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REVIEW 2 major objections 4 minor 53 references

Charmful two-body $\Omega_b$ decays in the light-front quark model

T0 review · 2 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper argues that charmful two-body decays of the $\Omega_b$ baryon have branching fractions up to $10^{-4}$, ten to one hundred times larger than earlier estimates and within reach of LHCb.

desk verdict Useful, mostly solid LFQM paper whose genuinely new external-W predictions are undercut only by an abstract that oversells the internal-W enhancement without flagging its N_eff dependence. read the letter →

arxiv 2412.11584 v2 pith:JE5SOWA2 submitted 2024-12-16 hep-ph hep-ex

Yan-Li Wang , Yu-Kuo Hsiao , Kai-Lei Wang , Chong-Chung Lih This is my paper · ORCID
classification hep-phhep-ex
keywords Omega_bdecayscharmfultwo-bodylight-frontquarkmodelbranchingfractionshelicityamplitudesgeneralizedfactorizationnon-factorizableQCDcorrectionsLHCb
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 sets out to predict the rates of two-body weak decays of the $\Omega_b$ baryon into a charmed meson plus a $\Xi$, $\Xi^*$, or $\Omega$ baryon, using the light-front quark model for the required transition form factors. Its central claim is that most of these charmful branching fractions are much larger than previous estimates: channels such as $\Omega_b^- \to \Xi^- D^0$ and $\Omega_b^- \to \Xi^- D^{*0}$ are predicted at the level of $10^{-4}$, ten to one hundred times the earlier values. The authors also use helicity amplitudes to explain why $\mathcal{B}(\Omega_b^- \to \Omega^- J/\psi)/\mathcal{B}(\Omega_b^- \to \Omega^- \eta_c) \simeq 3.4$, and they single out external W-emission modes such as $\Omega_b^- \to \Xi^0 D_s^-$ that have stable, measurable predictions around $10^{-5}$. If the paper is right, these decays become practical targets for LHCb and can help determine how often b quarks fragment into $\Omega_b$ baryons.

What carries the argument

The machinery is the light-front quark model applied to baryon transitions: $\Omega_b$ and the final $\Xi$, $\Xi^*$, or $\Omega$ are treated as quark--diquark bound states with Gaussian momentum wave functions, and the Melosh transformation relates the spin states. From these wave functions the paper extracts the transition form factors $f_i^{V,A}$ for spin-1/2 final baryons and $F_j^{V,A}$ for spin-3/2 final baryons, fits them to dipole functions of momentum transfer, and evaluates them at the charmed-meson masses. These form factors feed factorized weak-decay amplitudes whose two coefficients, $a_1$ and $a_2$, come from generalized factorization with an effective color number $N_{\rm eff}$; the internal-W channels depend strongly on $a_2$, while the external-W channels depend on the stable $a_1$. The helicity amplitudes built from the same form factors carry the argument for ratios such as $\mathcal{B}(\Omega_b^- \to \Omega^- J/\psi)/\mathcal{B}(\Omega_b^- \to \Omega^- \eta_c) \simeq 3.4$.

What would settle it

Measure $\mathcal{B}(\Omega_b^- \to \Xi^0 D_s^-)$ at LHCb: because this external-W mode is nearly independent of $a_2$, its value fixes the transition form-factor scale. Then measure $\mathcal{B}(\Omega_b^- \to \Xi^- D^0)$, the internal-W flagship: the paper predicts roughly $10^{-4}$ for $N_{\rm eff}\simeq2$ and roughly $10^{-6}$ for $N_{\rm eff}=3$, so the two measurements together decide whether the enhancement is real. A secondary check is the ratio $\mathcal{B}(\Omega_b^- \to \Xi^- D^{*0})/\mathcal{B}(\Omega_b^- \to \Xi^- D^0)$, predicted near 2.

Watch

Extended reading notes

Core claim

The central discovery is a systematic calculation of the singly and doubly charmful two-body $\Omega_b^-$ decays in which the $\Omega_b \to \Xi$, $\Xi^*$, and $\Omega$ transition form factors are obtained from the light-front quark model and then inserted into factorized weak amplitudes. The paper finds that most branching fractions come out far above earlier calculations; for example, $\mathcal{B}(\Omega_b^- \to \Xi^- D^0) = (1.4 \pm 0.3) \times 10^{-4}$ for the effective color number $N_{\rm eff}=2$, compared with $1.4 \times 10^{-6}$ from the previous study, while $\mathcal{B}(\Omega_b^- \to \Xi^- D^{*0})$ is $(3.0 \pm 0.9) \times 10^{-4}$. The enhancement is traced to the axial form factor $f_1^A$ being comparable to $f_1^V$ at the D-meson momentum transfer, whereas earlier models had a small $f_1^A$. The same table shows that $N_{\rm eff}=3$ gives $\mathcal{B}(\Omega_b^- \to \Xi^- D^0) \simeq 1.2 \times 10^{-6}$, so the large internal-W rates are tied to $N_{\rm eff}$ near 2. The external W-emission modes induced by $b \to u \bar c s$ avoid the $a_2$ uncertainty and are predicted at $(4.0\text{--}5.5) \times 10^{-5}$ for $\Xi^0 D_s^-$ and up to $2.2 \times 10^{-4}$ for $\Xi^{*0} D_s^{*-}$. The paper also interprets the ratio $\mathcal{B}(\Omega_b^- \to \Omega^- J/\psi)/\mathcal{B}(\Omega_b^- \to \Omega^- \eta_c) \simeq 3.4$ as a helicity effect, with vector-meson helicity-1 and helicity-3/2 amplitudes enhancing the $J/\psi$ mode.

Load-bearing premise

The headline hundred-fold enhancement of the internal-W channels rests on taking the effective color number near $N_{\rm eff}=2$, which makes $a_2\simeq 0.22$; if non-factorizable QCD corrections correspond instead to $N_{\rm eff}=3$, then $a_2\simeq 0.02$ and those branching fractions fall by about two orders of magnitude, back to the earlier estimates.

Editorial extensions

If this is right

  • With $N_{\rm eff}\simeq 2$, the channels $\Omega_b^- \to \Xi^- D^0$, $\Xi^- D^{*0}$, $\Xi^{*-} D^0$, and $\Xi^{*-} D^{*0}$ sit at branching fractions around $10^{-4}$, roughly a hundred times above the earlier estimate and inside LHCb's expected sensitivity.
  • The external W-emission modes $\Omega_b^- \to \Xi^0 D_s^-$, $\Xi^0 D_s^{*-}$, $\Xi^{*0} D_s^-$, and $\Xi^{*0} D_s^{*-}$ vary only mildly with $N_{\rm eff}$, so a measurement of any one of them would test the form-factor scale without waiting for the non-factorizable corrections to be resolved.
  • The predicted ratio $\mathcal{B}(\Omega_b^- \to \Omega^- J/\psi)/\mathcal{B}(\Omega_b^- \to \Omega^- \eta_c) \simeq 3.4$ gives a helicity-sensitive observable that a future LHCb measurement can confirm or exclude.
  • Because the absolute rates are large, $\Omega_b$ charmful decays become a workable independent route to the fragmentation fraction $f_{\Omega_b}$, complementing the current use of $\Omega_b^- \to \Omega^- J/\psi$.

Reading between the lines

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

  • A corollary the authors leave implicit: the external-W channels are nearly pure form-factor probes, so the first measured rate among $\Omega_b^- \to \Xi^0 D_s^-$, $\Xi^0 D_s^{*-}$, and $\Xi^{*0} D_s^-$ would calibrate the whole internal-W prediction by fixing the $\Omega_b \to \Xi$ transition strength.
  • The ratio $\mathcal{B}(\Omega_b^- \to \Xi^- D^{*0})/\mathcal{B}(\Omega_b^- \to \Xi^- D^0) \simeq 2$ is almost independent of both $a_2$ and the overall form-factor normalization; it therefore offers a sharp, low-theory test of the helicity decomposition once both modes are observed.
  • One could export the same form-factor machinery to $\Lambda_b$ and $\Xi_b$ charmful decays; their measured branching fractions would provide an independent check of the large axial form factor that drives the enhancement here.
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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 / 4 minor

Summary. The paper studies singly and doubly charmful two-body Omega_b^- decays using the light-front quark model (LFQM). It computes the Omega_b -> Xi, Xi*, Omega transition form factors, then uses naive/generalized factorization with effective color number N_eff^c = 2, 3, infinity to predict branching fractions for internal and external W-emission channels. The headline claim is that rates such as B(Omega_b^- -> Xi^- D^0) and B(Omega_b^- -> Xi^- D*^0) are 10-100 times larger than previous calculations, reaching 10^-4, and that external-W channels like B(Omega_b^- -> Xi^0 D_s*^-) are also at the 10^-5-10^-4 level, promising for LHCb. The paper also interprets the ratio B(Omega_b^- -> Omega^- J/psi)/B(Omega_b^- -> Omega^- eta_c) ~ 3.4 via helicity amplitudes.

Significance. If the large internal-W predictions were robust, this would substantially raise the anticipated LHCb sensitivity for charmful Omega_b decays and help pin down the fragmentation fraction f_Omega_b. The external-W predictions are stable under the N_eff ambiguity and follow from standard factorization, and the LFQM form factors with dipole parametrizations are provided in enough detail to be reproducible. The helicity decomposition of the D*/D and J/psi/eta_c ratios is pedagogically useful. However, as discussed below, the headline 10-100x enhancement is conditional on an undetermined input, so the significance of the central claim is currently weakened.

major comments (2)
  1. [Section IV, paragraph starting 'It is possible that N_eff...'] The preference for N_eff ~ 2 is justified only by extrapolating the authors' earlier B3c determination (N_eff^c = 2.15 ± 0.17) to Omega_b decays. This is an external input, not a prediction of this paper. Since the internal-W branching fractions span two to three orders of magnitude across N_eff = 2, 3, infinity, the central quantitative results for those channels are essentially unconstrained by the present analysis. The paper should either derive N_eff from a fit to available Omega_b data (e.g., the R(Omega_b/Xi_b) measurement in Eq. (1)) or clearly demote the internal-W predictions to a conditional illustration rather than a headline finding.
  2. [Section IV, Eq. (41)] The sentence 'According to Table III, we present B(Omega_b^- -> Xi^- D^0) = ...' cites Table III, but the branching fractions are listed in Table IV. This is a minor citation error, but it is indicative of a larger presentation issue: the numerical results in Section IV are introduced in a way that obscures the N_eff-dependence until the end. The abstract, in particular, should be rewritten to state the N_eff-dependence explicitly, e.g., 'for N_eff ~ 2' rather than presenting the 10-100x enhancement as a model-independent finding.
minor comments (4)
  1. [Section IV, Eq. (35) and surrounding text] In the decomposition of |H_Xi D|^2, the notation C^+_D and C^-_D is used, but the definitions of C^±_M are given only after the first equation; please define all symbols at first use.
  2. [Section III, Eq. (33)] The list of input parameters includes m_b, m_s, m_n but not m_c. This is acceptable because the baryon transitions are b -> q (q = d, s, u) and the charm quark enters only through meson decay constants, but a brief comment would prevent reader confusion.
  3. [Section I, Eq. (1)] The ratio R(Omega_b/Xi_b) is defined with f_Omega_b/f_Xi_b multiplied by the branching-fraction ratio, but the text then says 'R(Omega_b/Xi_b) = 0.28 ± 0.13' from PDG; please ensure the definition and the reported value are consistent (the notation f_Omega_b/f_Xi_b is used in the text but the equation uses the same symbol as the ratio).
  4. [General] The paper would benefit from a table or figure summarizing the N_eff-dependence of all internal-W channels at a glance, since Table IV already does this but the abstract and introduction emphasize only the N_eff = 2 / infinity values.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation; the only notable self-citation is the N_eff estimate used to motivate one row of a three-way sensitivity table.

full rationale

The derivation is not circular. Form factors for Ω_b→Ξ^(*), Ω are computed in the LFQM from published constituent quark masses and β parameters (Eq. (33)); the vector/axial transition matrix elements are projected with Eqs. (26)–(29), fitted to dipole curves (Eq. (34)), and evaluated at the physical meson masses. Branching fractions then follow from Eq. (16) with CKM elements, decay constants, and Wilson coefficients taken from PDG and the literature. The only input controlling the Abstract's "ten to one hundred times larger" claim is N_eff: Eq. (32) gives a2=(0.22,0.02,-0.37) for N_eff=(2,3,∞), and since the amplitudes in Eq. (4) are linear in a2, the internal-W branching fractions scale as a2^2, producing the N_eff=(2,3,∞) columns of Table IV. The paper does not predict N_eff from Ω_b data; it explicitly states: "whether N_eff is close to 2 or not depends on the extractions from more accurate experimental results, which have not been provided." The plausibility remark for N_eff≈2 does cite the authors' own B3c determination (N_eff=2.15±0.17, Refs. [19,22]), which is a self-citation, but it is not used to derive the branching fractions; it is a sensitivity rationale, and the external-W predictions (a1≈1) are independent of this ambiguity. No equation in the paper reduces to its inputs by construction, and no fit to Ω_b data is presented as a prediction.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The central predictions rest on a set of model inputs taken from earlier work. The most important is the effective color number, which is not predicted and changes the headline rates by orders of magnitude. The LFQM shape parameters and quark masses are standard for this model but are external inputs. No new entities are introduced.

free parameters (5)
  • Effective color number N_eff^c = 2, 3, infinity (a2 = 0.22, 0.02, -0.37)
    Chosen by hand to bracket non-factorizable QCD corrections; the '10 to 100 times larger' claim is driven by N_eff=2 or infinity, while N_eff=3 gives rates close to earlier work.
  • LFQM Gaussian shape parameter beta_b[ss] = 0.78 +/- 0.04 GeV
    Controls the momentum distribution of the b quark relative to the [ss] diquark; taken from Refs. [41,46,47] and affects all form factors.
  • LFQM shape parameter beta_s[ss] = 0.44 +/- 0.02 GeV
    Same role for strange spectator quarks; entered in Eq. (33).
  • LFQM shape parameter beta_n[ss] = 0.44 +/- 0.02 GeV
    Same role for u/d spectator quarks; entered in Eq. (33).
  • Constituent quark masses mb, ms, mn = 5.00, 0.38, 0.275 GeV
    Model inputs from Refs. [41,46,47]; the charm quark mass m_c is not listed even though half the channels use b -> c transitions.
assumptions (3)
  • domain assumption Weak decay amplitudes factorize into current matrix elements, with non-factorizable QCD corrections absorbed into effective color number N_eff
    Used in Eq. (4) and Eq. (32); the spread of a2 with N_eff shows the central rates depend on this assumption.
  • domain assumption The Omega_b baryon is described as a quark-diquark bound state in the light-front quark model with a Gaussian momentum distribution
    Eqs. (19)-(25); all form factors are derived from this ansatz.
  • domain assumption Pole masses mV=6.05 GeV and mA=6.32 GeV for the vector and axial-vector currents
    Adopted in Section III from parity assignments of Omega_b and Omega_b(6316); used in the dipole parametrization Eq. (34).

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Cite this review

Pith. "Pith review of Charmful two-body $\Omega_b$ decays in the light-front quark model." pith.science (2026). https://pith.science/paper/JE5SOWA2

@misc{pith2026241211584,
  author       = {Pith},
  title        = {Pith review of: Charmful two-body $\Omega_b$ decays in the light-front quark model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JE5SOWA2}},
  note         = {Machine review of arXiv:2412.11584}
}
abstract

We investigate the singly and doubly charmful two-body $\Omega_b^-$ decays using the light-front quark model. Our findings reveal that most branching fractions calculated in this study, such as ${\cal B}(\Omega_b^-\to\Xi^- D^0,\Xi^{-}D^{*0})$, can be ten to one hundred times larger than those reported in previous calculations. Additionally, we interpret the ratio ${\cal B}(\Omega_b^-\to\Omega^- J/\psi)/{\cal B}(\Omega_b^-\to\Omega^- \eta_c)\simeq 3.4$ within the helicity framework. While the decay involving external $W$-boson emission appears to be suppressed by the $b\to u \bar c s$ weak transition, it still yields a significant branching fraction. For instance, ${\cal B}(\Omega_b^-\to\Xi^0 D_s^{*-})=(5.9-14.2)\times 10^{-5}$, ${\cal B}(\Omega_b^-\to\Xi^{*0}D_s^{-})=(6.7-12.1)\times10^{-5}$, and ${\cal B}(\Omega_b^-\to\Xi^{*0}D_s^{*-})=(12.8-26.7)\times10^{-5}$, with values reaching as large as $10^{-4}$. These predictions are well within the experimental reach of LHCb.

Figures

Figures reproduced from arXiv: 2412.11584 by the authors.

Figure 1
Figure 1. FIG. 1. Feynman diagrams for the charmful two-body Ω [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

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Reviewed August 11, 2026 · model on record in the stance chip above.