{"id":"0002d137-3941-4bc4-a612-ecfb52d1d509","arxiv_id":"2504.18664","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"In leptoquark-like new physics, rare top decays to quarks and electron/muon pairs are predicted to occur at branching ratios of about 10^-8 to 10^-6, putting some within reach of LHC searches.","lead":"This paper computes upper bounds, called targets, on how often the top quark can decay into a lighter quark plus electron and muon pairs in leptoquark-like new physics models. The bounds sit near current LHC sensitivity, making rare top decays a useful test for distinguishing types of new physics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified","rationale":"The reader's ACCEPT verdict is well supported. The paper scopes its claim to leptoquark-dominated UV completions, derives the new sum rule in a traceable way, and provides two sets of targets, one relying on less robust B/Z constraints and one relying only on tree-level probes. The main limitation is the restricted model class, which is disclosed. My independent check of the target numerics (e.g., 'up LR' without B/Z) gives BR ~10^-7, consistent with the quoted 3.5e-7. The only soft spot is the approximate recast of CMS tt+ll constraints, but it is disclosed and would not change the headline range. No change to the verdict is needed.","tokens_in":27816,"tokens_out":51473,"duration_ms":434673,"concrete_test":"Recompute the 'up LR' target in Sec. 4.2 using the published CMS likelihood from TOP-22-006 directly instead of the Gaussian-polynomial approximation in Eqs. (68)-(71); if the extracted bound on C^{LR}_{eett} changes by more than a factor of 2, the robust BR(t->u mu e) target would shift by more than an order of magnitude, weakening the claim that CMS is already probing the sum-rule region.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is explicitly conditional on the Remmen-Rodd positivity assumptions: a scalar- or vector-dominated UV completion, improved forward-amplitude scaling, and no loop-induced or Z'-mediated operators. This restriction is stated prominently in Sec. 2 and footnote 1, so the targets are not overclaimed as generic new-physics predictions. Within that stated class, the derivation of the new Delta F=2 sum rule (Eq. 11) is traceable and is saturated by single-leptoquark UV completions, and the numerical targets follow from the quoted flavor-conserving constraints. I find no internal inconsistency or unstated assumption that would undermine the claim. The least secure numerical input is the recast of the CMS tt+ll constraints in Sec. 3.7, which uses Gaussian polynomial fits to public likelihood plots; an error there would shift the robust (parenthetical) targets by an O(1) factor, but not alter the qualitative conclusion that targets are comparable to current LHC bounds.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper applies the analyticity/unitarity-based sum rules of Remmen and Rodd to semileptonic four-fermion operators relevant for rare top decays t→qℓ+ℓ- and t→qℓℓ' (q=u,c; ℓ,ℓ'=e,μ). After restating the existing ΔF=1 bounds (Eq. (4)), the authors derive a new ΔF=2 sum rule (Eq. (11)) that bounds the sum of the two lepton-flavor-violating, top-flavor-violating Wilson coefficients in terms of flavor-conserving coefficients. They compile experimental constraints from μ→e conversion, LEP single-top searches, rare B decays, LHC di-lepton production, Z decays, tt+ℓℓ production, and CMS rare-top searches, and then numerically maximize the rare-top branching ratios subject to the sum rules and these constraints in several three- and six-coefficient scenarios. They find target upper limits around 10^-8–10^-7 for up-quark channels and 10^-7–10^-6 for charm channels, and note that current CMS limits on t→qeμ are already comparable to these targets. The targets are explicitly and repeatedly framed as conditional on a leptoquark-like UV completion satisfying the positivity assumptions, not as model-independent predictions.","tokens_in":27913,"tokens_out":11061,"duration_ms":116248,"significance":"If the targets are correct, they provide concrete, falsifiable expectations for a restricted but physically well-motivated class of new-physics models and a potential discriminator between leptoquark-like UV completions and Z' or loop-induced models. The central derivation of Eq. (11) is explicit and appears sound, and the authors are honest that it is a necessary rather than sufficient condition. The analysis is not circular: the experimental constraints on the flavor-conserving Wilson coefficients are independent of the predicted rare-top rates, and no fitted parameter is used to produce the targets. The paper also clearly discloses the assumptions under which the sum rules hold. The main weaknesses are the under-documented numerical maximization procedure in Sec. 4 and the approximate recast of the CMS tt+ℓℓ constraints in Sec. 3.7, both of which feed directly into the quoted target values.","major_comments":[{"comment":"The numerical maximization procedure is not described in enough detail to be reproduced. Please state how the maxima were computed (e.g., grid scan, random scan, gradient-based optimization, or analytic reduction), how many parameters were varied simultaneously, how the experimental likelihoods from the various probes were combined (in particular whether all constraints are imposed simultaneously or one at a time), and how the Δχ²<4 criterion is applied in the multi-coefficient scenarios. Since the quoted target branching ratios are the central quantitative output of the paper, this information is needed for the reader to verify the results.","section":"Sec. 4, Eqs. (82)-(89) and (94)-(97)"},{"comment":"The per-flavor constraints on C_LR_ℓℓtt and C_RR_ℓℓtt are obtained by fitting fourth-order polynomials to published CMS likelihood curves and by assuming identical electron and muon selection efficiencies. These extracted constraints directly determine the parenthetical 'robust' targets in Sec. 4, which are quoted in the abstract. Please validate the recast, for example by cross-checking against the recent ATLAS analysis [129] or against the full CMS two-dimensional likelihood, and provide a quantitative estimate of the uncertainty in the extracted polynomial coefficients. It would also be helpful to state how the coefficients were digitized and whether the CMS constraints on C_LR and C_RR are treated as independent or correlated.","section":"Sec. 3.7, Eqs. (68)-(73)"}],"minor_comments":[{"comment":"There are typos in the text: 'certain classe of new physics models' should be 'certain classes', and 'dominated by scalars of vectors' should be 'dominated by scalars or vectors'.","section":"Abstract and Sec. 2"},{"comment":"Equation (5) is written as a positivity inequality on a potentially complex quantity; it should state explicitly that the inequality applies to the real part (or that phases have been chosen so that the expression is real), since the Wilson coefficients are in general complex. This is relevant because Sec. 4 later assumes real coefficients and notes that imaginary parts could soften constraints.","section":"Sec. 2, Eq. (5)"},{"comment":"The assumption that selection cuts and detection efficiencies are approximately the same for e+e- and μ+μ- events should be justified or relaxed, since electron and muon reconstruction and isolation requirements at CMS differ; a sentence on the expected size of this effect would help the reader assess the robustness of the recast.","section":"Sec. 3.7"},{"comment":"Figure 1 is useful, but the information would be easier to digest if accompanied by a table that maps each Wilson coefficient to its best probe and lists the section and equation where the corresponding bound is derived; several coefficients are mentioned only in the text.","section":"Fig. 1"},{"comment":"Reference [41] appears to have an incorrect journal/year format ('JHEP23(2020) 082'); please check the entry and correct the volume and year.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is well within the scope of the journal and the central physics claim is defensible: the new ΔF=2 sum rule is derived cleanly and the target branching ratios are explicitly conditional on the Remmen-Rodd positivity assumptions. My recommendation of major revision is driven by the need to document and validate the numerical procedure and the approximate CMS recast, rather than by any identified error in the core derivation. With those additions, I would expect the paper to be suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing is Eq. (11), a sum rule bounding the sum of the two Delta F=2 semileptonic Wilson coefficients by products of flavor-conserving coefficients. The authors use it to turn existing flavor-conserving constraints into branching-ratio targets for t->q e mu, and show those targets are already close to current CMS limits. That is a meaningful result, not a repackaging of their earlier paper.\n\nThe derivation of Eq. (11) from the Remmen-Rodd inequality is traceable and honest: the two-flavor parameterization is explicitly a necessary condition, and the authors say so. The scope is stated prominently: the targets apply to scalar/vector leptoquark-dominated UV completions, not Z' or loop-induced models. That conditionality is exactly right. The phenomenological survey in Sec. 3 is thorough, covering mu->e conversion, rare top decays, single top at LEP, B decays, dilepton production, Z decays, and tt+ll. The distinction between robust tree-level constraints (tt+ll, dilepton) and less robust loop-level B/Z constraints is clearly drawn, and the parenthetical numbers without B/Z show how much depends on those inputs. Updating RK/RK* with CMS data is a legitimate improvement over [11].\n\nSoft spots, in proportion: the Sec. 4 numerical scans are described verbally (\"numerically determine the maximal value\") without an algorithm or reproducibility details. That is a moderate issue; a referee should ask for a documented scan procedure. The tt+ll recast uses Gaussian polynomial fits to public CMS likelihood plots; an error there shifts targets by O(1), not qualitatively. The B and Z constraints rely on leading-log dominance, which the authors disclose but is still a real limitation; the robust numbers are the parenthetical ones. Minor: the abstract has a typo (\"classe\"). The phase-averaging step from Eq. (8) to (9) is compressed, but plausible.\n\nOverall, the central argument holds up within the stated class of models. The paper is conditionally scoped, clearly written, and the new bound is a genuine addition. The citation pattern looks fine; reuse of [11] is appropriate and not circular.\n\nThis paper is for top/flavor pheno readers, LHC search optimizers, and SMEFT positivity practitioners. It deserves a serious referee. I would not desk reject it. Send it to peer review.","headline":"A clean, well-scoped extension of the positivity sum-rule program to LFV top decays; the new Delta F=2 bound is real and the t->q e mu targets are worth taking seriously.","tokens_in":28511,"tokens_out":1848,"would_cite":true,"duration_ms":19562,"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":"Within a broad class of leptoquark-like new physics, current flavor-conserving measurements pin the rare top decays $t\\to q\\ell^+\\ell^-$ and $t\\to q e\\mu$ into narrow branching-ratio targets near $10^{-8}$ to $10^{-6}$, and existing LHC…","keywords":["rare top decays","flavor-changing neutral currents","lepton flavor violation","positivity sum rules","leptoquarks","effective field theory","top quark","branching ratio targets"],"falsifier":"A search that observes $t\\to u e\\mu$ with a branching ratio above the scenario's upper target, for example above $1.2\\times10^{-8}$ in the up-LR scenario or above $2.9\\times10^{-7}$ in the charm-RR scenario, would contradict the sum-rule target for that channel; equivalently, a null result at the quoted maxima would leave the leptoquark class viable but would not test $Z'$ models.","tokens_in":2395,"feed_emoji":"🎯","tokens_out":9604,"duration_ms":138036,"temperature":0.7,"pith_summary":"This paper argues that in new-physics models whose ultraviolet completion is dominated by scalar or vector leptoquarks, the same analyticity and unitarity relations that constrain flavor-conserving four-fermion interactions also cap the rates of the flavor-violating top decays $t\\to q\\ell^+\\ell^-$ and $t\\to q e\\mu$. Combining those sum-rule bounds with current measurements of di-lepton production, $t\\bar t$ plus leptons, $Z$ and $B$ decays, and $\\mu\\to e$ conversion, the authors convert the bounds into target branching ratios: roughly $10^{-8}$ to $10^{-7}$ for up-quark channels and $10^{-7}$ to $10^{-6}$ for charm channels. For the lepton-flavor-violating decays $t\\to q e\\mu$, they derive a new bound on the $\\Delta F=2$ Wilson coefficients and find that the resulting targets are comparable with existing LHC limits. The payoff is diagnostic: if the LHC observes a rare top decay above the target range, the responsible new physics must be of a type that evades the sum rules, such as a $Z'$ boson or a loop-induced operator.","feed_headline":"Sum rules put rare top decay rates in a testable window","feed_subtitle":"Flavor-conserving data pin rare top decay rates to 10^-8 to 10^-6; LHC searches already probe the e mu channel.","key_machinery":"The machinery is the set of positivity sum rules derived from S-matrix analyticity and partial-wave unitarity for dimension-six four-fermion operators. For UV completions dominated by scalars or vectors, the relative signs of the $\\Delta F=0$ coefficients are fixed, and the size of every $\\Delta F=1$ coefficient is bounded by the geometric mean of two $\\Delta F=0$ coefficients, $|C^{XY}_{\\ell\\ell' qq'}|\\le\\sqrt{C^{XY}_{\\ell\\ell qq}C^{XY}_{\\ell'\\ell' qq'}}$. The paper's new result extends this to $\\Delta F=2$: choosing two-flavor test vectors in the master inequality gives $|C^{XY}_{\\ell\\ell' qq'}|+|C^{XY}_{\\ell'\\ell qq'}|\\le \\sqrt{C^{XY}_{\\ell\\ell qq}C^{XY}_{\\ell'\\ell' q'q'}} + \\sqrt{C^{XY}_{\\ell\\ell q'q'}C^{XY}_{\\ell'\\ell' qq}}$. These inequalities are necessary conditions, not sufficient ones, and they hold for single or multiple scalar or vector leptoquarks, which saturate the relations.","core_discovery":"The central claim is that flavor-conserving data already in hand force the flavor-violating semileptonic top operators into a specific, small range, so the branching ratios for $t\\to q\\ell^+\\ell^-$ and $t\\to q e\\mu$ are not free parameters even before a dedicated search. For the eight lepton-flavor-conserving scenarios, the paper finds maximal branching ratios between $1.2\\times10^{-8}$ and $3.7\\times10^{-7}$ when $Z$ and $B$ constraints are included, and between $1.6\\times10^{-7}$ and $1.8\\times10^{-6}$ when only the more robust tree-level constraints are used. For the lepton-flavor-violating decays, the analogous maxima are $1.2\\times10^{-8}$ to $2.9\\times10^{-7}$ with all constraints and $3.0\\times10^{-7}$ to $4.1\\times10^{-6}$ without the loop-level ones. The paper's new $\\Delta F=2$ sum rule, bounding $|C^{XY}_{\\ell\\ell' qq'}|+|C^{XY}_{\\ell'\\ell qq'}|$ by products of flavor-conserving coefficients, is what makes the $e\\mu$ targets possible. Because current LHC limits on $t\\to q e\\mu$ already sit at $2.2\\times10^{-8}$ for $t\\to u e\\mu$ and $3.7\\times10^{-7}$ for $t\\to c e\\mu$, the next LHC run can cover the entire sum-rule-allowed window.","pith_inferences":["Because the $\\Delta F=2$ bound is stated as necessary but not sufficient, extending the derivation to all three quark and lepton generations at once could sharpen the targets and lower the maximal branching ratios below the quoted values.","The diagnostic logic implies that a null LHC result at the quoted levels would not rule out new physics in rare top decays; it would only rule out the leptoquark-dominated class, leaving models such as $Z'$ bosons with flavor-changing couplings untouched by these positivity relations.","The sign-fixed relations suggest correlated predictions across channels: within a given scalar or vector leptoquark scenario, a signal near the upper end of the $t\\to u e\\mu$ target should be accompanied by specific signs of the flavor-conserving coefficients, which are testable in $t\\bar t\\ell\\ell$ production and high-mass di-lepton tails.","The paper's distinction between robust tree-level constraints and less robust loop-level $Z$ and $B$ constraints provides a way to rank which targets are most trustworthy; future improvements in $Z$-pole and rare-$B$ measurements will narrow the spread between the two quoted numbers."],"forward_implications":["If the central claim is correct, the quoted branching ratios become concrete search goals: for example, $t\\to u e^+e^-$ near $10^{-8}$ and $t\\to c\\mu^+\\mu^-$ near $10^{-7}$, both within reach of the high-luminosity LHC.","An observed $t\\to q e\\mu$ rate above the target range would be evidence for new physics outside the leptoquark sum-rule class, most plausibly a $Z'$ boson or a loop-induced operator.","The existing LHC limits on $t\\to q e\\mu$ already overlap the predicted window, so the next round of searches will either find a signal or close the sum-rule-allowed region.","Better future constraints on di-lepton production and $t\\bar t\\ell\\ell$ will push the targets lower, so the target band is not fixed but moves with improved flavor-conserving measurements.","The same sum-rule logic can be applied to final states with tau leptons, giving complementary targets for rare top decays beyond the electron and muon channels considered here."],"supporting_citations":[{"why":"Derives the positivity sum rules that bound flavor-violating four-fermion Wilson coefficients by flavor-conserving ones; the whole target construction rests on these relations.","marker":"[18]"},{"why":"The authors' earlier analysis of lepton-flavor-conserving rare top decays, updated here with new data and extended to the $\\Delta F=2$ coefficients.","marker":"[11]"},{"why":"Gives the current LHC limits on $\\mathrm{BR}(t\\to q e\\mu)$ that are compared with the lepton-flavor-violating targets.","marker":"[45]"},{"why":"Provides the recast of $t\\to qZ$ searches that sets the existing bounds on $t\\to q\\ell^+\\ell^-$ used in the flavor-conserving analysis.","marker":"[8]"},{"why":"High-mass di-lepton production at the LHC constrains the light-quark flavor-conserving coefficients and drives the tightest bounds in several scenarios.","marker":"[105]"},{"why":"Search for $t\\bar t$ production with additional leptons gives the robust tree-level constraints on $C^{XY}_{\\ell\\ell tt}$ used when loop-level $Z$ and $B$ constraints are dropped.","marker":"[126]"},{"why":"Low-energy $\\mu\\to e$ conversion in nuclei provides very strong constraints on the lepton-flavor-violating, quark-flavor-conserving coefficients.","marker":"[30]"},{"why":"Search for $B_s\\to \\mu e$ constrains the lepton-flavor-violating $B$-decay coefficients that enter the numerical analysis.","marker":"[91]"},{"why":"Search for $B^+\\to K^+\\mu e$ provides additional lepton-flavor-violating $B$-decay limits used in the analysis.","marker":"[92]"},{"why":"Searches for $B^0\\to K^{*0}\\mu e$ and $B_s\\to \\phi\\mu e$ give the strongest rare-$B$ constraints on several lepton-flavor-violating top coefficients.","marker":"[93]"}],"fun_headline_variants":["Sum rules shrink allowed window for rare top decays","LHC already probes predicted e-mu top decays","New sum rule makes rare top decay targets testable","Flavor-conserving data bound rare top decay rates"],"cache_read_input_tokens":30720,"weakest_assumption_plain":"The target band stands or falls with the assumption that the new physics is a tree-level, scalar-or-vector leptoquark-like ultraviolet completion that satisfies the analyticity and unitarity conditions; in $Z'$ or loop-induced models the sum rules, and therefore the targets, do not apply.","fun_headline_variants_meta":{"raw":{"variants":["Sum rules shrink allowed window for rare top decays","LHC already probes predicted e-mu top decays","New sum rule makes rare top decay targets testable","Flavor-conserving data bound rare top decay rates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00105,"raw_usage":{"total_tokens":4463,"prompt_tokens":1049,"completion_tokens":3414,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":665,"completion_tokens_details":{"reasoning_tokens":3351}},"tokens_in":665,"tokens_out":3414,"duration_ms":28072,"temperature":1.0,"reasoning_tokens":3351,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:14:03.762969+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A search that observes $t\\to u e\\mu$ with a branching ratio above the scenario's upper target, for example above $1.2\\times10^{-8}$ in the up-LR scenario or above $2.9\\times10^{-7}$ in the charm-RR scenario, would contradict the sum-rule target for that channel; equivalently, a null result at the quoted maxima would leave the leptoquark class viable but would not test $Z'$ models.","supporting_citations":[{"cited_title":"New flavor physics in di- and tri-lepton events from single-top at the LHC and beyond","cited_arxiv_id":"2101.05286","evidence_quote":"Derives the positivity sum rules that bound flavor-violating four-fermion Wilson coefficients by flavor-conserving ones; the whole target construction rests on these relations."},{"cited_title":"Rare Top Decays as Probes of Flavorful Higgs Bosons","cited_arxiv_id":"1904.10956","evidence_quote":"The authors' earlier analysis of lepton-flavor-conserving rare top decays, updated here with new data and extended to the $\\Delta F=2$ coefficients."},{"cited_title":"electron-up LR","cited_arxiv_id":null,"evidence_quote":"Provides the recast of $t\\to qZ$ searches that sets the existing bounds on $t\\to q\\ell^+\\ell^-$ used in the flavor-conserving analysis."}],"review_version":1}