{"id":"1186915a-b574-4041-bb77-3b3f4cd4ffe3","arxiv_id":"1908.08964","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Dropping renormalizability in effective theories of vector-like quarks opens five new multiplet types whose widths can be so suppressed that the quarks become long-lived R-hadrons at the LHC.","lead":"This paper studies what happens if new heavy quarks interact with known particles through higher-dimensional, non-renormalizable operators instead of the usual simple ones. It finds five new types of such quarks whose decays can be so slow that they would evade standard LHC searches and show up as long-lived particles.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table 6's long-lifetime thresholds are extrapolated from an unshown width calculation; the parametric scaling is sound, but the numerical boundaries need the explicit width formulas to be verified.","rationale":"The reader's weakest assumption points to the width calculation behind Table 6, and that is indeed the least documented part of the paper. I agree that the quantitative thresholds (1/y ~ 10^6-10^8 TeV for displaced/stable regimes) are not fully substantiated because the width formulas are absent and the sub-QCD values are explicitly extrapolated. However, I find the concern less severe than the reader frames it: the parametric scaling Gamma ~ y^2 v^2 M/(16*pi) follows directly from power counting for the dimension-5 Yukawa operators, and the heavy-quark expansion justifies the free-quark width for the hadron up to small QCD corrections. Crucially, the reader's suggested alternative source of larger widths, dimension-6 four-fermion operators, is negligible in the long-lived regime: for Lambda ~ 10^6 TeV, M = 2 TeV, a coefficient 1/Lambda^2 gives Gamma_6 ~ M^5/(16*pi)^3 Lambda^4 ~ 10^-20 GeV, far below the dimension-5 width ~ 10^-12 GeV. Non-natural couplings would only rescale the Lambda threshold, not remove the qualitative prediction of long lifetimes for sufficiently large Lambda. The remaining legitimate issue is that Table 6 and Figure 7 state numbers without showing the underlying calculation; this justifies the CONDITIONAL verdict (i.e., require the authors to provide the width formulas or a reproducible calculation) but does not invalidate the central claim. Hence I recommend UNCHANGED, preserving the reader's CONDITIONAL verdict.","tokens_in":30008,"tokens_out":21209,"duration_ms":215380,"concrete_test":"Ask the authors to provide (or independently recompute) the explicit partial-width expressions for each component (T, B, X, Y, X', Y') in the T5, T4, F1, F5 and F7 models from the dimension-5 Lagrangian in Eqs. (11)-(15), and verify that the total width at M = 2 TeV, y = (5.3 TeV)^-1 reproduces the Lambda_QCD entry in Table 6; then check the scaling Gamma(y) down to 10^-16 GeV to confirm the extrapolated columns.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central long-lifetime claim rests on the total decay width of each NRVLQ component. Figure 7 and Table 6 quote numerical thresholds (e.g., 1/y = 5.3 TeV for T5 T at Gamma = Lambda_QCD, and 10^6-10^8 TeV for Gamma = 10^-12/10^-16 GeV) without giving the width formulas. The text states only that the sub-QCD values were 'obtained by extrapolation of the results calculated for larger couplings.' Power counting for the dimension-5 Yukawa operator gives Gamma ~ y^2 v^2 M/(16*pi) times multiplicity, so the quadratic scaling Gamma proportional to y^2 below Lambda_QCD is plausible, and the heavy-quark expansion supports using the free-quark width after hadronization up to O(Lambda_QCD/M) corrections. However, a factor of a few in the width shifts the Lambda thresholds by only a factor of about 2-10, so the qualitative conclusion that NRVLQs become long-lived for very large Lambda is robust. The concern is therefore with the numerical substantiation of Table 6, not with the central claim; the missing formulas and extrapolation should be documented or the calculation made reproducible.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a model-independent effective field theory for Standard Model extensions with vector-like quarks, truncated at canonical dimension 5. It classifies the multiplets that can have linear couplings to SM fields at that order, identifying seven 'renormalizable' vector-like quarks (RVLQ) and five 'non-renormalizable' vector-like quarks (NRVLQ). For each multiplet the authors present mass matrices, mixing angles, indirect constraints from electroweak and Higgs observables, LHC production cross sections, decay branching ratios, and a formula for recasting pair-production mass limits when additional decay channels are present. The central new claim is that NRVLQs, whose leading interactions are dimension-5, have widths suppressed by the cutoff scale and become long-lived for large Λ, so that the hadrons they form evade prompt-decay searches and give R-hadron-like signatures such as anomalous ionization, time-of-flight signals, and displaced vertices.","tokens_in":30296,"tokens_out":12130,"duration_ms":139619,"significance":"If the quantitative claims hold, this is a useful systematic addition to the vector-like quark literature. The paper provides a complete classification of multiplets and dimension-5 operators, explicit mass matrices, SMEFT-matching results, and a practical mass-limit recast formula in Eq. (49). The prediction that certain vector-like quarks can be long-lived for Λ around or above 10^6 TeV is falsifiable and differs qualitatively from the standard prompt-decay assumption. The qualitative lifetime suppression follows from power counting and is robust, and the paper is careful to distinguish renormalizable and non-renormalizable multiplets. The main weakness is that the quantitative thresholds in Table 6 and Figure 7, which are the numerical basis for the long-lifetime claim, are not backed by explicit width formulas or a documented extrapolation procedure.","major_comments":[{"comment":"The numerical backbone of the long-lifetime claim is not documented. Table 6 gives values of 1/y at which the total width equals Λ_QCD, 10^-12 GeV, and 10^-16 GeV (for example, 5.3 TeV for a T5 T, and 10^6-10^8 TeV for the displaced-vertex and detector-stable thresholds), and Figure 7 plots the total widths, but no partial- or total-width formulas are shown. The text says only that the sub-QCD values were 'obtained by extrapolation of the results calculated for larger couplings.' Since the abstract and conclusions present the long lifetime as the most dramatic effect, the authors should provide the explicit width formulas used, specify the extrapolation method, and quantify the sensitivity to neglected dimension-6 operators and to O(Λ_QCD/M) corrections. Without this, the numerical thresholds in Table 6 cannot be checked or reproduced.","section":"Section 6, Figure 7, Table 6"}],"minor_comments":[{"comment":"The statement that NRVLQs contribute to the SMEFT at tree level only from dimension 8 is not correct as stated: connecting two dimension-5 Qbar-q-phi-phi type vertices with a heavy-quark propagator generates a dimension-7 operator of the form qbar-q-phi^4, not dimension 8. This does not change the qualitative conclusion that the indirect effects are small, but the sentence should be corrected or qualified.","section":"Section 4"},{"comment":"The symbols in the last three columns of Table 1 are not legible in the typeset text and their meaning is not defined; please use explicit check and cross symbols or add a legend.","section":"Table 1"},{"comment":"The caption of Figure 7 says 'total decay width of T and B', but the six panels display X', X, T, B, Y, and Y'; the caption should be updated to describe all panels.","section":"Figure 7"},{"comment":"The typesetting of the recast formula obscures the exponents; it should read M_Sigma = (M_1^{1/2} + f^{1/2} log Sigma)^2.","section":"Equations (36) and (49)"},{"comment":"Please state the proper decay length corresponding to the thresholds Lambda_disp and Lambda_longlived (for example, c tau values) so that the relation between Table 6 and the detector-stability discussion is transparent.","section":"Section 6"},{"comment":"There are several typographical errors: 'loosing' near the end of Section 2, 'the later eventually becomes' in Section 5, 'proceses' in Section 7, 'statisfied' in Appendix C, and 'The always decay' in Section 6.","section":"Various"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid EFT phenomenology contribution, and the stress-test concern from the reader lands: the missing width calculation behind Table 6 is the one blocking issue. If the authors supply the explicit formulas and extrapolation details, and fix the dimension-7 versus dimension-8 statement, the paper should be publishable. I do not see circularity or an attribution problem; the relation to ref. [21] is stated clearly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a solid EFT paper doing something genuinely new. It classifies all dimension-5 interactions of vector-like quarks, identifies five multiplets (T4, T5, F1, F5, F7) that only have linear couplings at that order, and shows their decay widths can be suppressed enough to make R-hadron, displaced-vertex, and long-lived signatures relevant. The reader's conditional verdict is right. The machinery is standard but applied carefully: mass matrices, SMEFT matching, branching-ratio triangles, and a genuinely useful formula to recast LHC pair-production limits when the branching ratios no longer sum to one. I checked that recast logic; the exponential approximation for the production cross section with f = 20.5 GeV is a reasonable interpolation, and the claimed 3% agreement over the relevant mass range is credible.\n\nCredit where it is due: the classification itself, the inclusion of the magnetic operators, the treatment of the dimension-5 Yukawa operators, and the observation that the no-dimension-4 multiplets have widths set by y^2 v^2 M/(16 pi), so lifetimes grow roughly as 1/y^2. The qualitative long-lifetime conclusion follows from power counting and is robust to factors of a few in the width. The paper also states its limitations honestly about extrapolating below the QCD scale.\n\nThe soft spot is exactly where the reader put it. Figure 7 and Table 6 quote widths and 1/y thresholds, but the width formulas are not shown. The text says the sub-QCD values are obtained by extrapolation from larger couplings. I do not think the central claim collapses: a factor of a few in the width shifts the thresholds by a factor of 2-10, not orders of magnitude. But Table 6 is presented as quantitative, and right now it is not independently checkable. No code or data are shipped. This should be fixable by putting the total-width expressions in an appendix or providing a small calculation script. One minor slip: the conclusions say the five NRVLQs are \"two triplets and four quadruplets\"; the table shows three quadruplets. Cosmetic, but it will annoy a careful referee. The citation pattern is fine; the self-citations are to earlier dictionary/matching results, not inputs making this circular.\n\nBottom line: this is a BSM phenomenology paper for LHC exotica people and EFT practitioners. It deserves a serious referee. My recommendation: send it to peer review, and ask the authors to document the width calculation and correct the multiplet count before acceptance.","headline":"Solid, systematic EFT paper that finds five vector-like quark multiplets whose leading couplings are dimension-5 and whose lifetimes can become long; the qualitative result is convincing, but the quantitative width table needs the missing formulas before publication.","tokens_in":30813,"tokens_out":2835,"would_cite":true,"duration_ms":28326,"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":"Dropping the assumption of renormalizability turns some hypothetical heavy quarks into long-lived particles that escape the usual prompt-decay searches.","keywords":["vector-like quarks","non-renormalizable interactions","dimension-five operators","effective field theory","long-lived particles","R-hadrons","LHC phenomenology","branching ratios"],"falsifier":"Measure the decay length of pair-produced heavy quarks in the T4 or F5 models with M=2 TeV and 1/y≈5 TeV: the paper predicts widths at or below Λ_QCD≈0.2 GeV, so events should show hadronization, displaced vertices, or late ionizing tracks; observing prompt decays at these parameters would falsify the extrapolated widths. A direct computation of the full partial widths (two-body and three-body) for these multiplets at the Table 6 values of 1/y would also settle the crossing points.","tokens_in":29807,"feed_emoji":"⏳","tokens_out":11832,"duration_ms":114766,"temperature":0.7,"pith_summary":"This paper asks what changes if vector-like quarks—heavy hypothetical quarks common in extensions of the Standard Model—are allowed to interact through non-renormalizable terms as well as the usual renormalizable ones. It argues that once dimension-five operators are included, five new multiplets of vector-like quarks, which the paper calls NRVLQ, can mix with and decay into Standard Model quarks even though they have no dimension-four Yukawa coupling. Because their leading interactions are suppressed by inverse powers of the cutoff scale Λ, their decay widths shrink as Λ grows; for Λ around or above 5 TeV the quarks hadronize before decaying, and for much larger Λ they become long-lived. The paper works out the resulting collider phenomenology: pair production remains, new single-production and decay channels appear, branching ratios no longer obey the standard sum rule, and long-lived signatures such as displaced vertices, anomalous ionization, and delayed time-of-flight replace the prompt decays that current searches assume.","feed_headline":"Nonrenormalizable decays make heavy quarks live long","feed_subtitle":"Five new vector-like quark multiplets would hadronize and show up as displaced vertices or late tracks.","key_machinery":"The key machinery is the dimension-five effective Lagrangian for a single extra quark multiplet, truncated at order $1/\\Lambda$, with two classes of operators: Yukawa-type $\\bar Q q \\phi \\phi$ and magnetic-type $\\bar Q \\sigma^{\\mu\\nu} q F_{\\mu\\nu}$, plus the quadratic $\\bar Q Q \\phi \\phi$ and $\\bar Q \\sigma^{\\mu\\nu} Q F_{\\mu\\nu}$ terms. The classification of which multiplets can have linear couplings rests on the representation condition $T + Y + 1/3 \\in \\mathbb{Z}$ for colour triplets, proved in the paper for products of Standard Model fields; applying it at dimension five adds the five NRVLQ multiplets to the seven renormalizable ones. The power-counting mechanism that carries the long-lifetime claim is that every leading NRVLQ interaction carries at least one inverse power of $\\Lambda$, so decay amplitudes and mixing angles receive a suppression of order $v^2/(\\Lambda M)$ or $v/\\Lambda$; the total width is a decreasing function of $\\Lambda$, crossing the QCD scale and then the displaced-vertex and detector-stability scales as shown in Figure 7 and Table 6 of the paper.","core_discovery":"The central claim is that relaxing renormalizability while keeping gauge invariance and a cutoff Λ above the heavy-quark mass M enlarges the list of vector-like quark multiplets with linear couplings to Standard Model fields from seven at dimension four to twelve at dimension five. The five new multiplets—two triplets and three quadruplets, denoted T4, T5, F1, F5, F7—have no renormalizable linear interaction, so their leading couplings are dimension-five operators of the forms $\\bar Q q \\phi \\phi$ and $\\bar Q \\sigma^{\\mu\\nu} q F_{\\mu\\nu}$. These operators generate mixing with the third generation suppressed by $y v^2/M$ (with $y$ a coupling of dimension inverse mass), so the new quarks evade precision constraints without tuning, while pair production via QCD remains unsuppressed. The decisive consequence is the cutoff dependence of the lifetime: for natural couplings and $\\Lambda \\gtrsim 5$ TeV the width falls below the QCD scale, so hadronization precedes decay, and for $\\Lambda$ around $10^6$ TeV the resulting R-hadrons are long-lived within detector distances and would appear as tracks with anomalous ionization, long time of flight, or displaced vertices rather than as prompt decays. The paper also shows that non-renormalizable operators open new single-production channels and new decay modes, so the standard branching-ratio triangle is replaced by a tetrahedron, and provides the recasting formula $M_\\Sigma = (M_1^{1/2} + f^{1/2}\\log\\Sigma)^2$ for LHC mass limits when the sum of branching ratios to $Hq$, $Zq$, $W^\\pm q'$ is $\\Sigma<1$.","pith_inferences":["Editorial extension: if the long-lifetime regime is realized, existing searches for long-lived supersymmetric particles can be reinterpreted to constrain vector-like quarks, but the distinctive final states (e.g., $Ht$, $Zt$, $W b$) require dedicated displaced-vertex analyses; the paper's estimate of a ~1.5 TeV lower bound is only a first approximation.","Editorial extension: the long-lifetime conclusion is sensitive to the assumed scaling of the width; dimension-six four-fermion operators of the form $qqqQ$, which the paper leaves for future work, could provide additional decay channels and shorten the lifetime, so the window $\\Lambda \\gtrsim 10^6$ TeV is robust only if those operators are suppressed.","Editorial extension: the approximate equality of $Hq$ and $Zq$ branching ratios, traced in the paper to an isospin condition that holds for all multiplets except $F_1$, could be used experimentally as a quantum-number diagnostic: measuring that ratio distinguishes the $F_1$ quadruplet from the other NRVLQ candidates.","Editorial extension: the NRVLQ framework naturally embeds in pseudo-Goldstone composite Higgs models with $\\Lambda=f$; in low-$f$ versions the width is not suppressed enough for long lifetimes, so the long-lived window selects UV completions where the dimension-five operators are generated at a genuinely high scale, such as tree-level heavy-scalar exchange."],"forward_implications":["Pair production of NRVLQ through QCD remains the main production channel up to about 3.5 TeV, so LHC searches for pair-produced heavy quarks can probe them even when single production is suppressed.","For NRVLQ, the branching ratios to $Hq$, $Zq$ and $W^\\pm q'$ no longer sum to one; the recasting formula $M_\\Sigma = (M_1^{1/2}+f^{1/2}\\log\\Sigma)^2$ converts existing LHC mass limits into bounds for the enlarged parameter space.","For $\\Lambda \\gtrsim 10^6$ TeV, the hadrons containing NRVLQ are effectively stable in the detector, so searches for long-lived coloured particles—anomalous ionization, time-of-flight, displaced vertices—become the relevant probes, with an estimated lower mass bound near 1.5 TeV from reinterpreted LHC limits.","Non-renormalizable interactions also modify Higgs physics: the $\\bar Q Q \\phi \\phi$ coupling $Y_1$ contributes to $gg\\to H$ and $H\\to gg$ at one loop with a coefficient unsuppressed by mixing, giving a bound $|{\\rm Re}\\,Y_1|/M \\lesssim 1/[(2T+1)(1.25\\ {\\rm TeV})^2]$.","New decay channels such as $T\\to b W^+ Z$, $T\\to b H W^+$, $B\\to t H W^-$, $B\\to t Z W^-$, and $\\gamma$/$g$ plus a third-generation quark can have branching ratios above 0.01 and alter the standard branching-ratio triangle."],"supporting_citations":[{"why":"Supplies the result that gauge-invariant vector-like quark masses suppress mixing when M is large, the basis for the small mixing angles the paper assumes.","marker":"[3]"},{"why":"Wrote the general renormalizable extension with the seven RVLQ multiplets that this paper extends to dimension five.","marker":"[4]"},{"why":"Provides the standard RVLQ phenomenology, electroweak precision limits, and single-production results that serve as the baseline for the non-renormalizable corrections.","marker":"[10]"},{"why":"Earlier study of dimension-five Higgs operators for the first three multiplets, which the paper generalises to all relevant multiplets and operators.","marker":"[21]"},{"why":"Establishes the method for recasting LHC mass limits when additional decay channels are present, adapted in Appendix B to derive the corrected mass-limit formula.","marker":"[22]"},{"why":"Analyzes bound states and long-lived coloured particles, supporting the hadronization and R-hadron signature discussion for narrow NRVLQ states.","marker":"[23]"},{"why":"Describes hadronization and decay properties of ultraheavy quarks, the basis for treating the heavy quark as a spectator inside R-hadrons.","marker":"[39]"},{"why":"Supplies the LHC pair-production mass limits that the paper rescales to account for branching-ratio sums below one.","marker":"[44]"}],"fun_headline_variants":["Dimension-5 operators extend vector-like quark lifetimes","Nonrenormalizable couplings produce long-lived vector-like quarks","Five new vector-like quark multiplets decay via displaced vertices","Non-renormalizable interactions make new heavy quarks live long"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The long-lifetime claim rests on the assumed parametric size and scaling of the NRVLQ decay widths, whose sub-QCD values in Table 6 are obtained by extrapolation; if the true widths are larger (from neglected four-fermion operators, non-natural couplings, or higher-order corrections), the lifetimes shorten and the boundary where usual searches stop working moves to higher Λ or disappears.","fun_headline_variants_meta":{"raw":{"variants":["Dimension-5 operators extend vector-like quark lifetimes","Nonrenormalizable couplings produce long-lived vector-like quarks","Five new vector-like quark multiplets decay via displaced vertices","Non-renormalizable interactions make new heavy quarks live long"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001265,"raw_usage":{"total_tokens":5188,"prompt_tokens":961,"completion_tokens":4227,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":577,"completion_tokens_details":{"reasoning_tokens":4159}},"tokens_in":577,"tokens_out":4227,"duration_ms":28703,"temperature":1.0,"reasoning_tokens":4159,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:26:05.805069+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the decay length of pair-produced heavy quarks in the T4 or F5 models with M=2 TeV and 1/y≈5 TeV: the paper predicts widths at or below Λ_QCD≈0.2 GeV, so events should show hadronization, displaced vertices, or late ionizing tracks; observing prompt decays at these parameters would falsify the extrapolated widths. A direct computation of the full partial widths (two-body and three-body) for these multiplets at the Table 6 values of 1/y would also settle the crossing points.","supporting_citations":[{"cited_title":"The Possibility of New Fermions With ∆ I = 0 Mass,","cited_arxiv_id":null,"evidence_quote":"Supplies the result that gauge-invariant vector-like quark masses suppress mixing when M is large, the basis for the small mixing angles the paper assumes."},{"cited_title":"Light Higgs and Vector-like Quarks without Prejudice","cited_arxiv_id":"1304.4219","evidence_quote":"Earlier study of dimension-five Higgs operators for the first three multiplets, which the paper generalises to all relevant multiplets and operators."},{"cited_title":"Production and Decay Properties of Ultraheavy Quarks,","cited_arxiv_id":null,"evidence_quote":"Describes hadronization and decay properties of ultraheavy quarks, the basis for treating the heavy quark as a spectator inside R-hadrons."}],"review_version":1}