From topological amplitudes to rescattering dynamics in charmed baryon decays

Di Wang; Ying-Xin Lai

REVIEW 4 major objections 4 minor 2 cited by

From topological amplitudes to rescattering dynamics in charmed baryon decays

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper argues that long-distance rescattering in charmed baryon decays violates the Koerner-Pati-Woo theorem because gluons can change quark colors, and that penguin rescattering amplitudes are comparable to tree amplitudes, making…

desk verdict The (1,1)-rank tensor bridge and isospin checks are solid and useful, but the claimed refutation of the Koerner-Pati-Woo theorem attacks a premise the theorem does not require and should be read as a model-dependent artifact, not a theorem violation. read the letter →

arxiv 2507.06914 v2 pith:SWQNQKLU submitted 2025-07-09 hep-ph

Ying-Xin Lai , Di Wang This is my paper

classification hep-ph

keywords charmedbaryondecaystopologicaldiagramapproachrescatteringdynamicsfinal-stateinteractionKoerner-Pati-WootheoremCPviolationSU(3)flavorsymmetryisospinsumrules

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

Charmed baryon decays into a baryon octet and a pseudoscalar meson can be described either by quark-level topological diagrams or by hadron-level final-state rescattering. This paper tries to show they are the same physics by using the $(1,1)$-rank amplitudes as a bridge: rescattering amplitudes built by tensor contractions from the single emission topology match the amplitudes built directly from the chiral Lagrangian. If correct, long-distance rescattering generates the other topological amplitudes, including quark-loop penguin contributions, and those penguin rescattering amplitudes are as large as the tree amplitudes, so CP violation in some singly Cabibbo-suppressed charmed baryon decays could be observable at the $10^{-4}$ to $10^{-3}$ level. It would also mean the Koerner-Pati-Woo theorem, long used to reduce topological diagrams, is inconsistent with rescattering dynamics because gluons can change quark colors.

What carries the argument

The load-bearing device is the set of $(1,1)$-rank octet-tensor amplitudes $A_1,\dots,A_{14}$, defined as linear combinations of the third-rank topological amplitudes; they have the same tensor structure as the chiral Lagrangian vertices ($VPP$, $BBP$, $BBV$), so they can serve as the bridge between quark-level topology and hadron-level rescattering. The argument is carried by explicit tensor contractions (Eqs. (16)-(63)) that convert the emission amplitude $A_2$ into the other amplitudes via $u$-, $t$-, and $s$-channel triangle and bubble diagrams, together with the $SU(3)_F$ completeness relations (Eq. (70)) that produce Table I.

What would settle it

Measure the branching fractions of $\Lambda_c^+\to\Sigma^+K_S^0$ and $\Lambda_c^+\to\Sigma^0K^+$ precisely: the Koerner-Pati-Woo theorem plus isospin predicts $\sqrt{2}\,A(\Lambda_c^+\to\Sigma^0K^+)=A(\Lambda_c^+\to\Sigma^+K^0)$. If the measured ratio matches this prediction to better than the roughly $1\%$ isospin-breaking scale, the paper's central claim is wrong; if it is violated at the several-percent level, the theorem is broken. The paper notes that current data for the $\Sigma^0K^+$ mode from two experiments differ, so the $\Sigma^+K_S^0$ mode is the decisive one to measure.

Watch

Extended reading notes

Core claim

The paper's central claim is that the $(1,1)$-rank amplitudes $A_1,\dots,A_{14}$, which are linear combinations of the third-rank topological amplitudes for $B_{c\bar 3}\to B_8 P$ decays, provide a tensor bridge between quark-level topological diagrams and hadron-level rescattering amplitudes. Starting from the assumption that only the short-distance emission diagram $T$ feeds the weak vertex, the paper constructs every $u$-, $t$-, and $s$-channel rescattering amplitude by tensor contractions and finds that the results reproduce the amplitudes derived directly from the chiral Lagrangian; the resulting Table I lists which combinations of strong couplings contribute to each $A_i$ in the $SU(3)_F$ limit. Because Table I does not satisfy the Koerner-Pati-Woo relations $A_1=-A_3$, $A_5=-A_7$, $A_6=-A_8$, $A_9=-A_{10}$, the paper concludes that the theorem is inconsistent with rescattering dynamics. The explanation is that the classic proof requires quark colors to stay frozen from the weak vertex until baryon formation, whereas gluon exchange can change quark colors, so the color-antisymmetry step in the proof fails. As a consequence, the quark-loop amplitudes $A_{11}$ and $A_{12}$ receive long-distance contributions comparable to the tree amplitudes, which the paper argues could make CP asymmetries in some singly Cabibbo-suppressed charmed baryon decays reach $10^{-4}$ to $10^{-3}$.

Load-bearing premise

The load-bearing premise is that the only short-distance contribution to the weak vertex is the emission diagram $T$, so every other topological amplitude is generated purely by long-distance rescattering; if additional short-distance topologies contribute, the derived $A_i$ are not the full physical amplitudes and the claimed violation of the Koerner-Pati-Woo relations need not hold for the actual decay amplitudes.

Editorial extensions

If this is right

The $u$-, $t$-, and $s$-channel rescattering amplitudes derived from topological diagrams coincide with those derived from the chiral Lagrangian in the $SU(3)_F$ limit, so a single short-distance emission topology plus hadron rescattering reproduces the topological amplitude pattern.
Isospin sum rules for all isospin systems of $B_{c\bar 3}\to B_8 P$ decays hold when written in terms of rescattering amplitudes.
Quark-loop (penguin) rescattering contributions are comparable to tree-level ones, so some singly Cabibbo-suppressed charmed baryon decays could exhibit CP asymmetries of order $10^{-4}$ to $10^{-3}$.
The Koerner-Pati-Woo relations $A_1=-A_3$, $A_5=-A_7$, $A_6=-A_8$, $A_9=-A_{10}$ fail in rescattering dynamics, so the theorem should not be used to reduce topological diagrams.
A testable consequence is the violation of $\sqrt{2}\,A(\Lambda_c^+\to\Sigma^0K^+)=A(\Lambda_c^+\to\Sigma^+K^0)$, which the paper proposes to probe by measuring the $\Lambda_c^+\to\Sigma^+K_S^0$ branching fraction.

Reading between the lines

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

If the Koerner-Pati-Woo violation survives scrutiny, amplitude relations in other charmed-baryon analyses that use the theorem, such as the $\Omega_c^0\to\Sigma^+K^-$ versus $\Omega_c^0\to\Sigma^0K_S^0$ relation and the $B_{c\bar 3}\to B_{10}P$ equalities, should be rederived without it because those derivations share the same color-antisymmetry assumption.
The same color-change loophole applies wherever rescattering generates charm observables, including doubly charmed baryon production, so a natural extension is to build the same $(1,1)$-rank bridge for $B_{c\bar 3}\to B_{10}P$ and $B_{c\bar 3}\to B_8V$ decays.
A quantitative prediction of the CP asymmetries would require fixing the strong coupling constants and loop integrals, which the paper does not do; fitting the full $B_{c\bar 3}\to B_8P$ rate and asymmetry dataset could turn the claimed $10^{-4}$ to $10^{-3}$ range into mode-by-mode numbers.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The tensor machinery is the real content and it is mostly solid. The headline claim about the Koerner-Pati-Woo theorem, however, is a bridge too far: it attacks a premise the theorem never needed, and the paper's own T-only assumption undercuts the conclusion.

What is actually new: the (1,1)-rank tensor bridge between the third-rank topological amplitudes and the chiral Lagrangian, Table I's systematic list of u-, t-, and s-channel rescattering amplitudes in the SU(3)F limit, and the isospin sum rule checks carried out entirely in rescattering language. The explicit Xi_c -> Xi pi worked example reproduces the chiral Lagrangian result, and the appendix verification that every isospin system satisfies its sum rule is a genuine consistency test. This part is formal, reproducible algebra, and I trust it substantially more than the interpretative claims.

The soft spot is the KPW section, and the stress-test note is right about it. The KPW theorem is a selection rule on the local four-quark operator after Fierz rearrangement. Combined with the color-singlet constraint on the final baryon, the operator symmetry forces flavor antisymmetry of the two quarks that come from the weak vertex. Nothing in that argument requires quark colors to be frozen between production and hadronization. Gluon exchanges conserve flavor and belong to the long-distance dressing already encoded in the topological amplitudes. When one final baryon quark comes from the intermediate meson, the theorem's premise does not apply, so those diagrams cannot contradict it. The color-counting relations in Fig. 3 describe contractions of a particular FSI model, not the weak operator's symmetry. So the conclusion that the theorem is 'illogical' is not supported by the presented argument.

There is a second, independent issue: the whole derivation assumes only the short-distance emission diagram T seeds the rescattering chain. If other short-distance topologies contribute at a non-negligible level, the derived A_i do not coincide with the physical decay amplitudes, and the failure of A1 = -A3 says something about the model rather than about KPW. The CP violation statements are also speculative: 'comparable' amplitudes do not amount to a numeric prediction, and the existing branching fraction data for Lambda_c+ -> Sigma0 K+ and Sigma+ K0_S look consistent with the KPW relation at the current precision.

Who is it for: charm hadron decay practitioners and anyone using topological amplitude plus FSI methods. It deserves a serious referee because the technical apparatus is detailed, explicit, and checkable. I would send it to review, but ask for a major revision that either removes the KPW refutation or rephrases it strictly as a model-dependent observation within a T-only rescattering picture, and that separates the solid framework section from the speculative phenomenology. The Belle II suggestion (precise Lambda_c+ -> Sigma+ K0_S) is a reasonable experimental test of the isospin+KPW relation; it just is not a clean test of KPW alone.

Referee Report

4 major / 4 minor

Summary. The paper proposes a tensor-based framework that connects topological amplitudes for B_{c3} -> B8 P decays to hadronic rescattering amplitudes. The key device is a set of (1,1)-rank amplitudes Ai that bridge the third-rank tensor language of topological diagrams and the (1,1)-rank tensor language of the meson-baryon chiral Lagrangian. The authors list tensor contractions for the transitions A2 -> Ai, derive the SU(3)_F-limit rescattering contributions in Table I, and verify isospin sum rules for several decay systems. On this basis they claim that penguin-type rescattering contributions are comparable to tree-type ones, implying possible observable CP violation in charmed baryon decays, and that the Koerner-Pati-Woo (KPW) theorem is inconsistent with rescattering dynamics because gluon exchanges can change quark colors.

Significance. If the framework is valid, it provides a useful dictionary between topological amplitudes and meson-baryon rescattering contributions and gives a systematic way to test isospin sum rules. The explicit check against the chiral Lagrangian for the Xi_c -> Xi pi system, the verification of isospin sum rules in Appendix A, and the transparent tensor algebra are genuine strengths of the manuscript. However, the headline physical claims are not supported by the presented analysis. The KPW-violation conclusion rests on a misreading of what the theorem requires, and the CP-violation estimate is qualitative, without numerical evaluation of loop functions or strong phases. The enduring value of the paper, after revision, would be the bridge formalism and its consistency checks rather than the claimed contradictions with the KPW theorem.

major comments (4)

[Sec. III.B, Eqs. (80)-(82), Fig. 3] The argument that gluon-induced color changes invalidate the Koerner-Pati-Woo theorem is based on a premise that the theorem does not require. The theorem follows from the symmetry of the local four-quark operator under simultaneous interchange (alpha,i) <-> (gamma,k) after Fierz, together with the fact that any two quarks in a color-singlet baryon must be color-antisymmetric; it does not assume that quark colors are frozen between production and hadronization. Gluon exchanges conserve flavor and belong to the long-distance dressing already contained in the topological amplitudes. Moreover, in the rescattering diagrams of Fig. 3 one of the final baryon quarks comes from the intermediate meson rather than from the weak vertex, so the KPW theorem does not apply to those diagrams. The color-counting statements delta=epsilon and gamma=delta=epsilon are properties of a particular FSI model, not of the weak operator symmetry, so the conclusion that the theorem is 'illogical' is unsupported.
[Sec. II.A and Sec. III.B] The derivation explicitly assumes that only the short-distance emission diagram T contributes to the weak vertex and that all other topological amplitudes are generated purely by rescattering from A2. Consequently, the Ai computed in this paper are only the long-distance rescattering parts of the physical amplitudes. Since the Koerner-Pati-Woo theorem is a selection rule on the full weak amplitudes, a violation of the relations A1=-A3, A5=-A7, etc. by these long-distance parts does not imply that the theorem fails for the actual decay amplitudes; the neglected short-distance contributions could restore the relations. The paper should either remove the claim that the theorem is 'not consistent with rescattering dynamics' or demonstrate the conclusion for the full amplitudes, rather than for the T-only rescattering model.
[Sec. III.C, Table I] The statement that the rescattering contributions to A11 are identical to those to A6 is not correct as read from Table I: A11 receives Delta_{beta+,beta-} and Theta_{beta+,beta-}, whereas A6 receives Delta_{beta-,beta+} and Theta_{beta-,beta+}. These are equal only in the unstated limit beta+ = beta-, and in general the D and F couplings differ. Furthermore, the conclusion that CP asymmetries can reach 10^-4 to 10^-3 is not derived: no numerical loop functions, strong phases, or Wilson coefficients are evaluated, so the tensor-structure comparison alone does not establish that the penguin-type rescattering is quantitatively 'comparable' to the tree-type amplitudes.
[Sec. II.A, Eqs. (16)-(63)] The list of coupling structures is asserted to cover all possible sub-structures 'without repetition,' but no proof of completeness is provided. The derivation of Table I and all subsequent isospin sum-rule checks depend on this completeness. I suggest either providing a systematic enumeration of all independent tensor contractions, for example via a contraction-counting or Young-tableau argument, or cross-checking the full Table I against a direct chiral-Lagrangian calculation for more than the single Xi_c -> Xi pi system.

minor comments (4)

[Sec. III.B, Eq. (91)] Please clarify the relation between K0 and K0_S in Eq. (85) and Eq. (91), since the reader must infer the factor of 1/2 between the K0 and K0_S branching fractions. In the same passage, the sentence 'This value is smaller than the branching fraction for the Lambda_c+ -> Sigma0 K+ decay' appears to be a typo; presumably the intended comparison is with the Lambda_c+ -> Sigma+ K0_S mode or with the BESIII value.
[Sec. III.B, Sec. A] There are several typos: 'cannot to used' should be 'cannot be used', and 'resacttering' in the Appendix heading should be 'rescattering'.
[Sec. III.C, Eq. (103)] Please check the denominator |Ad - As|^2 in the CP-asymmetry formula; if Ad and As are nearly equal, this form is not the standard expansion and may be misleading without a derivation or a stated approximation.
[Table I] Please define explicitly in the caption or text the subscript convention for Delta and Theta, indicating which subscript corresponds to which vertex coupling, since the notation Delta_{alpha+,gamma-} is used extensively before being explained.

Circularity Check

0 steps flagged · score 2.0 of 10

No demonstrated circular reduction; the central KPW-vs-rescattering claim is a model-dependent derivation, though the paper leans heavily on the authors' prior framework.

full rationale

We find no step where a prediction reduces to its input by construction. The bridge relation Eq. (11) and the statement that only the emission diagram T contributes at short distance are framework assumptions, but they are explicit ('If we neglect the short-distance contributions of other topological diagrams, as assumed in rescattering dynamics') and are cross-checked against the chiral Lagrangian and isospin sum rules, which are external constraints. The KPW-violation claim follows from computing different tensor contractions for A1 and A3 (Eqs. 18-29 and Table I); it is a consequence of the rescattering model, not a restatement of its definition. The reinterpretation of the KPW proof as requiring no gluon color change is a substantive physical argument, not a circular reduction. The paper's reliance on Refs. [52,63,64,76,80,81] is heavy, but those are parameter-free published frameworks with stated assumptions; no uniqueness theorem is imported to forbid alternatives, and the main result is validated against chiral dynamics and isospin constraints. Score 2 reflects the self-citation load rather than an identified circular step.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper fits no data and introduces no new particles. The central results rely on the flavor-SU(3) framework, the chiral Lagrangian couplings, and the modeling assumption that rescattering from a single short-distance emission topology generates the long-distance amplitudes. These assumptions, rather than fitted constants, carry the physics content.

assumptions (6)

domain assumption SU(3)_F symmetry limit for the flavor decomposition of decay amplitudes.
Table I and the (1,1)-rank amplitude construction assume exact flavor SU(3); SU(3) breaking terms A_15-A_18 are introduced separately in Eq. (13).
ad hoc to paper Only the short-distance emission diagram T contributes to the initial weak vertex; all other topological diagrams' short-distance contributions are neglected.
Stated in Sec. II.A: 'If we neglect the short-distance contributions of other topological diagrams, as assumed in rescattering dynamics'. This is the load-bearing modeling assumption for deriving rescattering amplitudes from A_2 only.
ad hoc to paper Only vector mesons and octet baryons are kept as intermediate propagators in the rescattering loop diagrams.
Stated in Sec. II.A: 'we consider only vector mesons and octet baryons as propagators'. Other resonances and decuplet baryons are omitted.
ad hoc to paper The set of coupling structures in Eqs. (16)-(63) is complete for the A_2 to A_i transitions.
The paper asserts completeness without a proof; the coverage is verified only through the explicit isospin sum rule checks.
standard math Wigner-Eckart theorem and standard SU(3) tensor contraction rules.
Used throughout to decompose amplitudes into reduced matrix elements and Clebsch-Gordan coefficients (Eq. (4)).
domain assumption The chiral Lagrangians in Eq. (6) correctly describe the strong-interaction vertices for VPP, BBP, and BBV couplings.
The rescattering vertices are taken from chiral perturbation theory; the paper maps them to tensor amplitudes in Eq. (14).

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Cite this review

Pith. "Pith review of From topological amplitudes to rescattering dynamics in charmed baryon decays." pith.science (2026). https://pith.science/paper/SWQNQKLU

@misc{pith2026250706914,
  author       = {Pith},
  title        = {Pith review of: From topological amplitudes to rescattering dynamics in charmed baryon decays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SWQNQKLU}},
  note         = {Machine review of arXiv:2507.06914}
}

abstract

Charmed baryon decays play an important role in studying the weak and strong interactions, which have been studied in the rescattering dynamics and topological diagram approach. In this work, we establish a theoretical framework to correlate the topological diagram at quark level and rescattering dynamics at hadron level. Note that the chiral Lagrangian involving octet baryons is constructed via (1,1)-rank octet tensors, while topological diagrams are constructed by 3-rank octet tensors. We propose that, the (1,1)-rank amplitudes, which are linear combinations of topological diagrams, will be a bridge between topological amplitudes and rescattering dynamics. The possible meson-meson or meson-baryon coupling configurations are constructed via tensor contractions. The rescattering amplitudes derived from topological amplitudes are consistent with those derived directly from the chiral Lagrangian. The $u$-, $t$-, and $s$-channel rescattering amplitudes contributing to each (1,1)-rank amplitudes in the $SU(3)_F$ limit are derived. Isospin sum rules for all isospin systems in $ B_{c\overline{3}}\to B_8P$ decays are checked in terms of rescattering amplitudes. The rescattering amplitudes contributing to penguin diagrams are found to be comparable to those contributing to tree diagrams, indicating potential observable $CP$ violation in charmed baryon decays. Furthermore, it is found that the K\"orner-Pati-Woo theorem is not consistent with the rescattering dynamics. The proof of the K\"orner-Pati-Woo theorem is questionable when the color changes of quarks arising from gluons are considered. We suggest precisely measuring the branching fraction of the $\Lambda^+_c\to \Sigma^+K^0_S$ mode on Belle (II) to test the K\"orner-Pati-Woo theorem.

Figures

Figures reproduced from arXiv: 2507.06914 by the authors.

**Figure 2.** FIG. 2: Two topological diagrams contributing to the Λ [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗

**Figure 3.** FIG. 3: The long-distance contributions in the topologies [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

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

Puzzles in charmed baryon semileptonic decays with $SU(3)_F$ flavor symmetry and lattice inputs
hep-ph 2026-03 accept novelty 6.0 of 10

Lattice-matched SU(3)_F with first-order breaking predicts B(Ξ_c^+→Σ^0 ℓν)/B(Ξ_c^+→Ξ^0 ℓν)=(2.6±0.3)% and B(Ξ_c^+→Λ ℓν)/B(Ξ_c^+→Ξ^0 ℓν)=(1.1±0.1)%.
$CP$ asymmetries in the $\Lambda_c^+\to pK^0_S$ and $\Xi^+_c\to \Sigma^+K^0_S$ decays
hep-ph 2025-09 conditional novelty 5.0 of 10

The Xi_c+ to Sigma+ K0_S decay can show an interference-induced CP asymmetry up to about 10^-3, several times larger than in D meson decays.

Reference graph

Works this paper leans on

90 extracted references · 50 canonical work pages · cited by 2 Pith papers

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work page Pith review arXiv 2015
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Ξ c →ΣKsystem (1) 20
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Ξ c →ΣKsystem (2) 21
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The long-distance contributions include U(A 3)[u, d, s, u] =−∆α+,γ− (Ξ0 c, π+,Ξ −, ρ+, π0,Ξ 0), T(A 3)[u, d, s, u] = ∆β−,β− (Ξ0 c, π+,Ξ −,Ξ −,Ξ 0, π0), U(A 5)[u, d, s, d] = ∆α+,γ− (Ξ0 c, π+,Ξ −, ρ+, π0,Ξ 0), S(A5)[u, d, s, d] = Θβ−,β− (Ξ0 c, π+,Ξ −,Ξ 0, π0,Ξ 0).(75) SummingA 3 andA 5 amplitudes, we have AL(Ξ0 c →Ξ 0π0) = 1√ 2 λ1{U(A 3)[u, d, s, u] +T(A3)[...
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INTRODUCTION Charmed baryon decays provide an important platform for studying non-perturbative baryonic transitions

Ξ c →Σπsystem 27 References 34 I. INTRODUCTION Charmed baryon decays provide an important platform for studying non-perturbative baryonic transitions. Among charmed baryon decays, the decays of the charmed baryon anti-triplet (B c3) into a baryon octet (B 8) and a pseu- doscalar meson (P) are the most widely investigated. Extensive data on theB c3 →B 8Pde...
[6]

The rescattering amplitudes contribute to the Λ+ c →Σ 0π+ decay include U(A 7)1[s, d, u, u] =−1 6 ∆α+,γ− (Λ+ c , π+,Λ 0, ρ0, π+,Σ 0)− 1 6 ∆α+,γ− (Λ+ c , π+,Λ 0, ω, π+,Σ 0), U(A 7)2[s, d, u, u] =−1 6 ∆α+,γ+ (Λ+ c , π+,Λ 0, ρ0, π+,Σ 0)− 1 6 ∆α+,γ+ (Λ+ c , π+,Λ 0, ω, π+,Σ 0), T(A 7)1[s, d, u, u] =−1 3 ∆β+,β+ (Λ+ c , π+,Λ 0,Σ −,Σ 0, π+), T(A 7)2[s, d, u, u] =...
[7]

(A2) and Eq

The rescattering amplitudes contributing to the Λ+ c →Σ +π0 decay include U(A 7)1[s, d, u, d] =−1 3 ∆α+,γ− (Λ+ c , π+,Λ 0, ρ+, π0,Σ +), U(A 7)2[s, d, u, d] =−1 3 ∆α+,γ+ (Λ+ c , π+,Λ 0, ρ+, π0,Σ +), T(A 7)1[s, d, u, d] =−1 6 ∆β+,β+ (Λ+ c , π+,Λ 0,Σ 0,Σ +, π0)− 1 18 ∆β+,β+ (Λ+ c , π+,Λ 0,Λ 0,Σ +, π0), T(A 7)2[s, d, u, d] =−1 6 ∆β+,β− (Λ+ c , π+,Λ 0,Σ 0,Σ +,...
[8]

The rescattering amplitudes contribute to the Ξ0 c →Σ 0K 0 decay include T(A 6)[u, d, u, s] = ∆β−,β+ (Ξ0 c, π+,Ξ −,Σ −,Σ 0, K 0 ), U(A 4)[u, d, u, s] = ∆α+,γ+ (Ξ0 c, π+,Ξ −, K∗+, K 0 ,Σ 0), T(A 4)[u, d, u, s] = ∆β+,β+ (Ξ0 c, π+,Ξ −,Σ −,Σ 0, K 0 ), S(A6)[u, d, u, s] = Θβ−,β+ (Ξ0 c, π+,Ξ −,Ξ 0, K 0 ,Σ 0).(A8) Summing all long-distance contributions, we have...

Show all 90 references

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The rescattering amplitudes contribute to the Ξ0 c →Σ 0K 0 decay include U(A 4)[u, s, u, d] = ∆α+,γ+ (Ξ0 c, K+,Σ −, ρ+, K0,Σ 0), T(A 4)[u, s, u, d] = ∆β+,β+ (Ξ0 c, K+,Σ −,Ξ −,Σ 0, K0), U(A 5)[u, s, d, d] = ∆α+,γ− (Ξ0 c, K+,Σ −, ρ+, K0,Σ 0), S(A5)[u, s, d, d] = Θβ−,β− (Ξ0 c, K+...
[10]

The rescattering amplitudes contribute to the Ξ+ c →Σ 0K + decay include U(A 2)1[d, s, d, u] =−1 4 ∆α+,γ+ (Ξ+ c , K+,Σ 0, ρ0, K+,Σ 0) + 1 4 ∆α+,γ+ (Ξ+ c , K+,Σ 0, ω, K+,Σ 0) − 1 12 ∆α+,γ+ (Ξ+ c , K+,Λ 0, ρ0, K+,Σ 0) + 1 12 ∆α+,γ+ (Ξ+ c , K+,Λ 0, ω, K+,Σ 0), U(A 2)2[d, s, d, u]...
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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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Measurement of the absolute branching fraction for $\Lambda^+_{c}\to \Lambda e^+\nu_e$

M. Ablikimet al.[BESIII], Phys. Rev. Lett.115, 221805 (2015) [arXiv:1510.02610 [hep-ex]]

work page Pith review arXiv 2015

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Ξ c →ΣKsystem (1) 20

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Ξ c →ΣKsystem (2) 21

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The long-distance contributions include U(A 3)[u, d, s, u] =−∆α+,γ− (Ξ0 c, π+,Ξ −, ρ+, π0,Ξ 0), T(A 3)[u, d, s, u] = ∆β−,β− (Ξ0 c, π+,Ξ −,Ξ −,Ξ 0, π0), U(A 5)[u, d, s, d] = ∆α+,γ− (Ξ0 c, π+,Ξ −, ρ+, π0,Ξ 0), S(A5)[u, d, s, d] = Θβ−,β− (Ξ0 c, π+,Ξ −,Ξ 0, π0,Ξ 0).(75) SummingA 3 andA 5 amplitudes, we have AL(Ξ0 c →Ξ 0π0) = 1√ 2 λ1{U(A 3)[u, d, s, u] +T(A3)[...

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INTRODUCTION Charmed baryon decays provide an important platform for studying non-perturbative baryonic transitions

Ξ c →Σπsystem 27 References 34 I. INTRODUCTION Charmed baryon decays provide an important platform for studying non-perturbative baryonic transitions. Among charmed baryon decays, the decays of the charmed baryon anti-triplet (B c3) into a baryon octet (B 8) and a pseu- doscalar meson (P) are the most widely investigated. Extensive data on theB c3 →B 8Pde...

[6] [6]

The rescattering amplitudes contribute to the Λ+ c →Σ 0π+ decay include U(A 7)1[s, d, u, u] =−1 6 ∆α+,γ− (Λ+ c , π+,Λ 0, ρ0, π+,Σ 0)− 1 6 ∆α+,γ− (Λ+ c , π+,Λ 0, ω, π+,Σ 0), U(A 7)2[s, d, u, u] =−1 6 ∆α+,γ+ (Λ+ c , π+,Λ 0, ρ0, π+,Σ 0)− 1 6 ∆α+,γ+ (Λ+ c , π+,Λ 0, ω, π+,Σ 0), T(A 7)1[s, d, u, u] =−1 3 ∆β+,β+ (Λ+ c , π+,Λ 0,Σ −,Σ 0, π+), T(A 7)2[s, d, u, u] =...

[7] [7]

(A2) and Eq

The rescattering amplitudes contributing to the Λ+ c →Σ +π0 decay include U(A 7)1[s, d, u, d] =−1 3 ∆α+,γ− (Λ+ c , π+,Λ 0, ρ+, π0,Σ +), U(A 7)2[s, d, u, d] =−1 3 ∆α+,γ+ (Λ+ c , π+,Λ 0, ρ+, π0,Σ +), T(A 7)1[s, d, u, d] =−1 6 ∆β+,β+ (Λ+ c , π+,Λ 0,Σ 0,Σ +, π0)− 1 18 ∆β+,β+ (Λ+ c , π+,Λ 0,Λ 0,Σ +, π0), T(A 7)2[s, d, u, d] =−1 6 ∆β+,β− (Λ+ c , π+,Λ 0,Σ 0,Σ +,...

[8] [8]

The rescattering amplitudes contribute to the Ξ0 c →Σ 0K 0 decay include T(A 6)[u, d, u, s] = ∆β−,β+ (Ξ0 c, π+,Ξ −,Σ −,Σ 0, K 0 ), U(A 4)[u, d, u, s] = ∆α+,γ+ (Ξ0 c, π+,Ξ −, K∗+, K 0 ,Σ 0), T(A 4)[u, d, u, s] = ∆β+,β+ (Ξ0 c, π+,Ξ −,Σ −,Σ 0, K 0 ), S(A6)[u, d, u, s] = Θβ−,β+ (Ξ0 c, π+,Ξ −,Ξ 0, K 0 ,Σ 0).(A8) Summing all long-distance contributions, we have...