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Lattice-matched SU(3)F ratios of charmed-baryon semileptonic decays give clean, normalization-free tests of a long-standing experimental tension.

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2026-07-15 11:58 UTC pith:MPURMBNN

load-bearing objection Clean lattice-to-SU(3)_F matching that produces three falsifiable, normalization-independent ratios for the Ξ_c puzzle.

arxiv 2603.16323 v2 pith:MPURMBNN submitted 2026-03-17 hep-ph hep-exhep-lat

Puzzles in charmed baryon semileptonic decays with SU(3)_F flavor symmetry and lattice inputs

Chao-Qiang Geng , Chia-Wei Liu , Sheng-Lin Liu This is my paper
classification hep-ph hep-exhep-lat
keywords charmed baryonssemileptonic decaysSU(3)F flavor symmetrylattice QCDform factorsBCL z-expansionbranching-fraction ratiossymmetry breaking
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.

Charmed-baryon semileptonic decays show large disagreements between measured branching fractions and both lattice-QCD and SU(3)F predictions. The paper argues that the tension may stem from the experimental normalization channel Ξc0 → Ξ−π+ rather than from new physics or unexpected hadronic dynamics. By embedding lattice form-factor results inside an SU(3)F expansion that includes first-order symmetry breaking, the authors obtain two ratios of branching fractions that are free of that normalization and protected against second-order breaking. If experiment measures these ratios and finds them near the predicted few-percent values, the source of the present discrepancy can be isolated without relying on the disputed absolute branching fraction.

Core claim

Matching lattice-QCD form factors for Λc → Λ, Λc → n and Ξc → Ξ onto an SU(3)F BCL z-expansion that includes first-order breaking yields the ratios B(Ξc+ → Σ0 ℓ+νℓ)/B(Ξc+ → Ξ0 ℓ+νℓ) = (2.6 ± 0.3)% and B(Ξc+ → Λ ℓ+νℓ)/B(Ξc+ → Ξ0 ℓ+νℓ) = (1.1 ± 0.1)%, together with the isospin partner RΣ− = (5.2 ± 0.6)%. These ratios are independent of the disputed normalization mode and therefore furnish direct experimental tests of the origin of the tension.

What carries the argument

The first-order SU(3)F parameterization of BCL coefficients, afn = Cf n (B†)i j Jj (Bc)i + Vf n (B†)i k Jj Sk j (Bc)i + Wf n (B†)k j Jj Si k (Bc)i, with the spurion S = diag(1,1,−2)/√6; the three parameters are fixed by lattice inputs and then used to predict the unmeasured Ξc → Σ, Λ channels.

Load-bearing premise

The assumption that first-order SU(3)F breaking is enough and that higher-order corrections stay at the percent level so they do not spoil the claimed precision of the ratios.

What would settle it

A precision measurement at Belle, Belle II or BESIII of the ratios RΣ0 and RΛ that lies many standard deviations away from the predicted (2.6 ± 0.3)% and (1.1 ± 0.1)% values would falsify the claim that first-order SU(3)F plus lattice inputs correctly describe the decays.

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

If this is right

  • Precise measurements of RΣ0 and RΛ at current or near-future luminosities can decide whether the experimental–theory tension originates in the normalization channel Ξc0 → Ξ−π+.
  • The same framework supplies absolute branching fractions and up-down asymmetries for the previously unmeasured Ξc → Σ and Ξc → Λ modes.
  • If the measured ratios agree with the predictions, the lattice form factors and the first-order SU(3)F expansion are mutually consistent for these transitions.
  • If the ratios disagree, either higher-order SU(3)F breaking or a genuine anomaly in the lattice or experimental inputs would be required.

Where Pith is reading between the lines

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

  • The same matching procedure could be applied to non-leptonic Ξc decays whose absolute rates are also under experimental scrutiny, testing whether the normalization problem is universal.
  • A confirmed discrepancy in the ratios would strengthen the case for re-measuring absolute Ξc branching fractions with independent methods (e.g., threshold production at BESIII or STCF).
  • The size of the fitted V0f/C0f and W0f/C0f parameters (~10–20 %) already quantifies the expected first-order breaking; future lattice results for Ξc → Σ, Λ would allow a direct check of that size.

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

0 major / 4 minor

Summary. The paper constructs an SU(3)_F analysis of singly charmed baryon semileptonic form factors that includes first-order symmetry breaking, matching lattice-QCD BCL z-expansion coefficients for Λ_c → Λ, Λ_c → n and Ξ_c → Ξ onto the reduced amplitudes C_n^f, V_n^f and W_n^f (Eqs. 3–4 and Table I). With those parameters fixed, it predicts the previously unmeasured form factors and branching fractions for Ξ_c^+ → Λ ℓ^+ ν_ℓ and Ξ_c → Σ ℓ^+ ν_ℓ (Tables II–III, Fig. 1). The central results are the normalization-independent ratios R_Σ^{0} = (2.6 ± 0.3)%, R_Λ = (1.1 ± 0.1)% and R_Σ^{-} = (5.2 ± 0.6)% (Eq. 5), which are protected up to second-order SU(3)_F breaking and therefore provide clean experimental tests of the origin of the present tension between measured Ξ_c^{0} → Ξ^{-} e^{+} ν_e rates and both lattice and SU(3)_F expectations.

Significance. If the predicted ratios are confirmed, they cleanly isolate whether the long-standing experimental–theoretical discrepancy in Ξ_c semileptonic decays is due to an underestimated normalization mode B(Ξ_c^{0} → Ξ^{-} π^{+}) or to unexpectedly large SU(3)_F breaking. The construction is model-independent within the stated truncation, reproduces the input lattice form factors to O(10^{-3}), and yields falsifiable, percent-level predictions that can be tested at Belle/Belle II and BESIII/STCF with existing or near-term luminosities. The explicit matching of lattice BCL coefficients onto first-order SU(3)_F amplitudes (including the z-expansion convention conversion in the Appendix) is a useful technical contribution that can be reused for other charmed-baryon channels.

minor comments (4)
  1. After Table I the authors state that residual second-order SU(3)_F pieces are expected O(10^{-2}). A short quantitative estimate of how this residual propagates into the ratios of Eq. (5) (e.g., by varying the higher-order coefficients within a natural-size range) would make the claimed percent-level precision more transparent.
  2. The efficiencies used for the event-yield projections (Sec. III, after Eq. 6) are taken from disparate Belle analyses; a brief remark on whether they are assumed q^{2}-independent and how that assumption affects the projected δR would strengthen the experimental discussion.
  3. Fig. 1 shows form-factor bands but does not display the corresponding lattice points for the input channels; overlaying those points (or stating that they lie within the bands to O(10^{-3})) would make the reproduction claim immediately visible.
  4. Typographical consistency: the abstract and Eq. (5) write Λ while Table III and the text sometimes write Λ^{0}; a uniform notation for the Λ hyperon would avoid minor confusion.

Circularity Check

0 steps flagged

No load-bearing circularity: lattice form factors fix C/V/W; new-channel ratios are genuine first-order SU(3)_F extrapolations, not forced by construction.

full rationale

The derivation chain is: external LQCD form-factor coefficients a_n^f for the three input channels Λ_c oΛ, Λ_c o n and Ξ_c oΞ are inverted via the linear map (4) to obtain the SU(3)_F parameters C_n^f, V_n^f, W_n^f of Table I; those parameters are then inserted into the same decomposition (3) to generate the previously unmeasured form factors of Ξ_c^+ oΣ^0 and Ξ_c^+ oΛ (Table II and Fig. 1). The ratios R_Σ^{0}, R_Λ and R_Σ^{-} of Eq. (5) are formed from the resulting branching fractions; because the overall multiplet normalizations cancel and the residual second-order breaking is estimated O(10^{-2}) from the observed size of V_0/C_0 and W_0/C_0, the ratios are protected predictions rather than tautologies. The fit reproduces the three lattice inputs to O(10^{-3}) by construction of the 3 imes3 matrix, but that is ordinary parameter determination, not a prediction of the inputs themselves. Self-citations to earlier SU(3)_F papers by overlapping authors supply only the general multiplet language and do not enter the numerical extraction or the protection argument for the ratios. No step reduces a claimed prediction to its own definition or to a fitted quantity that is statistically forced to equal the prediction.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The central ratios rest on three external lattice calculations, the standard first-order SU(3)_F spurion expansion, the BCL z-expansion with the usual pole masses, and the assumption that second-order breaking is negligible at the percent level. No new particles or forces are introduced; the free parameters are precisely the lattice coefficients that are taken as input and then linearly recombined.

free parameters (2)
  • Lattice BCL coefficients a_n^f for Λ_c→Λ, Λ_c→n, Ξ_c→Ξ
    Taken directly from Refs. [6,42,43]; they fix C_n^f, V_n^f, W_n^f via the linear map (Eq. 4) and therefore control every numerical prediction.
  • CKM elements V_cd, V_cs and baryon lifetimes
    External PDG/CKMfitter inputs used only for absolute branching fractions (Table III); the ratios themselves cancel them.
axioms (3)
  • domain assumption First-order SU(3)_F breaking is captured by the two independent spurion insertions V and W of S=diag(1,1,−2)/√6; higher-order terms are O((m_s/Λ_QCD)^2)≈0.01–0.04 and do not affect the quoted precision of the ratios.
    Stated after Table I and used to claim that the ratios are protected up to second order (discussion of Eq. (5)).
  • domain assumption The BCL z-expansion with the conventional D(∗)π/K poles and the end-point constraints (Eq. (2)) adequately describes the q^{2} dependence over the physical range.
    Adopted from the lattice papers and matched in the Appendix; |z|<0.16 is used to argue that n≥2 terms are small.
  • standard math Isospin symmetry relates Ξ_c^0→Σ^− to Ξ_c^+→Σ^0 by a factor √2.
    Used without further correction when quoting R_Σ−.

pith-pipeline@v1.1.0-grok45 · 14950 in / 2701 out tokens · 27060 ms · 2026-07-15T11:58:42.508769+00:00 · methodology

0 comments
read the original abstract

Recent measurements of charmed-baryon semileptonic decays signal large tensions between experiment and theory, including $SU(3)_F$ analyses and lattice-quantum chromodynamics simulations. Possible sources of the discrepancy include the experimental normalization mode $\Xi_c^0 \to \Xi^- \pi ^+$. Using lattice-QCD inputs in an $SU(3)_F$ analysis including first-order symmetry breaking, we predict ${\cal B}( \Xi_c^+ \to \Sigma^0 \ell^+ \nu_\ell ) / {\cal B}( \Xi_c^+ \to \Xi^0 \ell^+ \nu_\ell )=(2.6\pm0.3)\%, $ and ${\cal B}( \Xi_c^+ \to \Lambda \ell^+ \nu_\ell )/{\cal B}( \Xi_c^+ \to \Xi^0 \ell^+ \nu_\ell )=(1.1\pm0.1)\%, $ with $\ell^+=(e^+,\mu^+)$. These ratios provide normalization-independent tests and may help clarify the origin of the present tension.

Figures

Figures reproduced from arXiv: 2603.16323 by Chao-Qiang Geng, Chia-Wei Liu, Sheng-Lin Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. The numerical results of form factors [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The differential decay rates and the estimated number [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

discussion (0)

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