Revisiting two-body charmed anti-charmed baryonic $B$ decays

Chun-Khiang Chua

REVIEW

Revisiting two-body charmed anti-charmed baryonic $B$ decays

Chun-Khiang Chua

High Energy Physics - Phenomenology · Submitted 7 Sep 2026

Pith's verdict: Clean theoretical extension of topological amplitudes for B to charmed baryon pairs, but the numerical evidence for non-zero b→u contributions is weak and the central claim is overstated.

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arXiv ID2609.08053 (version 2)

Pith IDENTXWFQE, Pith's permanent record of this paper and its review

CitationChun-Khiang Chua. "Revisiting two-body charmed anti-charmed baryonic $B$ decays." arXiv:2609.08053 (2026). https://pith.science/paper/ENTXWFQE

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Editor's note

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This paper extends Chua's previous topological amplitude analysis of B→B_cB_c decays by including b→u ubar q contributions. The theoretical work is the real strength: the group-theoretic decomposition is carried through systematically for all four baryon-multiplet combinations, and the updated amplitude tables (Tables III–VI) are a useful reference. The CKM amplification argument is clear and correct. That part of the paper is solid.

The numerical fit is where it gets soft. Only four branching ratios are measured, and the b→u parameters (d1, f1, a1) are fit against those four points, with the b→c parameters taken from a previous fit. The result is a severely under-determined fit. The paper honestly reports that in case 1 the b→u contributions can vanish entirely—d1 = f1 = a1 = 0 is within χ²_min + 1. That means the old solution (ref. [16]) remains fully compatible with current data. The ’slight preference’ for non-zero b→u hinges on case 2, where the b→c inputs are tweaked to get χ² = 0, but that tweak acts as an extra degree of freedom, not new data.

The three headline predictions in Table IX—B⁻ → Ξ_c⁰ Ξ_c⁻, B_s⁰ → Λ_c⁺ Ξ_c⁻, and B⁰ → Ξ_c⁺ Ξ_c⁻—carry enormous asymmetric uncertainties that overlap the ref. [16] predictions at the low end. The paper’s claim that current data ’allow or even slightly prefer’ non-vanishing b→u contributions is stronger than the fit actually supports. The data allow it, but do not prefer it.

That said, this is a honest paper. It states its assumptions, reports the uncertainties, and flags the zero solution. The framework is sound and the predictions are, in principle, testable. The paper is written for specialists in hadronic B decays and will be useful when more data arrive. I would send it to peer review—it deserves a serious referee—and recommend that the authors tone down the central claim to match the evidentiary status. The theoretical update alone is worth publishing.

Referee report

Significance

The group-theoretic decomposition itself is a useful contribution: Tables III–VI extend the topological amplitudes in a systematic way, and the CKM-amplification argument in Eq. (2) is clear and correct as a ratio estimate. The author is also commendably transparent about the large uncertainties and explicitly notes that the vanishing-b→u solution is compatible with case 1. However, the paper's central empirical claim—that present data allow or even slightly prefer non-negligible b→u contributions—is not established by the fit in Section IV.A. With only four rates, three of which are in ΔS=-1 where b→u is CKM suppressed, the individual b→u amplitudes are essentially unconstrained, and the quoted Δχ² difference between cases is not a statistically meaningful preference. The paper is better understood as a framework paper that identifies modes where b→u effects could surface; as such it is significant, but the numerical conclusions need to be reframed or supported by a more careful statistical treatment.

Major objections (4)

[Section IV.A, Table VII] The statement that present data 'slightly prefer case 2' over case 1 is not supported by the quoted statistics. The paper itself notes that in case 1 the fitted values of d1, f1 and a1,v can vanish, and that the ref. [16] solution with χ²=0.315 lies within the χ²≤χ²_min+1 region of the case-1 best fit (χ²=0.198). With only four fitted rates, three of which are in ΔS=-1 where the b→u contributions are CKM suppressed, the zero-b→u solution is fully compatible with current data. The Δχ²=0.198 difference between the two cases therefore cannot be read as evidence for non-vanishing b→u contributions.
[Section IV.A, case 2] The perfect fit χ²=0.000 in case 2 is obtained by moving the input parameters c1, e1 and δc1_v within their quoted uncertainties. These shifts act as additional free parameters, but they are not introduced into a single fit, profiled, or assigned a joint covariance. Without treating the input parameters as nuisance parameters with their uncertainties from ref. [16], the comparison between χ²=0.198 and χ²=0.000 has no statistical meaning. Consequently, the abstract's conclusion that the data 'allow or even slightly prefer' non-negligible b→u contributions does not follow from the analysis as presented.
[Section IV.A, Table IX] The advertised enhancements for B^-→Ξ_c^0 anti-Ξ_c^-, B_s^0→Λ_c^+ anti-Ξ_c^- and B^0→Ξ_c^+ anti-Ξ_c^- are not robust predictions. Each of these modes depends on only one b→u amplitude (A'_{1,c}, D'_{1,s} and F'_{1,c}, respectively), and those individual amplitudes are essentially unconstrained by the four fitted rates: the only ΔS=0 input, B^0→Λ_c^+ anti-Λ_c^-, constrains the combination D'_1+F'_1, with C'_1+E'_1 taken from ref. [16]. The resulting first uncertainties in Table IX are enormous, for example case-2 B^-→Ξ_c^0 anti-Ξ_c^- at 11.86 +107.34/-11.65 with a second error of +48.80/-9.52, and the low sides of these ranges overlap the ref. [16] predictions. The data can accommodate large b→u contributions, but they do not currently prefer them.
[Section IV.A, input parameters and SU(3) breaking assumptions] The numerical results are anchored to several ad hoc assumptions: the b→c parameters are fixed to the central values of ref. [16], δe1_v is set to -δc1_v, δd1_v is set to δc1_v, δf1_v is set to δe1_v, and the unconstrained SU(3)-breaking parameters are assigned sizes at most |δc1_v|. The headline ΔS=0 rates depend on these choices through the combinations A'_{1,c}, D'_{1,s} and F'_{1,c}, which involve δa1_v, δd1_s and δf1_c. Since none of these combinations is determined by the four data points, a scan or profile over the unconstrained parameters is needed before the paper can claim that these modes 'can allow much larger rates'. As written, the enhancement claim is an illustration of what might happen, not a consequence of the fit.

Minor objections (5)

[Section IV.A] The sentence containing 'taken to ahve sizes' contains a typo; it should read 'taken to have sizes'.
[Table VII caption] The caption says the fitted parameters are 'f1, d1 and a1,v' in the text but the table header and case descriptions also mention e1; e1 is in fact an input parameter marked with an asterisk, so the caption should list only the b→u parameters d1, f1 and a1,v as fitted.
[Table IX caption] The caption states that the first uncertainties are from 'the fitted parameters, namely d1, e1 and a1,v'; this should read 'd1, f1 and a1,v', since e1 is an input parameter in both cases.
[Eq. (10)] In the E'_4 term, the Hamiltonian insertion appears as H^j rather than H'^j, unlike the corresponding C'_4 and D'_4 terms in the same equation; this is presumably a typographical inconsistency and should be corrected for notational consistency.
[Section III, Eq. (17)] The text notes that combinations such as M^{j'}_j H^{jk}_i or M^i_{i'} H^{jk}_i vanish; it would be helpful to state explicitly that this relies on the specific form of M and H, since the reader otherwise has to verify the index contractions by hand.

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The paper

The paper claims

B→uūq contributions, long overlooked, can dominate certain charmed baryonic B decays via a 20-fold CKM amplification in ΔS=0 transitions.

The reading

The paper revisits the topological amplitude analysis of two-body charmed anti-charmed baryonic B decays. It claims that contributions from the b→uūq transition, previously neglected, are not negligible and can significantly enhance decay rates in channels where the transition has ΔS=0. The enhancement stems from the CKM factor ratio: in ΔS=0 transitions, the relative size of b→uūq versus b→c\bar{c}q is amplified by roughly a factor of 20 ($λ^{{-2}}$) compared to ΔS=−1 transitions. Using existing data on four modes, the paper shows that b→uūq contributions are allowed and even slightly preferred. If correct, the branching ratios of B^−→$Ξ_c^{0}$\bar{Ξ}_c^−, \bar{B}$_s^{0}$→Λ_c^+\bar{Ξ}_c^−, and \bar{B}^0→Ξ_c^+\bar{Ξ}_c^− could be much larger than predictions that only include b→c\bar{c}q contributions.

What carries the argument

The key machinery is the topological amplitude approach extended to include b→uūq contributions, encoded in the new parameters D, F, A for internal W‑tree, W‑exchange, and annihilation diagrams. The amplification mechanism is the double CKM ratio of Eq. (2): |A'_u/A'_c| / |A_u/A_c| ≈ $λ^{{-2}}$ ≈ 20, which makes b→uūq effects prominent in ΔS=0 transitions. The paper also introduces SU(3) breaking parameters for these new amplitudes.

Extended reading notes

Core claim

The central claim is that the b→uūq transition, though CKM-suppressed in ΔS=−1 decays, becomes competitive in ΔS=0 decays because the relevant CKM factor ratio |V_{ub}V^*_{ud}/V_{cb}V^*_{cd}| is about 20 times larger than |V_{ub}V^*_{us}/V_{cb}V^*_{cs}|. The paper provides updated topological amplitude decompositions for all B→B_c\bar{B}_c decays that include both b→c\bar{c}q and b→uūq contributions. Fits to the four currently measured B→B_c(\bar{3}_f)\bar{B}_c(3_f) modes show that b→uūq parameters can be non-zero and improve agreement with data, especially for the B^−→$Ξ_c^{0}$\bar{Λ}_c^− and $B^{0}$→Ξ_c^+\bar{Λ}_c^− rates. The consequence is that three ΔS=0 modes—B^−→$Ξ_c^{0}$\bar{Ξ}_c^−, \bar{B}$_s^{0}$→Λ_c^+\bar{Ξ}_c^−, and \bar{B}^0→Ξ_c^+\bar{Ξ}_c^−—receive dominant or sizable contributions from b→uūd and can have branching ratios orders of magnitude larger than previously estimated.

Load-bearing premise

The load-bearing assumption is that the topological parameters for the b→c\bar{c}q contributions (c1, e1, δ_{c1}^v) can be taken from a previous fit [16] and used as fixed inputs while fitting only the b→uūq parameters, even though the previous fit had uncertainties and may shift when the new contributions are included consistently.

Editorial extensions

If this is right

The branching ratio of B^−→Ξ_c^0\bar{Ξ}_c^− is predicted to reach up to ~10^{-3} in case 2, compared to ~10^{-5} from b→c\bar{c}q only, making it accessible at hadron colliders and B factories.
Similarly, \bar{B}_s^0→Λ_c^+\bar{Ξ}_c^− and \bar{B}^0→Ξ_c^+\bar{Ξ}_c^− could have branching ratios of order 10^{-4}, far above previous estimates and within reach of current experiments.
The existing tension in the SU(2) relation between B^−→Ξ_c^0\bar{Λ}_c^− and B^0→Ξ_c^+\bar{Λ}_c^− is naturally resolved by b→uūs contributions that break isospin.
The small rate of B^0→Λ_c^+\bar{Λ}_c^− does not imply small b→uūd contributions; rather, it results from destructive interference between D' and F' amplitudes.
In ΔS=−1 modes, b→uūs contributions remain subleading, so previous predictions for those modes are largely unchanged.

Reading between the lines

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

If the b→uūq contributions are as sizeable as case 2 suggests, they could also affect other ΔS=0 B decays into baryons, such as modes involving excited charmed baryons or decays into lighter baryon pairs.
The enhancement mechanism is generic: any ΔS=0 decay where the b→uūd amplitude appears without cancellation from the b→c\bar{c}d amplitude could show similar enhancements, motivating searches in other final states.
The fit is currently underdetermined (four data points, three new parameters), so the large reported uncertainties allow a range of possibilities; precise measurements of the three highlighted modes will decisively test the hypothesis.
The assumption that b→c\bar{c}q parameters can be taken from a previous fit without refitting alongside b→uūq parameters is a strong one; a global refit of all sectors simultaneously would provide more reliable constraints.

Original abstract

The study of two-body charmed anti-charmed baryonic $\overline B\to {\bf B}_c \overline {\bf B}_c$ decays using the topological amplitude approach is revisited. We include the $b\to u\bar u q$ contributions, in addition to the $b\to c\bar c q$ contributions, to these decays. The topological decomposition of $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ and ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf {\bar 6_f})$ decay amplitudes are updated accordingly. Although the $b\to u\bar u q$ contributions are Cabibbo-Kobayashi-Maskawa (CKM) suppressed in $\Delta S=-1$ transitions, their effects are significantly amplified in $\Delta S=0$ transitions, as the relative size of the CKM factors in $b\to u\bar u q$ and $b\to c\bar c q$ contributions in $\Delta S=0$ transitions is enlarged by $\lambda^{-2}$, roughly a factor of 20, from the one in $\Delta S=-1$ transitions. Present data in $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$ decay rates allow or even slightly prefer non-negligible $b\to u\bar u q$ contributions. These $b\to u\bar u q$ contributions can allow much larger rates for $B^-\to \Xi_c^0 \bar \Xi_c^{-}$, $\overline B{}_s^0\to \Lambda_c^+ \bar \Xi_c^{-}$ and $\overline B{}^0\to \Xi_c^+ \bar \Xi_c^{-}$ decays than those only have $b\to c\bar c d$ contributions. Several modes containing only $b\to u\bar u q$ contributions in $\overline B\to {\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ decays are also identified. Measuring these decays will be interesting and useful in clarifying the role of $b\to u\bar u q$ contributions in two-body charmed anti-charmed baryonic $\overline B$ decays.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,357 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.33 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.79 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The study of two-body charmed anti-charmed baryonic $\overline B\to {\bf B}_c \overline {\bf B}_c$ decays using the topological amplitude approach is revisited. We include the $b\to u\bar u q$ contributions, in addition to the $b\to c\bar c q$ contributions, to these decays. The topological decomposition of $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ and ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf {\bar 6_f})$ decay amplitudes are updated accordingly. Although the $b\to u\bar u q$ contributions are Cabibbo-Kobayashi-Maskawa (CKM) suppressed in $\Delta S=-1$ transitions, their effects are significantly amplified in $\Delta S=0$ transitions, as the relative size of the CKM factors in $b\to u\bar u q$ and $b\to c\bar c q$ contributions in $\Delta S=0$ transitions is enlarged by $\lambda^{-2}$, roughly a factor of 20, from the one in $\Delta S=-1$ transitions. Present data in $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$ decay rates allow or even slightly prefer non-negligible $b\to u\bar u q$ contributions. These $b\to u\bar u q$ contributions can allow much larger rates for $B^-\to \Xi_c^0 \bar \Xi_c^{-}$, $\overline B{}_s^0\to \Lambda_c^+ \bar \Xi_c^{-}$ and $\overline B{}^0\to \Xi_c^+ \bar \Xi_c^{-}$ decays than those only have $b\to c\bar c d$ contributions. Several modes containing only $b\to u\bar u q$ contributions in $\overline B\to {\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ decays are also identified. Measuring these decays will be interesting and useful in clarifying the role of $b\to u\bar u q$ contributions in two-body charmed anti-charmed baryonic $\overline B$ decays.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The study of two-body charmed anti-charmed baryonic $\overline B\to {\bf B}_c \overline {\bf B}_c$ decays using the topological amplitude approach is revisited.	contribution 0.54	0.46	0.04	asserted 0.80
s1	We include the $b\to u\bar u q$ contributions, in addition to the $b\to c\bar c q$ contributions, to these decays.	contribution 0.92	0.91	0.06	asserted 0.98
s2	The topological decomposition of $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ and ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf {\bar 6_f})$ decay amplitudes are updated accordingly.	contribution 0.65	0.88	0.05	asserted 0.99
s3	Although the $b\to u\bar u q$ contributions are Cabibbo-Kobayashi-Maskawa (CKM) suppressed in $\Delta S=-1$ transitions, their effects are significantly amplified in $\Delta S=0$ transitions, as the relative size of the CKM factors in $b\to u\bar u q$ and $b\to c\bar c q$ contributions in $\Delta S=0$ transitions is enlarged by $\lambda^{-2}$, roughly a factor of 20, from the one in $\Delta S=-1$ transitions.	result 0.72	0.64	0.24	asserted 1.00
s4	Present data in $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$ decay rates allow or even slightly prefer non-negligible $b\to u\bar u q$ contributions.	result 0.90	0.43	0.24	hedged possibility 0.87
s5	These $b\to u\bar u q$ contributions can allow much larger rates for $B^-\to \Xi_c^0 \bar \Xi_c^{-}$, $\overline B{}_s^0\to \Lambda_c^+ \bar \Xi_c^{-}$ and $\overline B{}^0\to \Xi_c^+ \bar \Xi_c^{-}$ decays than those only have $b\to c\bar c d$ contributions.	result 0.90	0.78	0.31	hedged possibility 0.96
s6	Several modes containing only $b\to u\bar u q$ contributions in $\overline B\to {\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ decays are also identified.	result 0.80	0.88	0.07	asserted 1.00
s7	Measuring these decays will be interesting and useful in clarifying the role of $b\to u\bar u q$ contributions in two-body charmed anti-charmed baryonic $\overline B$ decays.	future work 1.00	0.13	0.12	asserted 0.49

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from analysis of existing data 0.53.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: Topological diagrams of (a)

**Figure 2.** FIG. 2: Topological diagrams of (a)

Figures reproduced from arXiv:2609.08053 by the authors.

Discussion

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