{"id":"56df2d97-0b4d-4f29-bb07-5ee716ae4f76","arxiv_id":"2504.16022","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The paper shows that non-renormalizable SU(5) models can host light scalar leptoquarks with suppressed proton decay while explaining neutrino masses and unifying gauge couplings.","lead":"A new SU(5) grand unified model family keeps the color-triplet leptoquark light by using higher-dimensional operators to suppress proton decay, and generates neutrino masses through one-loop leptoquark mixing. The paper shows that TeV-scale leptoquarks can be compatible with proton stability and gauge unification in several benchmark scenarios.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Proton-decay suppression rests on Yukawa cancellations that the paper admits are not RG-invariant, so the viable light-triplet regime requires an unexplained ~10^-9 boundary-condition tuning at the proton-decay scale.","rationale":"The reader's judgment is essentially correct. The paper is an internally consistent EFT construction: the group-theoretic decompositions, mass matrices, and the benchmark neutrino fits check out as existence proofs. The strongest claim, however, goes beyond pure mathematics: it asserts that the light-triplet regime is a viable alternative to doublet-triplet splitting. The load-bearing step is the exact cancellation that removes the triplet's baryon-number-violating couplings. The paper explicitly acknowledges this cancellation is neither symmetry-protected nor RG-invariant, and the required precision is extreme. My stress-test therefore focuses there: a specific RGE calculation would show whether the claimed suppression can hold at the scale where proton decay is measured without a severe UV tuning. I find no other internal inconsistency that would change the verdict; the scalar-spectrum and unification issues noted by the reader are real but secondary. The CONDITIONAL verdict is appropriate; I do not recommend changing it.","tokens_in":23108,"tokens_out":21249,"duration_ms":210828,"concrete_test":"Compute the one-loop RGEs for all Yukawa operators in Eqs. (5) and (34) from Λ down to mT, impose Eqs. (20)-(21) (or (43)-(44)) at Λ, and evaluate the T-mediated p→π0e+ amplitude at the low scale. If the induced amplitude exceeds the experimental bound for O(1) high-scale coefficients, the suppression cannot be maintained without tuning the UV Wilson coefficients to 10^-9; if it remains below the bound for generic coefficients, the concern is resolved. Present the required cancellation accuracy as a function of Λ and mT.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that a light triplet T in 5H can be made safe from proton decay by higher-dimensional operators depends on the exact matrix conditions (20)-(21) (or (43)-(44)) that set the triplet's quark-quark couplings to zero. The paper itself states in Sec. 2.3 that these relations 'are certainly not invariant under the renormalization group equation running' and 'are not result of some particular symmetry,' and that the required cancellation level is mT/(10^12 GeV). For mT near the TeV scale, this is one part in 10^9. Because the Lagrangian is an effective theory with cutoff Λ, the Wilson coefficients at Λ are free; to make the physical combinations vanish at the proton-decay scale one must choose UV coefficients that cancel the one-loop RG mixing and threshold corrections to 10^-9 precision. That is not a demonstrated 'bypass' of the doublet-triplet splitting problem but a different, comparably severe fine-tuning. The paper's own benchmarks do not specify such a UV boundary condition, so the central claim is conditional on an unstated, unprotected tuning.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper advocates a light color-triplet scalar (leptoquark) T in the 5H of SU(5) as a viable alternative to the usual doublet–triplet mass splitting. The authors show that higher-dimensional SU(5)-invariant operators can in principle make the dangerous quark–quark (or quark–lepton) couplings of T vanish, in both the 24H and 75H symmetry-breaking scenarios. They then couple this idea to radiative neutrino mass generation by introducing 10H or 15H scalar representations, derive one-loop neutrino-mass formulae, perform gauge-coupling-unification scans, and present benchmark fits to neutrino oscillation data. They emphasize that the light triplet can be at collider scales while proton-decay bounds are evaded, and they discuss some collider signatures.","tokens_in":23339,"tokens_out":3327,"duration_ms":34911,"significance":"If the framework were fully realized, it would offer a qualitatively different resolution of the doublet–triplet splitting problem: instead of making the triplet heavy, one suppresses its baryon-number-violating couplings while keeping it light and testable. The group-theoretic decompositions, the derivation of the color-triplet couplings in Eqs. (15)–(19) and (38)–(42), and the one-loop neutrino-mass formulae appear internally consistent. The paper is also honest in several places about what it does not do, and the explicit benchmark fits (Table III) demonstrate that the proposed mechanisms can reproduce current neutrino-oscillation data. The 75H scenarios benefit from very high unification scales, which is a useful technical observation.","major_comments":[{"comment":"The central viability claim—that a light triplet T can be made safe from proton decay—rests on exact Yukawa-matrix cancellations that the authors themselves state are 'not invariant under the renormalization group equation running' and 'are not result of some particular symmetry.' For mT near the TeV scale and proton-decay-scale matching, the required cancellation precision is mT/(10^12 GeV) ~ 10^-9, as the paper notes. This means the framework does not bypass the doublet–triplet splitting problem; it relocates the fine-tuning into the Yukawa sector, with the additional burden that the cancellation must be imposed at the proton-decay scale and must survive radiative corrections and threshold effects. The manuscript provides no UV boundary condition, RG analysis, or symmetry argument that would produce the needed low-scale alignment. Because the light-triplet scenario is the paper's main thesis, this missing support is load-bearing and needs to be addressed or explicitly reframed as a proof-of-principle with a quantified fine-tuning budget.","section":"Sec. 2.3, Eqs. (20)–(23) and (43)–(46)"},{"comment":"In the 15H extension, the paper 'explicitly assume[s] that the one-loop contribution of Fig. 3 dominates over the tree-level contribution' of the type-II seesaw, but it provides no argument or numerical estimate for this assumption. Dominance requires either a sufficiently small VEV of the SU(2)_L triplet in 15H or sufficiently small Yukawa couplings Y_Y', and the scalar potential that would determine the triplet VEV is not shown. Since the neutrino-mass matrix of Eq. (82) depends on this loop being the leading contribution, this assumption is not peripheral; it should be backed by a concrete region of parameter space or by a demonstration that the tree-level contribution can always be made negligible without conflicting with other constraints.","section":"Sec. 4.1.2, around Eq. (78) and Fig. 3"},{"comment":"The quoted 'highest possible unification scale' is obtained by an automated scan in which all scalar masses except the leptoquark pair are treated as free parameters between 1 TeV and MGUT. This yields an upper bound under a specific fine-tuned spectrum, not a typical or natural value. The text sometimes reads as if this M_max_GUT is the scale of the scenario, and it is then compared to proton-decay bounds. The authors should state more prominently that this is a maximized quantity and that any realistic spectrum requires all the intermediate scalar masses to be arranged to achieve it; otherwise the comparison overstates the compatibility with proton-decay constraints.","section":"Tables I and IV"}],"minor_comments":[{"comment":"In the sentence about 'leptoquark multiplets η3 ∈ 10H and ∆3 ∈ 155 as well as leptoquark T ∈ 5H', '155' is a typo for '15H'.","section":"Sec. 4.1.2"},{"comment":"The word 'stiplulates' in the discussion of the decay pattern of η3^{2/3} should be 'stipulates'.","section":"Sec. 5"},{"comment":"The phrase 'if it defers from the 24-dimensional scenario' should read 'differs from'; also 'self-consistancy' in Sec. 4.2.1 should be 'self-consistency'.","section":"Sec. 3"},{"comment":"The claim that 'there are infinitely many ways to implement the suppression' is trivially true because of arbitrary unitary rotations, but it would be helpful to state that such rotations do not affect the size of the required cancellation, which is fixed by the matrix-element conditions.","section":"Sec. 2.3"}],"recommendation":"major_revision","confidential_remarks":"This is a model-building paper in the spirit of the authors' previous work, with the 75H analysis and the neutrino-mass constructions as new elements. The main issue is that the central 'light triplet made safe' claim requires an unexplained, RG-unstable fine-tuning that the authors partially acknowledge. I would not reject the paper, because the formal demonstration is coherent and the neutrino fits are useful; but the claim as worded ('entirely possible to bypass the experimental source of the doublet-triplet splitting problem') is stronger than what is shown. A major revision should either provide a concrete RG/threshold analysis showing that the cancellation can be realized from some UV boundary condition, or explicitly restrict the paper's claim to a proof-of-principle with an honest statement of the tuning involved. The scope fits hep-ph well and the paper is likely to be influential if the framing is corrected."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this if you track non-supersymmetric GUT model building. What is genuinely new: the 75H symmetry-breaking scenario, the d=6 operator accounting needed there, and the one-loop neutrino mass constructions in both the 24H and 75H versions. The group-theoretic decompositions look right, the benchmark fits to neutrino data are honest existence proofs (chi-square around 1.5, with all parameters listed), and the unification tables show where the scales can go. The authors also state plainly that they are not solving the doublet-triplet splitting problem, only relocating it.\n\nThe soft spot is exactly where the stress-test note points. The load-bearing condition is suppression of the triplet's quark-quark couplings, Eqs. (20)–(21) for 24H and (43)–(44) for 75H. The paper itself states that these relations are certainly not invariant under RG running and are not the result of some particular symmetry. For a TeV-scale triplet, the required cancellation is one part in roughly 10^9, enforced at the proton-decay scale. That is not a mechanism; it is a boundary condition chosen to make the phenomenology work. The paper deserves credit for not hiding this, but the central advertised claim — that the light triplet regime bypasses the experimental source of the doublet-triplet splitting problem — is consequently conditional, not established.\n\nThe 75H scenario is somewhat more robust than the 24H one, because the unification scale can be so high that gauge-mediated proton decay is irrelevant. Still, in all four variants the scalar spectrum is assumed rather than derived from a complete scalar potential, and the neutrinoless double-beta and cosmological bounds are noted but not deeply integrated. Those are secondary gaps, not fatal flaws.\n\nWho gets value: model builders working on non-SUSY SU(5), leptoquark phenomenology, and radiative neutrino mass. The paper is serious, internally consistent, and unusually candid about its limitations. It deserves peer review. The right referee should press for a quantitative RG analysis of the UV boundary conditions needed to maintain the Yukawa cancellations, or at least an explicit statement of how the tuning is to be stabilized. Without that, the framework is a proof of possibility, not a fully viable alternative.","headline":"A careful and mostly honest extension of the authors' light-triplet SU(5) program; the new 75H machinery is solid and the neutrino fits are genuine, but the proton-stability 'bypass' still rests on unprotected Yukawa cancellations, exactly as the paper itself admits.","tokens_in":743,"tokens_out":1429,"would_cite":true,"duration_ms":29966,"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":"This paper argues that the color-triplet scalar partner of the Higgs doublet in SU(5) can stay light and collider-accessible if higher-dimensional operators suppress its baryon-number-violating couplings, and that the same triplet can…","keywords":["doublet-triplet splitting","SU(5) grand unified theory","scalar leptoquark","proton decay suppression","radiative neutrino mass","higher-dimensional operators","gauge coupling unification"],"falsifier":"A high-precision renormalization-group and threshold calculation of the cancellation conditions, Eqs. (20)--(21) in the $24_H$ case and Eqs. (43)--(44) in the $75_H$ case, would settle the claim: if the low-scale proton-decay amplitude reappears above the current experimental bound, i.e., if the residual triplet-mediated coupling exceeds about $m_T/(10^{12}\\,\\mathrm{GeV})$, the framework fails. Conversely, observing a TeV-scale scalar with unsuppressed quark-quark couplings would immediately rule it out.","tokens_in":2109,"feed_emoji":"⚛️","tokens_out":2299,"duration_ms":91302,"temperature":0.7,"pith_summary":"This paper sets out to establish that the color-triplet scalar of SU(5) grand unification does not have to be banished to an extremely high mass. With non-renormalizable, higher-dimensional operators, the triplet's proton-decay-inducing couplings can be cancelled so that the triplet is light, possibly even within collider reach, while proton stability is preserved. The same triplet, mixed with leptoquarks from a 10- or 15-dimensional representation, generates neutrino masses at one loop, tying neutrino physics to a directly testable state. The authors demonstrate the mechanism in two SU(5) breaking schemes, one with a 24-dimensional Higgs and one with a 75-dimensional Higgs, and show that gauge coupling unification can be maintained in all four extensions. A sympathetic reader would care because this shifts the color triplet from a theoretical nuisance to an accelerator-accessible probe of the high-scale theory.","feed_headline":"One light leptoquark dodges proton decay and yields neutrino masses","feed_subtitle":"Higher-dimensional SU(5) operators suppress baryon-number violation, so the color triplet remains TeV-accessible and testable.","key_machinery":"The central object is the color-triplet scalar $T = (3,1,-1/3)$ inside the $5_H$ Higgs, whose SU(5)-invariant couplings to $10_F 5_F$ and $10_F 10_F$ are extended by higher-dimensional operators suppressed by the cutoff $\\Lambda$. The mechanism that carries the argument is the cancellation structure in the Yukawa sector: the relations (20)--(23) in the $24_H$ case and (43)--(46) in the $75_H$ case force the triplet's baryon-number-violating couplings to vanish while preserving charged-fermion masses. Neutrino masses come from the mixing of $T$ with another scalar leptoquark ($\\eta_3^{-1/3}$ in $10_H$ or $\\Delta_3^{-1/3}$ in $15_H$), with mixing angle $\\theta$ and the one-loop formula $M_N \\approx (3 \\sin 2\\theta / 32\\pi^2) \\ln(m_{S_1}^2/m_{S_2}^2)[\\ldots]$. The same objects control the unification economy: in $24_H$ scenarios a dimension-five gauge kinetic operator with parameter $\\epsilon_5$ raises $M_{\\mathrm{GUT}}$ to $(3.4$--$5.9)\\times 10^{14}$ GeV, while in $75_H$ scenarios the $\\Phi_3(8,3,0)$ multiplet allows $M_{\\mathrm{GUT}}$ up to $10^{19}$ GeV.","core_discovery":"The core claim is that the light color triplet $T$ in the $5_H$ representation can be made compatible with measured proton decay limits and can simultaneously be responsible for neutrino masses. Writing all dimension-four, dimension-five, and (where needed) dimension-six contractions between the fermion representations $10_F$ and $5_F$, the paper expresses the triplet's couplings to quark-quark and quark-lepton pairs through Yukawa matrices; imposing conditions such as $Y_d - Y_1 \\epsilon_{24} + Y_2 \\epsilon_{24} = 0$ and $(Y_u + Y_u^T) - (Y_3 + Y_3^T)\\epsilon_{24} + \\frac{1}{4}(Y_4 + Y_4^T)\\epsilon_{24} = 0$ kills tree-level proton decay while leaving viable charged-fermion masses. The same triplet mixes with a second leptoquark from a $10_H$ or $15_H$ representation, generating one-loop Majorana neutrino masses through the usual radiative formula; in the $24_H$ cases the unified scale becomes large enough only with higher-dimensional gauge kinetic terms and a specific suppression pattern for gauge-boson-mediated proton decay, while the $75_H$ cases can reach $M_{\\mathrm{GUT}} \\sim 10^{19}$ GeV without such suppression. Numerical fits reproduce the five neutrino observables with $\\chi^2 \\sim 1.5$.","pith_inferences":["If the cancellation relations are taken literally as exact at the cutoff scale, the light leptoquark's couplings to fermions are fully determined by the charged-fermion mass matrices; global fits of low-energy flavor observables could therefore indirectly test the structure even before direct production.","Because the cancellations are not protected by any symmetry, a UV completion of the higher-dimensional operators would need to explain the tuning; the framework would be sharpened by identifying a discrete symmetry that enforces the required relations.","The near-Planck-scale unification of the $75_H$ scenarios suggests the light-triplet idea could plausibly be embedded in a Planck-scale or string-motivated construction, where future proton-decay searches would see nothing from gauge bosons and the collider search for the triplet would be the only probe."],"forward_implications":["The light-triplet regime removes the need for an extreme mass hierarchy between the doublet and triplet partners in $5_H$: the triplet can sit near the TeV scale while the doublet is the Standard Model Higgs.","The same scalar that generates neutrino masses at one loop can be produced at colliders; in the $24_H+10_H+5_H$ scenario the $\\eta_3$ leptoquarks couple most strongly to the $d$ quark, giving characteristic final states, and improved proton-decay limits push the allowed leptoquark masses upward.","In the $24_H$ scenarios, gauge coupling unification with a light triplet requires higher-dimensional gauge kinetic terms plus suppression of gauge-boson-mediated proton decay, with $M_{\\mathrm{GUT}}$ in the $(3.4$--$5.9)\\times 10^{14}$ GeV range; the $75_H$ scenarios need no such suppression and can reach $M_{\\mathrm{GUT}}$ up to $10^{19}$ GeV.","Benchmark fits reproduce the solar and atmospheric mass-squared differences and all three lepton mixing angles, with the sum of neutrino masses at 76 meV (in the $24_H$ $10_H$ case) and a neutrinoless double-beta parameter of 2.69 meV near upcoming experimental sensitivity.","Scalar-mediated proton decay is rendered negligible, because the residual loop diagram requires two higher-dimensional vertices and is suppressed by the cutoff squared and a loop factor."],"supporting_citations":[{"why":"Supplies the original light-triplet proposal and the higher-dimensional contraction framework that this paper extends to neutrino masses and the 75H breaking scheme.","marker":"[4]"},{"why":"Establishes the required cancellation precision of $m_T/(10^{12}\\,\\mathrm{GeV})$ for the triplet-mediated proton-decay couplings.","marker":"[19]"},{"why":"Provides the one-loop radiative neutrino mass formula used for the scalar leptoquark mixing diagrams.","marker":"[26]"},{"why":"Gives the conditions for suppressing gauge-boson-mediated proton decay and the associated lower bound on $M_{\\mathrm{GUT}}$.","marker":"[14]"},{"why":"Provides the updated effective-theory analysis of minimal SU(5) that sets the current bound on $M_{\\mathrm{GUT}}$ used for comparison.","marker":"[48]"},{"why":"Introduces the 75-dimensional representation and its symmetry breaking pattern used in the alternative scenarios.","marker":"[21]"},{"why":"Earlier work showing non-supersymmetric SU(5) unification with light leptoquarks and radiative neutrino mass, the backdrop this paper revises.","marker":"[16]"},{"why":"NuFit-6.0 neutrino oscillation data that serve as inputs for the benchmark fits of the neutrino sector.","marker":"[49]"}],"fun_headline_variants":["Light leptoquark gives neutrino mass, avoids proton decay","SU(5) leptoquark: TeV-scale neutrino mass, no decay","Higher-dim SU(5) kills proton decay, makes neutrinos","Leptoquark from SU(5) yields neutrino mass, survives","Accelerator-accessible leptoquark makes neutrinos"],"cache_read_input_tokens":25984,"weakest_assumption_plain":"The framework rests on exact cancellations among independent Yukawa matrices, relations (20)--(23) or (43)--(46), that are not guaranteed by any symmetry and must persist at the proton-decay scale to an accuracy the paper estimates as $m_T/(10^{12}\\,\\mathrm{GeV})$.","fun_headline_variants_meta":{"raw":{"variants":["Light leptoquark gives neutrino mass, avoids proton decay","SU(5) leptoquark: TeV-scale neutrino mass, no decay","Higher-dim SU(5) kills proton decay, makes neutrinos","Leptoquark from SU(5) yields neutrino mass, survives","Accelerator-accessible leptoquark makes neutrinos"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00022,"raw_usage":{"total_tokens":1501,"prompt_tokens":1051,"completion_tokens":450,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":667,"completion_tokens_details":{"reasoning_tokens":359}},"tokens_in":667,"tokens_out":450,"duration_ms":4498,"temperature":1.0,"reasoning_tokens":359,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:12:03.722313+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A high-precision renormalization-group and threshold calculation of the cancellation conditions, Eqs. (20)--(21) in the $24_H$ case and Eqs. (43)--(44) in the $75_H$ case, would settle the claim: if the low-scale proton-decay amplitude reappears above the current experimental bound, i.e., if the residual triplet-mediated coupling exceeds about $m_T/(10^{12}\\,\\mathrm{GeV})$, the framework fails. Conversely, observing a TeV-scale scalar with unsuppressed quark-quark couplings would immediately rule it out.","supporting_citations":[{"cited_title":"How Long Could We Live?","cited_arxiv_id":"hep-ph/0410198","evidence_quote":"Gives the conditions for suppressing gauge-boson-mediated proton decay and the associated lower bound on $M_{\\mathrm{GUT}}$."},{"cited_title":"SYMMETRY BREAKING MECHANISM IN AN ALTERNATIVE SU(5) MODEL,","cited_arxiv_id":null,"evidence_quote":"Introduces the 75-dimensional representation and its symmetry breaking pattern used in the alternative scenarios."}],"review_version":1}