{"id":"559a2afe-3359-4612-b539-f3c6a5fd33db","arxiv_id":"2412.14562","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A new SU(5) grand unified version of the Zee-Babu model predicts TeV-scale colored scalars, a vector-like down quark, and observable proton decay p→e+π0 at Hyper-Kamiokande.","lead":"Physicists embedded the Zee-Babu model, a well-known two-loop mechanism for tiny neutrino masses, into an SU(5) grand unified theory. The result predicts new particles at the TeV scale and a proton decay signal that could be seen within the first decade of the Hyper-Kamiokande experiment.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central 'realistic' claim is not supported in the neutrino sector: Sec. 3.4 never fits the two-loop mass matrix to oscillation data, so the TeV-scale and proton-decay predictions rest on an untested assumption that the model can reproduce the observed Δm² and PMNS angles.","rationale":"The reader's weakest assumption is the one I would emphasize: the central claim of a realistic UV completion depends on fitting all fermion masses, including neutrinos. The paper provides a detailed charged-fermion fit (Sec. 3.2, χ²=0.1) and a gauge coupling unification analysis (Sec. 5), but it stops at asserting det(A)≠0 and m1≪m2,3 for the neutrino sector. This is a genuine gap: the two-loop formula of Eq. (3.41) has a specific texture from the antisymmetric YA and symmetric YS, and the rank of the lepton-mediated contribution is at most 2. The colored contribution and the B quark can fill the rank, but no demonstration is given that the resulting 3x3 matrix has the large mixings and mass hierarchy observed. Since the model's testable predictions (TeV-scale colored states, proton decay at Hyper-K) are motivated only if the model is realistic, this gap is load-bearing. I considered whether a more severe internal inconsistency exists. The abstract's claim of asymptotic freedom is questionable: the full SU(5) one-loop beta coefficient is positive (b≈55/6>0), so the gauge coupling has a Landau pole, though at ∼10^20 GeV, above the Planck scale, so the extrapolate-to-Planck part is likely safe. This is a wording issue, not a fatal one. The missing neutrino fit is the substantive concern. The paper has real independent support: a benchmark charged-fermion fit with small pulls, a two-loop gauge coupling unification with explicit thresholds, and an MCMC scan of the mass parameter space. But these do not cover the neutrino mass and mixing angles. The proposed test is straightforward: scan the Yukawa sector and see if any point reproduces oscillation data within 3σ. Until that is shown, the verdict should remain conditional.","tokens_in":22752,"tokens_out":22252,"duration_ms":185130,"concrete_test":"Perform a numerical fit of the neutrino mass matrix in Eq. (3.41) using the rotated Yukawa matrices (3.38)-(3.40), the scalar masses from Table 2, and a scan over μ and the Yukawa couplings YA, YS within the perturbativity bounds of Sec. 4. Search for points that reproduce the observed Δm²21, Δm²31, and PMNS angles (including δCP) within 3σ, while satisfying lepton flavor violation constraints. If no such point exists, the model's realistic claim fails; if a point exists, the concern is resolved and the conditional verdict can be upgraded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"To establish the model as realistic and UV-complete, the two-loop neutrino mass matrix of Eq. (3.41) must reproduce the observed neutrino mass splittings and mixing angles. The paper only argues that det(A)≠0 and m1≪m2,3 (Sec. 3.4). No numerical scan or fit of the Yukawa matrices YA, YS and the mass parameters is presented. The color-neutral contribution is approximately rank-2 because the 3x3 part of the antisymmetric YA has vanishing determinant; the observed large mixings must therefore come from the colored diagram and from the small mixings of the heavy B quark. Whether this texture can yield θ12≈34°, θ23≈49°, and the measured Δm²'s within 3σ is completely unverified. Section 4 uses only a one-entry estimate mν∼0.05 eV to set the mass bound, which does not test the flavor structure. If the neutrino sector cannot fit oscillation data, the model is not realistic, and the predicted TeV-scale colored scalars and observable p→e+π0 lose their motivation. The absence of such a fit is therefore the load-bearing gap in the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper embeds the two-loop Zee-Babu neutrino mass model into a non-supersymmetric SU(5) GUT by adding 10H and 50H scalars and a vector-like 5F + 5bar_F fermion pair. The authors compute the two-loop neutrino mass matrix from both color-neutral and colored scalars, present a benchmark fit to charged-fermion masses and CKM parameters, derive perturbativity bounds on the new Yukawa couplings, and perform a two-loop gauge-coupling-unification analysis with an MCMC scan over multiplet masses. From this they conclude that the Zee-Babu scalars and their colored partners must lie near or below the TeV scale, that a vector-like down-type quark should be at the TeV scale, and that p -> e+ pi0 should be observable in the first decade of Hyper-Kamiokande. The abstract and conclusions further claim that the model is realistic, asymptotically free, and can be extrapolated to the Planck scale.","tokens_in":23240,"tokens_out":4636,"duration_ms":42078,"significance":"If the central claims are correct, the paper would provide an interesting and testable UV completion of a radiative neutrino mass model, with concrete collider and proton-decay predictions. The technical apparatus is substantial: the two-loop RGE coefficients for all new multiplets are given explicitly, the 50H mass relations are used systematically, and the MCMC exploration of the unification parameter space is a useful step beyond single benchmark studies. The explicit benchmark charged-fermion fit and the flavor-violation checks are also commendable. However, the significance is conditional on three load-bearing gaps: the neutrino sector is never fitted to oscillation data, the charged-fermion fit is overparameterized and is presented with incorrect degrees of freedom, and the asymptotic-freedom/Planck-scale-extrapolation claim is not demonstrated. These issues must be addressed before the 'realistic and UV-complete' conclusion can be accepted.","major_comments":[{"comment":"The central claim that the model is realistic and that the TeV-scale states are 'required from ... neutrino oscillation data' is not supported, because the two-loop mass matrix in Eq. (3.41) is never confronted with the measured neutrino mass splittings and mixing angles. The text only argues that det(A) != 0 and m1 << m2,3, and Eq. (4.14) uses a single one-entry estimate m_nu ~ 0.05 eV. No numerical scan or fit of YA, YS, and the scalar/fermion masses to Delta m^2_21, Delta m^2_31, and the PMNS angles is presented. If this flavor structure cannot accommodate oscillation data, the model is not realistic and the subsequent proton-decay and collider predictions lose their motivation. This is the load-bearing gap in the paper's central claim.","section":"Sec. 3.4 and Eq. (3.41)"},{"comment":"The charged-fermion fit is overparameterized in a way that weakens the claim of realistic fermion masses. The paper states that there are 13 magnitudes and 6 phases, i.e. 19 parameters, for 11 observables, and then says the number of degrees of freedom is 8. With 11 observables and 19 fitted parameters the number of degrees of freedom is actually 11 - 19 = -8, so the reported total chi^2 = 0.1 is not a meaningful goodness-of-fit statistic. This fit should be presented as an existence proof or benchmark, not as evidence that the model successfully predicts the charged-fermion sector.","section":"Sec. 3.2"},{"comment":"The abstract and introduction claim that the model is asymptotically free and can be extrapolated to the Planck scale, but this is not demonstrated anywhere in the paper. Section 4 only evolves the Yukawa couplings from the TeV scale to the GUT scale of 2 x 10^16 GeV and imposes |y| <= sqrt(4 pi); no gauge or Yukawa running from the GUT scale to M_Planck is shown, and no two-loop or higher-order analysis establishes asymptotic freedom. The Planck-scale extrapolation claim should either be supported by an explicit calculation or removed from the abstract and conclusions.","section":"Sec. 4 and Abstract"}],"minor_comments":[{"comment":"The text says the number of degrees of freedom is 8 for the charged-fermion fit; as noted in the major comments, this is arithmetically incorrect and should be corrected.","section":"Sec. 3.2"},{"comment":"There are several typographical errors: 'Oklahom State University' on the title page, 'F ermion' in the Section 3 heading, 'vectorike' in Table 1, 'T able 1' in the caption, and an extra '+' in Eq. (2.2) ('++Phi4').","section":"Throughout"},{"comment":"The notation for the Zee-Babu scalars is inconsistent: the introduction uses eta^+ and k^{++}, while Section 2 switches to eta1 and chi1; later text also uses 'm_h+ = m_k++' where eta1 and chi1 are meant. A single notation should be used throughout.","section":"Sec. 2 and Sec. 5"},{"comment":"The GUT-scale inputs from Ref. [51] are computed assuming only SM particles run between M_Z and M_GUT, whereas the model contains new TeV-scale states. The paper says it 'expects' the modifications to be insignificant, but this is not quantified; the systematic uncertainty in the fermion-mass inputs should at least be discussed quantitatively.","section":"Sec. 3.1 and Table 1"},{"comment":"The proton decay rate formula uses alpha_U, which is not explicitly defined; the text later refers to alpha_GUT = g_GUT^2/(4 pi). Please define alpha_U consistently in Eq. (5.17).","section":"Eq. (5.17)"}],"recommendation":"major_revision","confidential_remarks":"The neutrino-sector fit is the decisive issue. If the authors can supply a numerical scan or fit showing that Eq. (3.41) reproduces the observed neutrino mass splittings and mixing angles, and if they either support or remove the asymptotic-freedom claim, the paper could become a solid contribution. As it stands, the 'realistic and UV-complete' conclusion is not established. I would not reject outright, because the model-building and unification machinery are valuable and the missing pieces appear to be within the scope of a revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does something real: an explicit SU(5) UV completion of the Zee-Babu model using 10H+50H scalars, and the observation that colored scalar partners contribute to neutrino mass at the same order as the color-neutral ones is physically interesting. The MCMC scan for gauge coupling unification and the proton-decay lifetime predictions are genuinely useful: the model makes sharp predictions for Hyper-K, and the TeV-scale vector-like down quark is a testable signature. The charged fermion benchmark passes current flavor constraints, which is a nontrivial check.\n\nBut there are soft spots, and one is load-bearing. Section 3.4 never fits the neutrino mass matrix to oscillation data. The authors only argue det(A)≠0 and m1 << m2,3. Given that the neutrino-sector Yukawa couplings YA, YS are largely unconstrained by the charged fermion fit, it is plausible a fit exists, but the abstract and conclusions claim compatibility with neutrino oscillation data without demonstrating it. If the model cannot reproduce θ12, θ23, and the Δm² splittings, the TeV-scale and proton-decay predictions lose their motivation. This is not a fatal contradiction; it is a missing calculation. But it is exactly the sort of thing a referee should demand.\n\nThe asymptotic-freedom claim is also unsubstantiated. The one-loop beta coefficients listed in Eq. (4.1) have a2 = 4/3, positive, so SU(2) is not asymptotically free in the usual sense. The authors only check perturbativity of Yukawa couplings up to 2×10^16 GeV, not up to the Planck scale. The abstract's claim that the model can be extrapolated to the Planck scale goes beyond what is shown.\n\nThe charged fermion fit is overparameterized (19 parameters for 11 observables), but the authors disclose it is a benchmark, not a best fit. That is acceptable as a proof of principle, though the tiny χ² should not be oversold.\n\nOne more thing worth checking: the paper says it is the first embedding of Zee-Babu in SU(5), but one of the authors has a 2019 paper with a very similar title (Ref. [35]). The novelty may lie in the full realistic construction rather than the embedding itself, but the claim as written is too strong.\n\nOverall: the core mechanism is appealing, the two-loop machinery and RGEs look standard, and the predictions are sharp. The missing neutrino fit is the main blocker. This deserves a serious referee, but the referee should send it back for a neutrino oscillation fit and a more careful asymptotic-freedom statement before publication.","headline":"Real SU(5) embedding of the Zee-Babu model with sharp collider and proton-decay predictions, but the paper never demonstrates the model fits neutrino oscillation data, and the asymptotic-freedom claim outruns what is shown.","tokens_in":23659,"tokens_out":5926,"would_cite":true,"duration_ms":52349,"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":"Embedding the Zee-Babu model in SU(5) forces TeV-scale scalars and a proton decay signal within Hyper-Kamiokande's reach.","keywords":["Zee-Babu model","two-loop neutrino mass","SU(5) grand unification","gauge coupling unification","proton decay","vector-like quark","radiative neutrino mass","color-sextet scalar"],"falsifier":"A numerical scan of the Yukawa parameters entering Eq. (3.41) that either reproduces or fails to reproduce $\\Delta m^2_{21}$, $\\Delta m^2_{31}$, and the three PMNS angles would settle the model's realism; the paper's own Sec. 3.4 leaves this check undone.","tokens_in":22586,"feed_emoji":"⚛️","tokens_out":5202,"duration_ms":41975,"temperature":0.7,"pith_summary":"Radiative neutrino mass models usually live at the TeV scale without a reason to be connected to higher energies. This paper claims that the Zee-Babu two-loop model can be embedded into an SU(5) grand unified theory in a way that is realistic, asymptotically free, and consistent with gauge coupling unification. In that embedding the colored GUT partners of the original Zee-Babu scalars contribute to neutrino masses just as much as the color-neutral ones, and the combined constraints of unification, proton decay, and perturbativity force all of them below roughly $10^{3}$ TeV. If true, the model turns proton decay into a near-term experimental target: the Markov chain Monte Carlo analysis finds a high likelihood that Hyper-Kamiokande sees p→e+π0 in its first decade.","feed_headline":"Zee-Babu neutrino masses fit SU(5); proton decay in reach","feed_subtitle":"GUT embedding pushes Zee-Babu scalars to the TeV scale and puts proton decay in Hyper-K's reach.","key_machinery":"The load-bearing machinery is the two-loop Majorana neutrino mass formula combining the original color-neutral Zee-Babu diagram with the colored-partner diagram: $M_{\\nu}^{\\rm loop} = 16\\mu \\hat{Y}_A M_E^{\\rm diag} \\hat{Y}_S M_E^{\\rm diag} \\hat{Y}_A \\hat{I} + 48\\mu \\tilde{Y}_A M_D^{\\rm diag} \\tilde{Y}_S M_D^{\\rm diag} \\tilde{Y}_A \\tilde{I}$. The submultiplet mass relations of the 50H representation, for example $m_{\\chi_4}^2 = 3m_{\\chi_2}^2 - 2m_{\\chi_3}^2$, are what allow the colored partners to remain light while the color-triplet states that mediate proton decay are pushed above $10^{12}$ GeV.","core_discovery":"The central discovery claimed is a specific SU(5) embedding of the Zee-Babu model, with scalar content 10H + 50H and one vector-like 5F + 5F fermion pair, in which the original singly charged η1 and doubly charged χ1 scalars are accompanied by colored partners η3 (color triplet) and χ5 (color sextet). The paper shows from two-loop RGE running with the 50H mass relations that gauge coupling unification selects a spectrum where both the color-neutral and colored Zee-Babu states sit near the TeV scale, so the two-loop neutrino mass formula contains two comparable contributions. It further shows that the vector-like down-type quark must sit at the TeV scale, the vector-like lepton near the GUT scale, and that the unified coupling αGUT is enhanced to about 1/14, which shortens the proton lifetime by roughly an order of magnitude relative to typical non-supersymmetric unified theories. The paper does not provide a numerical fit to neutrino oscillation data; it argues only that the lightest neutrino mass can be nonzero and small, while the heavier two are compatible with the observed hierarchy.","pith_inferences":["If the model is right, the original Zee-Babu picture was incomplete: the colored partners are not optional but required by unification, so collider searches for the leptoquark-like η3 and diquark-like χ5 become as important as searches for the charged scalars.","The correlation between proton decay and the TeV-scale scalar masses means a null result at Hyper-Kamiokande would not kill the model but would push the spectrum toward its upper end, while a positive signal would pin down the unification scale and strengthen the case for TeV-scale scalars.","A decisive next step the paper leaves implicit is a full parameter scan of the neutrino sector: the claim that det(Mν)≠0 with m1≪m2,3 must be checked against the measured mass-squared differences and mixing angles."],"forward_implications":["New scalars η1, χ1, η3, and χ5 have masses below roughly 10^3 TeV, within reach of future collider experiments.","Proton decay p→e+π0 should be observable by Hyper-Kamiokande within about ten years if the model is correct.","A vector-like down-type quark B with mass near 3 TeV decays as B→W−t, B→Zb, and B→hb with relative rates 2:1:1.","The color-neutral and colored two-loop diagrams must contribute comparably to neutrino masses, and the lightest neutrino mass is nonzero but much smaller than the two heavier ones.","The theory is asymptotically free and can be extrapolated to the Planck scale."],"supporting_citations":[{"why":"Introduce the Zee-Babu two-loop radiative neutrino mass model that this paper embeds in SU(5).","marker":"[13,14]"},{"why":"Georgi-Glashow SU(5) grand unified theory that provides the embedding gauge group.","marker":"[19]"},{"why":"Shows that vector-like 5+5 matter corrects the wrong SU(5) fermion mass relations, the method used here.","marker":"[24]"},{"why":"Gives the 50H mass relations used in gauge coupling unification and the two-loop SU(5) neutrino mass origin.","marker":"[35]"},{"why":"Provides gauge and scalar boson mediated proton decay constraints used to set lower bounds on color-triplet masses.","marker":"[39]"},{"why":"Supplies the two-loop neutrino mass formula and loop function used in Eq. (3.41).","marker":"[62]"},{"why":"Zee-Babu model parameter study used for Yukawa dominance and perturbativity and unitarity estimates.","marker":"[67]"},{"why":"Super-Kamiokande current proton decay limit on p→e+π0, the baseline for Hyper-Kamiokande projections.","marker":"[87]"},{"why":"Hyper-Kamiokande design report giving the projected sensitivity used for the proton decay reach.","marker":"[23]"}],"fun_headline_variants":["SU(5) Zee-Babu: colored scalars crucial, proton decay in reach","GUT-embedded Zee-Babu: TeV colored scalars, proton decay in Hyper-K","Zee-Babu fits SU(5), predicts Hyper-K proton decay signal","Colored scalars key in Zee-Babu SU(5), proton decay predicted","Two-loop neutrino model in SU(5) yields TeV states, proton decay"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the neutrino mass matrix of Eq. (3.41) can reproduce the measured neutrino mass-squared differences and mixing angles; the paper does not demonstrate this numerically, only that the lightest neutrino mass can be nonzero and small.","fun_headline_variants_meta":{"raw":{"variants":["SU(5) Zee-Babu: colored scalars crucial, proton decay in reach","GUT-embedded Zee-Babu: TeV colored scalars, proton decay in Hyper-K","Zee-Babu fits SU(5), predicts Hyper-K proton decay signal","Colored scalars key in Zee-Babu SU(5), proton decay predicted","Two-loop neutrino model in SU(5) yields TeV states, proton decay"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000908,"raw_usage":{"total_tokens":3922,"prompt_tokens":980,"completion_tokens":2942,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":596,"completion_tokens_details":{"reasoning_tokens":2830}},"tokens_in":596,"tokens_out":2942,"duration_ms":17307,"temperature":1.0,"reasoning_tokens":2830,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:08:03.591768+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A numerical scan of the Yukawa parameters entering Eq. (3.41) that either reproduces or fails to reproduce $\\Delta m^2_{21}$, $\\Delta m^2_{31}$, and the three PMNS angles would settle the model's realism; the paper's own Sec. 3.4 leaves this check undone.","supporting_citations":[{"cited_title":"Realistic Fermion Masses and Nucleon Decay Rates in SUSY SU(5) with Vector-Like Matter","cited_arxiv_id":"1207.6388","evidence_quote":"Shows that vector-like 5+5 matter corrects the wrong SU(5) fermion mass relations, the method used here."},{"cited_title":"Two-loop Neutrino Mass Generation and its Experimental Consequences","cited_arxiv_id":"hep-ph/0212058","evidence_quote":"Supplies the two-loop neutrino mass formula and loop function used in Eq. (3.41)."}],"review_version":1}