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Targets for Flavor-Violating Top Decay

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2504.18664 v2 pith:IOUY3VLN submitted 2025-04-25 hep-ph

Wolfgang Altmannshofer , Zev Balme , Christopher M. Donohue , Stefania Gori , Siddharth Vignesh Mukundhan This is my paper · ORCID
classification hep-ph
keywords raretopdecaysflavor-changingneutralcurrentsleptonflavorviolationpositivitysumrulesleptoquarkseffectivefieldtheoryquarkbranchingratiotargets
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

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.

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 (2)
  1. [Sec. 4, Eqs. (82)-(89) and (94)-(97)] 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.
  2. [Sec. 3.7, Eqs. (68)-(73)] 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.
minor comments (5)
  1. [Abstract and Sec. 2] 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'.
  2. [Sec. 2, Eq. (5)] 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.
  3. [Sec. 3.7] 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.
  4. [Fig. 1] 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.
  5. [References] Reference [41] appears to have an incorrect journal/year format ('JHEP23(2020) 082'); please check the entry and correct the volume and year.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: targets are derived from external positivity bounds and independent flavor-conserving constraints.

full rationale

The paper's target branching ratios are not fitted to the quantities they predict. In Sec. 4.1 the authors state that they 'numerically determine the maximal value for the rare top branching ratios that is compatible with the relations given in equation (4), and with the flavor-conserving Wilson coefficients subject to the relevant constraints discussed in section 3.' The input constraints come from dilepton production, ttbar+ll production, Z decays, rare B decays and LEP single-top production—none of which is the predicted t->q l+l- branching ratio itself. The direct limits on BR(t->q l+l-) quoted from [11] are weak (~1e-4) and are not the maximization input; the derived targets are orders of magnitude smaller. For the LFV case, Sec. 4.2 similarly uses Eq. (11), derived in this paper from the external Remmen-Rodd positivity inequality (5), together with flavor-conserving constraints; the CMS t->q e mu bounds are explicitly compared after the fact ('these targets are in the same ballpark as the existing limits'), not imposed as inputs. The reliance on the authors' previous [11] is for notation, recast methodology and updated B/Z analyses; the new Delta F=2 sum rule and the LFV target derivation are independent of [11]. No equation reduces by construction to a fitted parameter or to a self-citation chain.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No free parameters or invented entities are introduced. The analysis depends on the stated positivity assumptions, leading-log approximations, and a restricted operator basis, all disclosed in the text.

assumptions (6)
  • domain assumption Positivity sum rules of Remmen and Rodd apply to the four-fermion operators.
    Invoked throughout Sec. 2; the paper notes in footnote 1 that they require a UV theory dominated by scalars or vectors, improved forward-amplitude scaling, and no loop-induced operators.
  • domain assumption UV completion is dominated by either scalar or vector leptoquark exchanges.
    Needed for the sign relations (2)-(3) and the bounds (4) and (11); Z-prime and loop-induced models violate them.
  • domain assumption Leading-log terms dominate the B and Z constraints.
    Secs. 3.4 and 3.6 keep only log-enhanced terms in C9, C10 and the Z widths; the authors state the bounds hold only barring O(1) finite corrections and cancellations.
  • domain assumption All Wilson coefficients are real.
    Sec. 4 assumes real coefficients; imaginary parts could soften some interference-sensitive constraints.
  • domain assumption Operator basis is restricted to right-handed up-type quarks and e, mu leptons.
    Sec. 2 excludes left-handed up-type quark operators and tau final states, so the result does not cover those sectors.
  • domain assumption Approximate Gaussian and lepton-universal recast of the CMS ttbar+ll constraints.
    Sec. 3.7 extracts polynomial likelihoods from published plots assuming equal electron and muon efficiencies and no significant fluctuations.

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Cite this review

Pith. "Pith review of Targets for Flavor-Violating Top Decay." pith.science (2026). https://pith.science/paper/IOUY3VLN

@misc{pith2026250418664,
  author       = {Pith},
  title        = {Pith review of: Targets for Flavor-Violating Top Decay},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IOUY3VLN}},
  note         = {Machine review of arXiv:2504.18664}
}
abstract

Analyticity and unitarity constrain certain classe of new physics models by linking flavor-conserving and flavor-violating four-fermion interactions. In this work, we explore how these theoretical relations impact flavor-violating rare top quark decays. Building on our previous results, we present an updated analysis of the decays $t \to q \ell^+ \ell^-$ and identify interesting target branching ratios in the range of $10^{-7}$ to $10^{-6}$ once current experimental constraints from flavor-conserving processes are taken into account. We extend the analysis to top decays with lepton flavor violation, deriving correlations among the relevant Wilson coefficients and confronting them with existing limits from LEP and the LHC. Notably, we find that current searches for $t \to q e \mu$ are already probing theoretically motivated regions of parameter space. These results strongly support continued efforts to explore flavor-violating top decays as a powerful probe of new physics.

Figures

Figures reproduced from arXiv: 2504.18664 by the authors.

Figure 1
Figure 1. FIG. 1: The Wilson coefficients of the four-fermion operators considered in this work and [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Example Feynman diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Example Feynman diagrams contributing to rare semileptonic top decays (left) [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Example Feynman diagram contributing to single top production at lepton [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Example Feynman diagram contributing to lepton flavor-conserving rare decays of [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Example Feynman diagram contributing to di-lepton production in proton-proton [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Example Feynman diagram for a 1-loop correction to the [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Example Feynman diagram for [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Bar charts illustrating the various constraints on the Wilson coefficients. The [PITH_FULL_IMAGE:figures/full_fig_p026_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Expected [PITH_FULL_IMAGE:figures/full_fig_p029_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: Expected [PITH_FULL_IMAGE:figures/full_fig_p030_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Expected [PITH_FULL_IMAGE:figures/full_fig_p031_12.png]

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Cited by 1 Pith paper

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