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REVIEW 2 major objections 6 minor 114 references

By counting b-jets alone, the FCC-ee can probe flavor-changing top contact interactions up to about 10 TeV.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-14 15:00 UTC pith:LROV5OCG

load-bearing objection Solid FCC-ee projection that turns the authors' old b-Parity idea into concrete multi-TeV reaches on poorly constrained eetu/eetc operators, with the only real vulnerability already stated in the abstract. the 2 major comments →

arxiv 2607.09856 v1 pith:LROV5OCG submitted 2026-07-10 hep-ph hep-ex

Counting b-jets at the FCC-ee as a probe of top-quark flavor physics

Shaouly Bar-Shalom , Jose Wudka This is my paper
classification hep-ph hep-ex
keywords FCC-eeb-Paritysingle top productionflavor-changing contact interactionsSMEFTb-jet taggingfour-fermion operators
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper shows that a future electron-positron collider running at 240 GeV can search for multi-TeV new physics that couples electrons to a top quark and a light up-type quark by simply counting how many b-tagged jets appear in two- and four-jet events. In the Standard Model an odd number of b-jets is almost forbidden once the small off-diagonal CKM elements are taken into account; the only appreciable background therefore comes from light jets being mis-tagged as b-jets. Flavor-changing four-fermion operators generate single-top events that leave exactly one b-jet after the top decays, producing a clean b-Parity-odd excess. With the high luminosity and flavor-tagging performance expected at the FCC-ee, that excess is large enough to reach new-physics scales of roughly 7–13 TeV—about forty times the collider energy—improving existing limits on several of these operators by an order of magnitude. The entire reach rests on the purity of the b-jet sample.

Core claim

By counting the number of final-state b-jets in multi-jet events at a 240 GeV FCC-ee, one can probe the scales of vector, scalar and tensor eetu and eetc contact interactions at Λ_eff ∼ 10 TeV (roughly 40 times the center-of-mass energy), improving current bounds on some of these operators by an order of magnitude.

What carries the argument

b-Parity (b_P = (−1)^n), an approximately conserved Standard Model quantum number that forbids an odd number of b-jets in e+e− collisions; flavor-changing single-top production violates it, so a simple b-jet count isolates the new-physics signal against a background that arises only from mis-tagging.

Load-bearing premise

The claimed multi-TeV sensitivity stands or falls with the assumption that the collider will achieve the projected high-purity b-tagging (false-positive rates as low as one part in ten thousand for light jets).

What would settle it

If the actual light-jet and c-jet mistag rates at the FCC-ee turn out only modestly worse than the tight-tagger benchmarks used in the paper, the mis-identification background will rise enough that the projected 10 TeV reach collapses in the same counting analysis.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A pure counting analysis of 2j + X and 4j + X final states at the 240 GeV FCC-ee run can set competitive limits on several poorly constrained four-fermion operators.
  • Applying a di-jet mass cut above the W peak further suppresses the dominant WW/ZZ background and can push the reach to 13 TeV for tensor operators.
  • The same b-Parity-odd excesses appear in multiple channels, so correlations among them can be used to strengthen or cross-check the limits.
  • The method extends, in principle, to higher-energy FCC-ee runs once single-top-plus-W/Z production becomes kinematically open.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the tight tagger performance is realized, a null result would push many tree-level leptoquark or Z′ models that generate eetu/eetc operators above 10 TeV, well beyond direct LHC reach for those states.
  • The same counting strategy could be applied at other high-luminosity e+e− machines or, with care about initial-state b content, at electron-ion colliders.
  • Because the interference with the Standard Model is CKM- and mass-suppressed, the limits remain essentially free of cancellations between operators of different chirality.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The paper studies the sensitivity of the FCC-ee at √s = 240 GeV (ZH phase, L ≈ 10 ab−1) to multi-TeV flavor-changing eetu and eetc contact interactions (vector, scalar, tensor) in the SMEFT. These operators mediate single-top production e+e− o tūk, tūkγ (+c.c.), which after top decay yield 2j+X and 4j+X final states containing a single b-jet. The analysis uses the approximately conserved SM quantum number b-Parity (bP = (−1)n) introduced in the authors’ earlier work: SM multi-jet production is bP-even to high accuracy (suppressed by |Vub|2, |Vcb|2), so the only relevant background is b-jet misidentification. Using LO MadGraph5_aMC@NLO + SMEFTsim cross sections, three benchmark tagger scenarios, and an optional mjj cut, the authors show that simple b-jet counting can probe Λ_eff ∼ 7–13 TeV (tight tagger + mjj ≳ 100 GeV), roughly 30–50 times the collider energy and an order-of-magnitude improvement on existing bounds for some operators.

Significance. If the projected high-purity b-tagging is realized, the result is a clean, experimentally simple probe of poorly constrained (2ℓ)(2q) four-fermion operators that improves current limits by roughly an order of magnitude and reaches Λ_eff ∼ 40 imes ECM. The method is transparent: the SM is bP-even once CKM off-diagonal elements are small, the only background is mis-tagging (quantified in Eqs. 17, 20 and Fig. 2), and the LO single-top formulae (Eqs. 10–11) match known results. The paper also maps the underlying heavy bosons that can generate the operators at tree level (Table IV) and shows how an mjj cut further improves S/B (Sec. VI, Fig. 6). These are concrete, falsifiable projections that strengthen the physics case for flavor tagging at the FCC-ee.

major comments (2)
  1. The central claim (Λ_eff ∼ 7–13 TeV, abstract and Sec. VI) is stated to “critically rely on high-purity b-jet tagging.” Table V and Fig. 6 show that the reach collapses from ∼7.5 TeV (tensor, tight) to ∼4.6 TeV (loose) already without the mjj cut, and the SM background in Fig. 2 rises by orders of magnitude when tj, tc degrade. The paper should quantify more explicitly how much the projected multi-TeV reach degrades if the tight scenario (εb = 0.7, tc = 0.001, tj = 0.0001) is not achieved, e.g., by adding a short table or paragraph that maps Λ_eff versus realistic ranges of tj for fixed εb, tc. This is the single load-bearing experimental assumption and should be presented with equal prominence to the optimistic numbers.
  2. All signal and background cross sections are LO parton-level with simple pT, η, ΔR cuts (Sec. V). While adequate for an exploratory sensitivity study, the dominant SM backgrounds are WW/ZZ (explicitly noted), for which NLO QCD and detector-level jet reconstruction can change both rates and the mjj shape used in Sec. VI. A brief estimate of the expected size of NLO/detector corrections (or a statement that they are deferred to a full simulation) would strengthen confidence that the quoted 30–50 imes ECM reach survives more realistic modeling.
minor comments (6)
  1. Abstract and p. 1: “the FCC-ee can can probe” — duplicate “can”.
  2. Sec. II, tagger table: the three scenarios are clear, but a short sentence noting that they are taken from the FCC-ee flavor-tagging literature [92–96] (already cited) would help the reader.
  3. Eqs. 15–20: the combinatorial factors Pni are standard but dense; a one-line reminder that they are binomial coefficients would improve readability.
  4. Fig. 4 caption: “per integrated luminosity of L = 1000 fb−1” while the rest of the paper uses 10 ab−1; a consistent luminosity (or an explicit rescaling note) would avoid confusion.
  5. Table V: the grouping of operators into vector/scalar/tensor classes is correct, but a footnote recalling that the small differences arise from the SU(2)-related eebq and eνbq contributions (already discussed in Sec. III) would make the table self-contained.
  6. Sec. VII: the summary states Λ ∼ 10 ± 3 TeV; this is a useful round number, but it should be tied more explicitly to the tight-tagger + mjj-cut results of Fig. 6 so that the reader sees the origin of the ±3 TeV range.

Circularity Check

1 steps flagged

Minor self-citation of the b-Parity concept from the authors' prior work; the FCC-ee sensitivity numbers are independent LO Monte-Carlo calculations that do not recycle fitted parameters or reduce by construction.

specific steps
  1. self citation load bearing [Abstract; Sec. I (Introduction); Sec. II (first two paragraphs)]
    "Our analysis exploits an approximately conserved Standard Model (SM) quantum number introduced in [1] and termed "b-Parity" (b_P) … In what follows, we will adopt the approach originally introduced by the authors more than two decades ago in [1]; to test FC BSM effects in 3rd generation quark interactions by simply counting the number of b-jets …"

    The search strategy (count odd numbers of b-jets) is taken from the authors' own 2001 paper. However the citation is not load-bearing for the numerical claim: the sensitivity figures themselves are recomputed with modern tools and do not inherit any fitted constant or uniqueness theorem from [1]. The step is therefore only a minor self-citation of a conceptual tool, not a circular reduction of the result.

full rationale

The paper's central claim is a prospective 95% CL reach of Λ_eff ∼ 7–13 TeV (depending on operator class and tagger) for scalar/vector/tensor eetu/eetc operators, obtained by counting single-b-jet events in e+e-→2j+X and 4j+X channels at √s=240 GeV with L=10 ab-1. That reach is computed from scratch: MadGraph5_aMC@NLO + SMEFTsim LO parton-level cross sections (Eqs. 10–11, 15–20), acceptance cuts, three explicit tagger benchmarks (ε_b, t_c, t_j), statistical+systematic+theory errors with δ_s=δ_t=0.01, and an optional m_jj cut (Sec. VI, Figs. 3–6, Table V). None of these numbers is fitted to data or taken from a prior fit. The only self-citation is the conceptual tool of b-Parity (b_P=(-1)^n), introduced in the authors' 2001 PRL [1] and re-derived in Sec. II from the approximate U(1)_b symmetry that appears when V_ub,V_cb o0. That citation supplies the search strategy, not a numerical input or a uniqueness theorem that forces the quoted reach. The SM background formulae (Eqs. 17, 20) and the statement that the irreducible CKM-suppressed b_P-odd SM rate is negligible are standard and independently verifiable. Consequently there is no self-definitional loop, no fitted-input-called-prediction, and no load-bearing uniqueness imported from the authors. Score 1 reflects only the ordinary (and non-circular) reuse of the authors' earlier idea.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central claim rests on standard SMEFT power counting, the approximate conservation of b-Parity (itself a consequence of small CKM angles), and a set of externally supplied collider and detector parameters. No new dynamical entities are postulated; the free parameters are the usual phenomenological inputs of a collider projection study.

free parameters (5)
  • b-tagging efficiency and purity (ε_b, t_c, t_j) = loose (0.9,0.01,0.001); medium (0.8,0.005,0.001); tight (0.7,0.001,0.0001)
    Three benchmark sets (loose/medium/tight) are chosen by hand from projected FCC-ee performance studies; the entire sensitivity scales directly with these numbers.
  • integrated luminosity L = 10 ab^{-1}
    Fixed to the planned 10 ab^{-1} for the ZH run; enters linearly in event yields.
  • acceptance × efficiency factor A = 0.8
    Set by hand to 0.8; multiplies all event counts.
  • systematic and theory relative errors δ_s, δ_t = 0.01
    Both fixed at 1 %; enter the total uncertainty budget in quadrature.
  • m_jj lower cut = ∼100 GeV
    Optimized by hand around 100 GeV to maximize S/√B; changes the quoted reach by several TeV.
axioms (4)
  • domain assumption b-Parity is approximately conserved in the SM because |V_ub| and |V_cb| are small; irreducible b_P-odd SM rates are negligible compared with mis-tag backgrounds.
    Stated in Sec. II and used throughout to claim that the only significant background is jet mis-identification.
  • domain assumption Dimension-6 SMEFT operators generated at tree level dominate; higher-dimensional and loop-generated operators can be neglected.
    Standard EFT power counting invoked in Sec. III.
  • domain assumption Interference between NP and SM amplitudes is negligible for the single-b-jet signals.
    Argued in Sec. V on the basis of CKM and light-fermion mass suppressions.
  • ad hoc to paper Leading-order parton-level cross sections with simple p_T, η and ΔR cuts are sufficient for sensitivity estimates.
    All numerical results (Secs. V–VI) are obtained at LO with MadGraph; no NLO or shower uncertainties are quantified.

pith-pipeline@v1.1.0-grok45 · 27570 in / 2858 out tokens · 28789 ms · 2026-07-14T15:00:06.020190+00:00 · methodology

0 comments
read the original abstract

We explore the sensitivity of a future FCC-ee to multi-TeV new physics (NP) that can generate vector, scalar and tensor flavor-changing (FC) $eetu_k$ contact interactions ($u_k=u,c$ for $k=1,2$), probed via single top-quark production, $e^+ e^- \to t \bar{u}_k, t \bar{u}_k \gamma$ (+ c.c.) and leading (following the top-quark decay) to two- and four-jet signals, $e^+ e^- \to 2j + X, 4j + X$, where $X$ denotes any non-jet final-state particles. Our analysis exploits an approximately conserved Standard Model (SM) quantum number introduced in [1] and termed "$b$-Parity" ($b_P$), which is applicable to scattering processes of the type $e^+ e^- \to n \cdot j_b + m \cdot j_\ell + X$, where $n$ and $m$ are the number of produced $b$-jets and light-jets ($u,d,c,s,$ and/or gluons) and $b_P=(-1)^n$. The FC $eetu_k$ four-fermion interactions can generate distinct $b_P$-odd ($b_P = -1$) signals in these multi-jet events, for which the only significant SM background stems from $b$-jet misidentification. We demonstrate that the FCC-ee, operating at a $\sqrt{s} = 240$ GeV (the $ZH$ run phase) with high luminosity and excellent flavor-tagging performance, is an ideal platform to search for these $b_P$-odd signatures. Indeed, by simply counting the number of final-state $b$-jets, the FCC-ee can probe NP scales of $\Lambda \sim 10$ TeV for the new heavy states that generate the vector, scalar and tensor $eetu$ and/or $eetc$ interactions. This reach, remarkably about 40 times the assumed FCC-ee center-of-mass energy, improves upon current bounds on some of these four-fermion operators by an order of magnitude and it critically relies on high-purity b-jet tagging.

Figures

Figures reproduced from arXiv: 2607.09856 by Jose Wudka, Shaouly Bar-Shalom.

Figure 1
Figure 1. Figure 1: FIG. 1: Representative Feynman diagrams for [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The expected SM (background) effective single [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Expected 95% CL sensitivity to scale [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Di-jet invariant mass distribution (stacked) for the SM and NP (for the tensor operator [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Expected 95% CL sensitivity to [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

discussion (0)

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Reference graph

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