issue: those affect reproducibility but not the physics argument itself.","tokens_in":31071,"tokens_out":1800,"duration_ms":18228,"concrete_test":"Estimate the dominant two-loop (s)neutrino contribution at benchmark P1. Compute at least the leading O(y_nu^4) diagram class (e.g. the two-loop Higgs self-energy/counterterm diagrams from neutrino/sneutrino loops, equivalently the O(y_nu^4) effective-potential terms) and the corresponding correction to the effective trilinear coupling. If the resulting shift in lambda_eff_hhh is below ~1% of the tree-level value across the valid scan region, the 10.5% claim survives as a stable higher-order prediction; if it is comparable to the quoted 10.5% effect or to the 7-15% one-loop ISS contribution, the claim must be restated as one-loop ISS dominance only.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central numeric claim is that the ISS-created (s)neutrino sector shifts the SM-like trilinear Higgs self-coupling by up to 10.5% relative to the vanilla NMSSM. But the prediction at O(alpha_t(alpha_s+alpha_t)) in Eq. 33 is assembled as one-loop NMSSM-nuSS corrections plus two-loop O(alpha_t alpha_s) and O(alpha_t^2) corrections evaluated in the CP-violating NMSSM without the (s)neutrino sector. The two-loop pieces therefore contain no dependence on y_nu, lambda_X, M_X, A_nu, or any ISS-created field. Consequently, the quoted Delta is, at two-loop order, only a ratio of one-loop (s)neutrino contributions to a known two-loop result; there is no estimate of two-loop corrections involving the new states. Since the scan deliberately uses |y_nu| up to ~0.95 (benchmark P1) and the one-loop (s)neutrino effect is claimed to be 7-15% (Eq. 65 and Fig. 1 discussion), one expects two-loop (s)neutrino corrections of order (alpha_y/pi) times the one-loop effect, or roughly a few percent of the tree-level coupling, compared with the claimed ~10.5% signal. Because the two-loop (s)neutrino diagrams are not calculated, the quoted 10.5% is a one-loop estimate of the ISS effect dressed with vanilla-NMSSM higher orders, not a complete higher-order prediction of the ISS contribution. The paper itself states (Sec. 3, after Eq. 33) that the two-loop terms can be embedded; it does not give a numerical estimate of the neglected ISS-dependent two-loop terms. Hence the central claim is conditional on an unquantified approximation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper computes the loop-corrected trilinear Higgs self-couplings in the NMSSM extended by an inverse seesaw sector (NMSSM-nuSS). The one-loop contributions are computed with full momentum dependence and include all sectors; for the effective zero-momentum SM-like coupling, the dominant top/stop and (s)neutrino contributions are combined with the O(αtαs) and O(αt^2) two-loop corrections previously obtained for the vanilla CP-violating NMSSM. The results are implemented in the public code NMSSMCALC-nuSS and used to compute heavy-Higgs Higgs-to-Higgs decay widths and branching ratios. After a parameter scan subject to Higgs, neutrino, lepton-flavor-violation, and oblique-parameter constraints, the authors find that the inverse-seesaw sector changes the effective SM-like trilinear coupling by up to 10.5% and the SM-like Higgs mass by up to 4.5% relative to the NMSSM without the seesaw sector, with a strong correlation between the two corrections.","tokens_in":31451,"tokens_out":10223,"duration_ms":101674,"significance":"If the numerical result is robust, the paper establishes a quantitatively significant and correlated imprint of a low-scale seesaw sector on the Higgs potential, which is relevant for Higgs-pair production and future collider measurements of the trilinear Higgs coupling. The calculation is internally checked (UV finiteness, agreement with previous results in limits), the scan employs realistic experimental constraints, and the implementation in a public Fortran code makes the results usable for further phenomenological studies. The main caveat is that the claimed ISS effect is a one-loop-level estimate; the assessment below concerns that caveat.","major_comments":[{"comment":"The two-loop contributions Δλ^{(2,αsαt)} and Δλ^{(2,α_t^2)} are imported unchanged from the CP-violating NMSSM without the inverse seesaw sector and therefore contain no dependence on yν, λX, MX, Aν or BμX. Since the quoted 10.5% effect (Sec. 4.1, Fig. 4) is generated entirely by the one-loop (s)neutrino diagrams, the paper's central number is a one-loop estimate of the ISS contribution dressed with common two-loop top/stop corrections, not a complete higher-order prediction. At the benchmark point P1, (yν)21 = 0.95, so mixed two-loop terms of O(yν^2 αt) and O(yν^4) are not a priori negligible; the authors should either compute or estimate them, or provide a conservative uncertainty band (e.g. from scale variation). Without this, the abstract's 'up to 10.5%' is conditional on an unquantified missing contribution.","section":"Sec. 3, Eq. (33)"},{"comment":"The neutral-Higgs–sneutrino couplings g_{h_i \\tilde n_j \\tilde n_k} that enter the central one-loop expression Eq. (54) are not written out; the text says they are 'very lengthy' and will be provided 'upon request'. This makes the derivation impossible to verify from the paper alone and blocks reproduction of the numerical results. Please include the full expressions in an appendix or supplementary material.","section":"Sec. 3.1, after Eq. (56)"},{"comment":"The one-parameter variations around P1 show SM-like Higgs masses up to 143 GeV (Fig. 2) and relative corrections Δ up to about 40%, far above the 10.5% quoted for the scan. The caption labels green triangles as points satisfying all constraints, but points with Mh = 143 GeV cannot satisfy the 122–128 GeV window of Eq. (58). The text should explicitly distinguish points that pass the Higgs-mass/Higgs-signal constraints from those that do not, and should state that the headline 10.5% applies only to the scan points that satisfy Eq. (58). As written, the reader cannot tell whether the extreme Δ values are included in the claim.","section":"Sec. 4.1, Figs. 2 and 3, with Eq. (58)"}],"minor_comments":[{"comment":"The abstract quotes 'up to 10%' while Sec. 4.1 and the conclusions quote 10.5%; please unify the number.","section":"Abstract and Sec. 5"},{"comment":"The effective couplings used for the numerical Δ are computed in the gaugeless limit and include only the (s)top and (s)neutrino one-loop contributions; the 'full one-loop' statement in the abstract would be clearer if it referred to the momentum-dependent calculation of Sec. 3.1 and the effective couplings were described as 'dominant one-loop' contributions.","section":"Sec. 3.2"},{"comment":"There is a typo 'In particuler' in the discussion of Fig. 3, and in Sec. 5 the phrase 'can reach reach 4.5%' contains a duplicated word.","section":"Sec. 4.1"}],"recommendation":"major_revision","confidential_remarks":"The paper is a natural continuation of the authors' program. The central missing piece is an estimate of two-loop corrections involving the new (s)neutrino sector; if the authors can supply such an estimate or explicitly reframe the claim as a one-loop-level result, the paper could be publishable. The self-citation pattern is justified by the direct use of previous results and does not appear problematic."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nBottom line: this is a competent and transparent extension of the group's earlier NMSSM higher-order program to the NMSSM with inverse seesaw (NMSSM-nuSS). It computes the full one-loop corrections to the trilinear Higgs self-couplings (THCs) and Higgs-to-Higgs decays, adds the dominant top-Yukawa/strong two-loop corrections from the vanilla complex NMSSM, and implements everything in the public code NMSSMCALC-nuSS. The genuinely new ingredient is the (s)neutrino one-loop contribution to the THCs; the rest is a combination of previously published machinery. The paper is honest about what is new.\n\nThe most important number, a shift of up to 10.5% in the effective SM-like THC (and 4.5% in the mass) when the ISS sector is present, passes a sanity check. The calculation is UV-finite, agrees with earlier results in the limit of vanishing neutrino Yukawas, and the scan respects Higgs, neutrino, LFV, and oblique parameter constraints. I see no fatal error. The correlation plot between THC and mass corrections is a nice selling point.\n\nThe main soft spot is exactly the one the stress-test note flags: the two-loop corrections are taken unchanged from the vanilla NMSSM and contain no dependence on the ISS parameters. The paper says this explicitly, but it does not estimate the size of the omitted two-loop contributions that involve the (s)neutrino sector. Since yν entries close to one are used, two-loop terms of order (α_y/π) times the one-loop effect are plausibly a few percent of the tree-level coupling--comparable to the quoted 10.5% (which is itself the one-loop ISS effect normalized to the full result). So the headline number is best read as a leading-order estimate of the ISS contribution, not a complete higher-order prediction of it. The paper would be stronger with a parametric estimate or a numerical study of the neglected terms.\n\nTwo minor points: the sneutrino-Higgs couplings are not given explicitly ('provided upon request'), which is slightly annoying even though the code is public; and there is no uncertainty estimate for the missing higher orders. The definition of Δ in Eq. (64) is also a bit confusing--the paper itself notes that normalizing to the same loop order cancels higher-order effects, which is why the 10.5% looks smaller than the δ of 7-15% defined in Eq. (65). The authors are aware of this, but it means the headline 10.5% is a conservative representation of the ISS effect.\n\nWho is this for: people doing precision Higgs phenomenology in SUSY models with seesaw sectors, and developers of spectrum generators. It deserves a serious referee. The missing two-loop estimate and the omitted couplings should be addressed, but the paper is not fatally flawed.\n\nRecommendation: send it to review, with a request that the authors add a discussion of the expected size of two-loop ISS corrections, and ideally make the full coupling expressions available in the paper or an ancillary file.","headline":"Solid one-loop-plus-vanilla-two-loop calculation of the Higgs trilinear couplings in the NMSSM with inverse seesaw; the 10.5% headline effect is a one-loop ISS contribution, and the missing two-loop (s)neutrino terms are the real soft spot.","tokens_in":31988,"tokens_out":4829,"would_cite":true,"duration_ms":42996,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The inverse-seesaw neutrino sector shifts the loop-corrected SM-like Higgs self-coupling by up to 10.5% and the Higgs mass by up to 4.5%.","keywords":["NMSSM","inverse seesaw","trilinear Higgs self-coupling","Higgs mass corrections","one-loop corrections","two-loop corrections","Higgs-to-Higgs decays","neutrino Yukawa couplings"],"falsifier":"For the benchmark point P1, evaluate the dominant two-loop contributions involving the new sector, such as $O(\\alpha_t y_\\nu^2)$ or $O(y_\\nu^4)$ corrections to the effective potential; if any of them shifts $\\lambda_{hhh}^{\\rm eff}$ or $M_h$ by more than about one percentage point, then the quoted numbers are not the complete higher-order prediction.","tokens_in":30871,"feed_emoji":"⚛️","tokens_out":8684,"duration_ms":81919,"temperature":0.7,"pith_summary":"This paper establishes that in the NMSSM extended with an inverse seesaw mechanism (NMSSM-nuSS), the new neutrino and sneutrino states leave a measurable imprint on the Higgs potential, not just on neutrino masses. It presents the full one-loop corrections to all trilinear Higgs self-couplings, with full momentum dependence, plus the dominant top-Yukawa and strong-coupling two-loop corrections, all computed in the same renormalization scheme as the Higgs mass corrections. For parameter points that pass Higgs, neutrino, lepton-flavor-violation, and oblique-parameter constraints, switching on the seesaw sector changes the effective SM-like trilinear coupling by up to 10.5% and the SM-like Higgs mass by up to 4.5% relative to the NMSSM without it. The two shifts are strongly correlated, so precision Higgs measurements can constrain the neutrino sector, and any future extraction of the Higgs self-coupling from di-Higgs production must include these corrections.","feed_headline":"Neutrino sector shifts Higgs self-coupling by up to 10.5%","feed_subtitle":"Full one-loop plus two-loop corrections tie a 4.5% Higgs-mass shift to a 10.5% self-coupling shift.","key_machinery":"The load-bearing object is the effective SM-like trilinear coupling $\\hat\\lambda_{hhh}^{\\rm eff}$, defined as the third derivative of the effective Higgs potential with respect to the neutral Higgs fields at zero external momenta, evaluated in the same mixed on-shell/$\\overline{\\rm DR}$ renormalization scheme used for the Higgs mass calculation. The inverse seesaw enters through a $9\\times9$ neutrino mass matrix with block structure $(0, M_D, 0;\\ M_D^T, 0, M_X;\\ 0, M_X^T, \\mu_X)$ and an 18-by-18 sneutrino mass matrix, and the new one-loop contributions come from triangle diagrams with (s)neutrinos in the loops. The two-loop part is the top/stop-sector contribution taken unchanged from the complex NMSSM without seesaw, which is what makes the mass and coupling corrections directly comparable and gives the reported correlation.","core_discovery":"The paper's claim is that the (s)neutrino sector contributes one-loop corrections to the effective SM-like trilinear Higgs self-coupling that are large enough to survive all applied constraints and are two to three times larger in relative terms than the corresponding corrections to the SM-like Higgs mass. The calculation is organized as an effective coupling at zero external momentum, built from the third derivative of the effective potential, and includes the full one-loop contributions from all sectors with complete momentum dependence, further reduced to the dominant one-loop (s)top and (s)neutrino contributions in the gaugeless limit, and then combined with the two-loop $O(\\alpha_t\\alpha_s)$ and $O(\\alpha_t(\\alpha_s+\\alpha_t))$ corrections from the complex NMSSM. After requiring a 122-128 GeV SM-like Higgs, LEP/LHC mass bounds, Higgs search and signal-rate constraints, neutrino oscillation data, lepton-flavor-violating decay bounds, and oblique parameters $S,T,U$, the relative difference between the model with and without the seesaw sector reaches 10.5% for the effective SM-like trilinear coupling and 4.5% for the Higgs mass at the highest included order; at the benchmark point P1, elements of the neutrino Yukawa matrix such as $(y_\\nu)_{21}=0.95$ drive the effect.","pith_inferences":["The paper's scan treats the neutrino parameters as real and diagonal except for $y_\\nu$; allowing complex phases with the same one-loop machinery could shift the quoted $\\Delta$ values and would also feed into electric dipole moments, which are not the dominant constraint here.","The 10.5% effect in $\\lambda_{hhh}^{\\rm eff}$ is comparable to the 3.5-8% accuracy projected for a 100 TeV collider, so such a machine could probe the inverse seesaw sector directly through di-Higgs production if the large-$y_\\nu$ points survive updated LHC searches.","A simplified SM-plus-inverse-seesaw study cited in the paper found effects of +20% to +30% for $|Y_\\nu|>3$; the supersymmetric case here yields smaller effects because fermion and sfermion contributions cancel, so scanning $y_\\nu$ beyond the values used here would test whether the cancellation pattern changes the size or sign of $\\Delta$.","Because the two-loop corrections involving the new sector are not computed, the most defensible reading of the 10.5% number is as an estimate of the one-loop (s)neutrino contribution on top of the NMSSM two-loop baseline rather than a complete next-to-next-to-leading-order prediction; a full two-loop calculation including $y_\\nu$ would settle the residual uncertainty."],"forward_implications":["At valid scan points like P1, the loop-corrected effective coupling $\\lambda_{hhh}^{\\rm eff}$ lies roughly in the range 195-229 GeV, so di-Higgs production rates computed with tree-level couplings would be off by several percent and should be recomputed with the corrected coupling.","The one-loop corrections to the heavy-Higgs decay $H_2\\to H_1H_1$ are about 40% larger than the tree-level rate, and the (s)neutrino sector changes the branching ratios of non-SM-like Higgs decays by up to about 3.4%, which matters for Higgs search exclusions.","The strong correlation between the (s)neutrino-induced shifts in $M_h$ and $\\lambda_{hhh}^{\\rm eff}$ means a future measurement of the trilinear coupling can be combined with the measured Higgs mass to discriminate these seesaw scenarios from the NMSSM without the seesaw sector.","The new corrections are implemented in the public program NMSSMCALC-nuSS, making the predictions usable for further phenomenological scans and collider studies."],"supporting_citations":[{"why":"Supplies the NMSSM-nuSS model setup, the previous loop-corrected Higgs mass calculation, the renormalization scheme, and the constraint strategy used for the scan.","marker":"[51]"},{"why":"Provides the full one-loop corrections to the trilinear Higgs self-couplings in the real NMSSM, which the present calculation checks against in the vanishing-neutrino-Yukawa limit.","marker":"[75]"},{"why":"Provides the two-loop $O(\\alpha_t\\alpha_s)$ corrections to the trilinear Higgs self-couplings in the complex NMSSM, embedded here as the dominant strong-interaction two-loop term.","marker":"[76]"},{"why":"Provides the two-loop $O(\\alpha_t^2)$ corrections in the CP-violating NMSSM and the correlation analysis that motivates combining mass and self-coupling corrections.","marker":"[77]"},{"why":"Shows that a single heavy Dirac neutrino can shift the SM trilinear Higgs coupling by tens of percent, motivating the investigation of the inverse seesaw sector.","marker":"[102]"},{"why":"Demonstrates large effects on the trilinear Higgs coupling in the SM with inverse seesaw for large neutrino Yukawa couplings, setting the expectation that the NMSSM-nuSS effects can be sizable.","marker":"[103]"},{"why":"Provides the $\\mu_X$ parameterization of the neutrino sector used in the parameter scan to fix the neutrino mass and mixing inputs.","marker":"[106]"},{"why":"Supplies the Higgs search and signal-strength constraints used to filter valid parameter points from the scan.","marker":"[119]"}],"fun_headline_variants":["Neutrino sector shifts Higgs self-coupling by up to 10.5%","Seesaw-driven neutrino corrections shift Higgs self-coupling 10.5%","Trilinear Higgs self-coupling corrected by up to 10.5% from neutrinos","Neutrino effects on trilinear Higgs coupling up to 10.5%","Higgs self-coupling sees 10.5% shift from inverse seesaw"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that the dominant two-loop corrections involving the new neutrino and sneutrino states are negligible, even though the scan uses neutrino Yukawa couplings of about one; if those missing two-loop terms are comparable to the one-loop neutrino contribution, the quoted 10.5% and 4.5% would change.","fun_headline_variants_meta":{"raw":{"variants":["Neutrino sector shifts Higgs self-coupling by up to 10.5%","Seesaw-driven neutrino corrections shift Higgs self-coupling 10.5%","Trilinear Higgs self-coupling corrected by up to 10.5% from neutrinos","Neutrino effects on trilinear Higgs coupling up to 10.5%","Higgs self-coupling sees 10.5% shift from inverse seesaw"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00135,"raw_usage":{"total_tokens":5556,"prompt_tokens":1095,"completion_tokens":4461,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":711,"completion_tokens_details":{"reasoning_tokens":4352}},"tokens_in":711,"tokens_out":4461,"duration_ms":28823,"temperature":1.0,"reasoning_tokens":4352,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:17:23.747926+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For the benchmark point P1, evaluate the dominant two-loop contributions involving the new sector, such as $O(\\alpha_t y_\\nu^2)$ or $O(y_\\nu^4)$ corrections to the effective potential; if any of them shifts $\\lambda_{hhh}^{\\rm eff}$ or $M_h$ by more than about one percentage point, then the quoted numbers are not the complete higher-order prediction.","supporting_citations":[{"cited_title":"Loop-corrected Higgs Masses in the NMSSM with Inverse Seesaw Mechanism","cited_arxiv_id":"2108.10088","evidence_quote":"Supplies the NMSSM-nuSS model setup, the previous loop-corrected Higgs mass calculation, the renormalization scheme, and the constraint strategy used for the scan."},{"cited_title":"Higher Order Corrections to the Trilinear Higgs Self-Couplings in the Real NMSSM","cited_arxiv_id":"1306.3926","evidence_quote":"Provides the full one-loop corrections to the trilinear Higgs self-couplings in the real NMSSM, which the present calculation checks against in the vanishing-neutrino-Yukawa limit."},{"cited_title":"The Order $\\mathcal{O}(\\alpha_t\\alpha_s)$ Corrections to the Trilinear Higgs Self-Couplings in the Complex NMSSM","cited_arxiv_id":"1506.03321","evidence_quote":"Provides the two-loop $O(\\alpha_t\\alpha_s)$ corrections to the trilinear Higgs self-couplings in the complex NMSSM, embedded here as the dominant strong-interaction two-loop term."},{"cited_title":"The Trilinear Higgs Self-Couplings at ${\\cal O}(\\alpha_t^2)$ in the CP-Violating NMSSM","cited_arxiv_id":"2210.02104","evidence_quote":"Provides the two-loop $O(\\alpha_t^2)$ corrections in the CP-violating NMSSM and the correlation analysis that motivates combining mass and self-coupling corrections."},{"cited_title":"Heavy neutrino impact on the triple Higgs coupling","cited_arxiv_id":"1603.00879","evidence_quote":"Shows that a single heavy Dirac neutrino can shift the SM trilinear Higgs coupling by tens of percent, motivating the investigation of the inverse seesaw sector."},{"cited_title":"Imprints of massive inverse seesaw model neutrinos in lepton flavor violating Higgs boson decays","cited_arxiv_id":"1405.4300","evidence_quote":"Provides the $\\mu_X$ parameterization of the neutrino sector used in the parameter scan to fix the neutrino mass and mixing inputs."}],"review_version":1}