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The Skyrme model, treating Λ_b as a heavy meson bound to a soliton, predicts the purely baryonic decay Λ_b→p̄pn with branching fraction (1.10±0.27)×10⁻⁶, matching earlier order-of-magnitude estimates.

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2026-08-02 18:15 UTC pith:ZHRZAHYD

load-bearing objection A coherent but preliminary Skyrme-model estimate of Lambda_b -> p pbar n that lands at the known O(10^-6) scale; the central number is plausible but rests on an under-specified time-like continuation, so it needs a serious referee and likely major revision. the 5 major comments →

arxiv 2603.12735 v1 pith:ZHRZAHYD submitted 2026-03-13 hep-ph

Purely Baryonic Weak Decays of Heavy Baryons in Skyrme Model

Chao-Qiang Geng , Chao Han This is my paper
classification hep-ph PACS 12.39.Dc13.30.-a
keywords Skyrme modelheavy baryonspurely baryonic weak decaysbranching fractiontime-like form factorsPadé approximationbound-state modelCP violation
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.

The paper aims to show that the Skyrme model — in which baryons are topological solitons and heavy baryons are bound states of a heavy meson and a soliton — can compute the rate of an as-yet-unobserved, purely baryonic weak decay, Λ_b → p p̄ n. Working in the large-N_c spectator/factorization approximation, it obtains the Standard Model prediction B(Λ_b → p p̄ n) = (1.10 ± 0.27) × 10⁻⁶, in line with earlier estimates at the 10⁻⁶ level. A sympathetic reader would care because this gives a concrete, testable Standard Model baseline for a channel sensitive to new sources of CP violation in the baryonic sector.

Core claim

Within the bound-state Skyrme picture, Λ_b is a proton (Skyrmion) plus a B meson. The weak transition b→u operates on the B component, producing the n p̄ pair through the time-like nucleon weak current, while the proton is a spectator. The decay rate is then driven by the combination |2M_N G_A(q²) + (q²/2M_N) G_P(q²)|² of the time-like axial and pseudoscalar form factors. These form factors are obtained by Padé-continuing space-like Skyrme form factors into the time-like region. Evaluated numerically, the branching fraction comes out at (1.10 ± 0.27) × 10⁻⁶, about half of previous estimates but of the same order of magnitude.

What carries the argument

The heavy baryon as a bound state of a heavy meson and a Skyrmion; the hedgehog soliton solution with collective quantization; time-like form factors built via multipoint Padé approximation of space-like form factors (through exponential-integral kernels H(α, β) from the pion tail); and the spectator/factorization reduction of the four-baryon transition matrix element to a product of a heavy-meson decay constant and a two-baryon current matrix element.

Load-bearing premise

The time-like form factors obtained by low-order Padé continuation of space-like Skyrme results remain accurate over the entire integration range q² ∈ [(2M_N)², (M_Λb−M_N)²] ≈ [3.5, 21.9] GeV², where the decay rate is integrated.

What would settle it

A branching-fraction measurement of Λ_b→p̄pn that falls well outside (1.10±0.27)×10⁻⁶ would contradict the prediction; a lattice-QCD calculation of the time-like axial and pseudoscalar nucleon form factors in that q² window would directly test the continuation step.

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

If this is right

  • If correct, LHCb and other experiments have a sharp Standard Model target: B(Λ_b→p̄pn) ≈ 10⁻⁶, within reach of current hadron-collider data.
  • The rate pins down a combination of the time-like axial and pseudoscalar nucleon form factors in the q² range from (2M_N)² to (M_Λb−M_N)², a region largely unconstrained by other data.
  • The factor-of-two discrepancy with earlier estimates indicates either missing contributions (nonfactorizable, relativistic, or higher 1/N_c effects) or overestimated earlier values; both are resolvable by refining the calculation.
  • The same bound-state machinery extends to other purely baryonic modes such as Λ_b→p̄pΛ, with a predicted suppression from phase space.
  • Because the final state contains four spin-1/2 baryons, T-odd triple-product correlations can be constructed; this rate provides the Standard Model baseline for those CP-violation searches.

Where Pith is reading between the lines

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

  • The Padé continuation's reliability could be tested directly: compare the continued time-like form factors against independent lattice-QCD results for G_A and G_P in this q² window, since the paper itself flags that only low-order approximants were used.
  • The near-threshold enhancement of the differential rate (the paper's Fig. 3) is a kinematic plus form-factor effect; if measured, the q² shape would discriminate between the Skyrme form-factor model and other parameterizations.
  • The smallness of the imaginary parts of G_A and G_P in the time-like region is a distinctive prediction; e⁺e⁻ → n p̄ cross-section data could constrain these imaginary parts and would directly probe the validity of the continuation.

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

5 major / 9 minor

Summary. This paper studies the purely baryonic weak decay Λ_b → p pbar n within the Skyrme model, treating the heavy baryon as a bound state of a heavy meson and a Skyrmion. The decay amplitude is evaluated via a spectator/factorization approximation, with the vacuum-to-(n,pbar) weak matrix element expressed through time-like axial and pseudoscalar form factors obtained by analytic continuation of numerically computed space-like Skyrme form factors through multipoint Padé approximants. The central result is a branching fraction B(Λ_b → p pbar n) = (1.10 ± 0.27) × 10^-6, compared with previous estimates of about 2 × 10^-6. The paper emphasizes that the calculation is preliminary, that only low-order Padé approximants are used for illustration, and that 1/N_c and 1/M_B uncertainties are not quantified.

Significance. If the result is sound, the paper would be significant in establishing a Standard Model estimate for an unobserved, potentially CP-sensitive class of baryonic decays, and would demonstrate the utility of the Skyrme bound-state method for time-like weak form factors. The explicit prediction of O(10^-6) with a differential distribution is a falsifiable target for LHCb and future colliders. The paper also carefully lists its own caveats. However, because the numerical central value controls the scientific message, the load-bearing steps need to be reproducible and controlled; at present, the manuscript does not provide enough information to verify the continuation or the uncertainty.

major comments (5)
  1. [IV, Fig. 2 and Eq. (35)] The central prediction B=(1.10±0.27)×10^-6 is governed by the integral of |2MN GA + (q^2/2MN) GP|^2 over q^2 up to ~21.9 GeV^2, where GA and GP come from the Padé continuation of the w functions. Yet the manuscript states in Sec. IV that 'only relatively low-order Padé approximants are adopted here for illustration' and does not report the Padé orders, the number and positions of poles zj, the residues Rj, nor the quality of the fit to the space-like w functions. Without this information the continuation cannot be reproduced or checked, so the central numerical result is not independently verifiable. Please provide the Padé poles/residues/orders and a validation plot (e.g. fit vs. exact space-like points; sensitivity to [n/m] order).
  2. [II.B.4, Eq. (14)] The analytic continuation step is not fully specified. H(α,β) in Eq. (14) is defined for Re(α)>0, but after the replacement Q→iq the H-functions in Eqs. (16)-(19) are evaluated at α = μ1 − iq or μ2 − iq (and μ1 + iq, μ2 + iq). For the upper part of the q^2 integration range, q exceeds Mπ (and even 3Mπ), so μ − q has negative real part for one of the two terms; the formulas nevertheless employ E1(−α z) outside its principal domain. The manuscript does not state the analytic continuation convention, branch choice, or how the low-order Padé poles cross the integration contour. Since the imaginary parts of GA and GP depend on this, the result depends on an unspecified choice. The authors should spell out the continuation rule or replace this step with a controlled method (e.g. contour deformation, dispersion relation, or multipole over a quoted range of validity).
  3. [IV, uncertainty budget] The quoted uncertainty ±0.27×10^-6 propagates only 'numerical inputs' (Sec. IV). The paper's own caveats identify three larger systematic effects: the unquantified 1/N_c and 1/M_B corrections, the unknown Padé-order dependence, and the neglected nonfactorizable diagram (Fig. 1b). The present error bar therefore strongly understates the theoretical uncertainty of the central claim and cannot be used to validate the O(10^-6) prediction against previous estimates. The paper should provide an estimate of the Padé-order sensitivity (e.g. different [m/n] values) and a statement of the expected size of 1/N_c corrections, or explicitly present the result as an order-of-magnitude estimate with a much larger error.
  4. [III, Eqs. (28)-(31)] The factorization/spectator reduction of Eq. (28) to Eq. (31) is asserted rather than derived. In particular, the identification of the initial proton with the final proton removes the initial-state soliton from the matrix element, and the q^2-dependence of the overlap ϕ(k*) is then computed from kinematics alone. The 'proton acts as a pure spectator' assumption is plausible at leading order in 1/N_c but the nonfactorizable topology is dropped. This may be acceptable for a first estimate, but it should be explicitly presented as an assumption (not merely 'assume this contribution to be suppressed'), since direct CP-violating observables would be sensitive to the dropped contributions.
  5. [II.B.4, text between Eqs. (10) and (13)] The relation between the multipoint Padé approximants in Eq. (11) and the Mittag-Leffler partial-fraction form in Eq. (13) is not justified. Eq. (11) contains polynomials P_(n) and Q_(m) of degrees n and m with m = n + p; Eq. (13) is a finite sum of simple poles only, which is not the generic partial fraction of a rational function unless there are no repeated poles and no polynomial part. If the Padé fit generates multiple poles, Eq. (13) is incomplete. This is a technical detail that needs to be fixed or clarified so the derivation is well-defined.
minor comments (9)
  1. [Abstract, Introduction] The notation for the branching fraction is inconsistent: '𝒪(10^{-6})' in the abstract and 'O(10−6)' later. Please unify.
  2. [II.B.4] The notation 'q^2' is used for both the momentum transfer and the dummy 'Q' in the Fourier-Bessel transforms; define Q^2 = -q^2 clearly to avoid confusion in Eqs. (16)-(19).
  3. [II.C] The heavy-meson decay constant is defined via ⟨0|qbar γμ γ5 Q|H(p)⟩, but Eq. (21) does not contain f_H nor the term that would relate it to the current; tie the definition to the actual Lagrangian or state it as external input.
  4. [III, Eq. (26)] The notation 'C_{s',s_B;s}' and the sum over spins are not fully specified; state the CG coefficients for the Λ_b (isospin 0, spin 1/2) to p + heavy meson decomposition.
  5. [IV, Fig. 2] The figure is not visible in the text; please ensure the plot includes axis labels, units, and the region q^2∈[3.52, 21.9] GeV^2 with the kinematic limits marked.
  6. [IV] The text says 'the uncertainty only reflects the numerical inputs used in the calculation', but the parameter list does not show which input drives the 24% uncertainty; give the breakdown.
  7. [II.D, Eq. (23)] The bound-state wavefunction ϕ(p) contains κ defined via F'''(0), whose numerical value is not given; specify κ or the resulting oscillator parameters.
  8. [References / IV] Refs. [1,2] are authored by the same group as the present paper; this is not a problem, but flag that 'previous estimates' are not independent checks unless the methods differ materially.
  9. [General] Typos: 'CG coefficiens' (Sec. III), the Källén function definition is missing a closing parenthesis, and 'timelike' vs 'time-like' are used inconsistently.

Circularity Check

0 steps flagged

No significant circularity: the branching fraction is computed from Skyrme-model inputs and is not used as a fitted input; prior estimates by overlapping authors are only comparisons.

full rationale

The computation is self-contained along the following chain: the Skyrme profile F(r) is obtained from Eq. (3) with external parameters e and g; the space-like form factors are built from w-functions via Eqs. (7)-(9); low-order Padé approximants are fitted to these space-like form factors and analytically continued by Q→iq to obtain time-like G_A(q^2) and G_P(q^2); the decay amplitude and rate are then evaluated in Eqs. (31)-(35) using f_B, CKM elements, and masses. The target branching fraction B(Λ_b→p \bar p n) never enters anywhere as an input; the Padé coefficients are fitted to space-like model form factors, not to the decay rate or to the comparison values in Refs. [1,2]. Those comparison values, although authored with the overlapping author C.Q. Geng, are used only for a posteriori comparison ('The result obtained here agrees with the previous estimates of O(10^-6)') and are not load-bearing. The paper itself flags the main reliability limitation: 'only relatively low-order Padé approximants are adopted here for illustration'—this is a caveat about numerical/systematic reliability, not an indication that the prediction is equivalent to an input. Similarly, the acknowledged omission of nonfactorizable contributions and unspecified theoretical uncertainties are correctness risks, not circularity. Thus no load-bearing step reduces to its own inputs, and no self-citation chain forces the result.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The calculation borrows a large model apparatus (Skyrme soliton, heavy-meson bound state, Padé continuation) and introduces one set of fitted Padé parameters. No genuinely new particle, force, or conserved quantity is postulated.

free parameters (3)
  • Skyrme coupling e = 4.84
    Sets the soliton profile F(r) and all Skyrme form factors; fixed from baryon phenomenology in earlier literature (input list, Sec. IV), not fitted to the decay rate.
  • heavy-meson axial coupling g = 0.54(3)
    Enters the bound-state wavefunction through κ in Eq. (23); taken from the input list and fitted elsewhere.
  • Padé fit amplitudes/poles for w0 and w1 = not stated
    A, B, residues R, and poles z in Eq. (13) are fitted to numerically computed space-like form factors. Their values and orders are not reported, yet they determine the time-like continuation and hence the decay rate.
axioms (5)
  • domain assumption Baryons are topological solitons of the chiral Lagrangian, with hedgehog ansatz and collective quantization (Sec. II.B).
    Standard Skyrme-model framework; not derived from QCD, but used throughout.
  • domain assumption Heavy baryons are bound states of a heavy meson and a Skyrmion with harmonic-oscillator wavefunction Eq. (23).
    Callan-Klebanov-type bound-state picture; the harmonic form is justified by a large-N_c approximation.
  • ad hoc to paper Low-order Padé approximants with pion-tail asymptotics provide a valid analytic continuation of space-like form factors to the time-like region up to q² ~ 22 GeV².
    This is the paper's central methodological step; its accuracy is unvalidated and the paper admits low-order approximants are used for illustration.
  • ad hoc to paper The factorizable spectator diagram dominates; nonfactorizable contributions in Fig. 1(b) are neglected.
    Assumed without quantitative estimate; the paper states this is a first test.
  • standard math The weak decay is described by the SM effective Hamiltonian Eq. (24) with CKM factors Vub and Vud.
    Standard model input, not specific to the paper.

pith-pipeline@v1.3.0-alltime-deepseek · 10198 in / 15154 out tokens · 132215 ms · 2026-08-02T18:15:48.039577+00:00 · methodology

0 comments
read the original abstract

Purely baryonic weak decays of heavy baryons are investigated within the framework of the Skyrme model. These decays belong to a new class of unobserved decay channels, which would help us to test the standard model, particularly potential sources of CP violation in the baryonic sector. By interpreting the heavy baryon as a bound state of a heavy meson and a baryon (Skyrmion), a direct calculation of the decay process $\Lambda_b \to p\,\bar p\,n$ is performed. The resulting branching fraction is of $\mathcal{O}(10^{-6})$, in agreement with previous estimates.

Figures

Figures reproduced from arXiv: 2603.12735 by Chao Han, Chao-Qiang Geng.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic diagrams for the tree-level contributions to the purely baryonic weak decay of [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Real and imaginary parts of the [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Differential decay rate as a function of the momentum transfer squared [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Observation of the charmless purely baryonic decay $\mathinner{\mathit{\Lambda}^0_b\!\to \mathit{\Lambda} p \overline{p}}$

    hep-ex 2026-05 conditional novelty 8.0

    First observation of Λ_b^0 → Λ p p-bar with 5.1σ significance and relative branching fraction (5.1 ± 1.3(stat) ± 0.3(syst)) × 10^{-2} to the reference mode Λ_b^0 → Λ K^+ K^-.

Reference graph

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