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$\Lambda_b \to \Lambda^{(\ast)}\nu\bar{\nu}$ decays and the recent Belle-II $B^+\to K^+\nu\bar{\nu}$ data

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read If the Belle-II anomaly is genuine new physics, the decay $\Lambda_b\to\Lambda\nu\bar{\nu}$ is forced into a narrow branching-ratio band, and the hadronic forward-backward asymmetry of its proton can discriminate between competing…

desk verdict Timely and mostly solid Λ_b → Λ(∗) νν EFT study built on the Belle-II excess, but the 'LFU' scenario is actually single-flavor NP, making the main scenario comparison mislabeled. read the letter →

arxiv 2507.01863 v2 pith:LBATQY5L submitted 2025-07-02 hep-ph

Diganta Das , Dargi Shameer , Ria Sain This is my paper
classification hep-ph
keywords Belle-IIbtosneutrino-antineutrinoLambda_bdecaysrarenewphysicseffectivefieldtheoryforward-backwardasymmetryright-handedneutrinos
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

The Belle-II experiment reports a rate for $B^+\to K^+\nu\bar{\nu}$ that is about 2.7 standard deviations above the Standard Model prediction. This paper takes that excess at face value and asks what it implies for two related decays of the $\Lambda_b$ baryon, one into a $\Lambda$ (which decays to a proton and a pion) and one into a $\Lambda^*(1520)$ (which decays to a nucleon and a kaon), both with a neutrino-antineutrino pair in the final state. Working in a low-energy effective field theory with right-handed neutrinos, the authors show that the Belle-II constraint fixes the $\Lambda_b\to\Lambda\nu\bar{\nu}$ branching ratio to a narrow band, and that the angular asymmetry of the final proton can tell apart different new-physics explanations. These modes are expected to be reachable at future Tera-Z factories, so the predictions give a concrete baryonic cross-check of the Belle-II anomaly.

What carries the argument

The central object is the effective Hamiltonian $$\mathcal{H}_{\rm eff} = -\frac{4G_F}{\sqrt{2}}\frac{\alpha_e}{4\pi}\lambda_t\left(C_{SM}O_{SM}+\sum_{A,B=L,R}\sum_{i,j}$C^{{ij}}$_{AB}$O^{{ij}}$_{AB}\right),$$ with the SM operator $O_{SM}=(\bar{s}\gamma_\mu P_L b)(\bar{\nu}\gamma^\mu P_L \nu)$ and the lepton-flavor-specific operators $O^{ij}_{AB}=(\bar{s}\gamma_\mu P_A b)(\bar{\nu}_i\gamma^\mu P_B\nu_j)$. The Belle-II data enter through the ratio formulas $R_K^{\nu\nu}$ and $R_{K^*}^{\nu\nu}$, which restrict the coefficients $C^{ij}_{AB}$. Those coefficients feed into the double-differential branching ratios for the two baryonic modes, built from lattice-QCD form factors, and the $q^2$-dependent observables $A_{h,\mathrm{FB}}$ and $F_L$ are what separate the NP scenarios.

What would settle it

If the Belle-II excess fades toward the Standard Model prediction of $(4.29\pm0.23)\times10^{-6}$ as more data are collected, the constrained new-physics coefficients and all derived bounds lose their force; conversely, a future Tera-Z measurement of $\Lambda_b\to\Lambda\nu\bar{\nu}$ that lands outside the band from $6.8\times10^{-6}$ to $1.1\times10^{-5}$ predicted here would falsify the new-physics interpretation presented in the paper.

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Extended reading notes

Core claim

Under the assumption that the Belle-II measurement of $B^+\to K^+\nu\bar{\nu}$, with $R_K^{\nu\nu}=5.4\pm1.6$, reflects new physics in the $b\to s\nu\bar{\nu}$ transition, the paper derives the consequences for the baryonic decays $\Lambda_b\to\Lambda(\to p\pi)\nu\bar{\nu}$ and $\Lambda_b\to\Lambda^\ast(\to N\bar{K})\nu\bar{\nu}$. Using a low-energy effective theory with light right-handed neutrinos, it translates the Belle-II constraint into allowed ranges for the Wilson coefficients $C^{ij}_{AB}$ and thereby obtains bounds on the branching ratios: $\mathrm{Br}(\Lambda_b\to\Lambda\nu\bar{\nu})$ is forced into a band between roughly $6.8\times10^{-6}$ and $1.1\times10^{-5}$, while $\mathrm{Br}(\Lambda_b\to\Lambda^\ast\nu\bar{\nu})$ remains at most a few times $10^{-8}$. The paper's central diagnostic is the hadronic-side forward-backward asymmetry $A_{h,\mathrm{FB}}^{\Lambda}$, whose $q^2$-dependence distinguishes the lepton-flavor-universal, lepton-flavor-universality-violating, and lepton-flavor-violating NP scenarios, whereas $F_L^{\Lambda^\ast}$ stays near $2/3$ because the $g$-type form factors vanish in the heavy-quark limit.

Load-bearing premise

The whole chain of bounds rests on the assumption that the Belle-II excess in $B^+\to K^+\nu\bar{\nu}$ is caused by genuinely new physics, rather than a statistical fluctuation or misestimated background.

Editorial extensions

If this is right

  • Under the new-physics interpretation, the $\Lambda_b\to\Lambda\nu\bar{\nu}$ branching ratio is confined to a narrow band of roughly $7\times10^{-6}$ to $1.1\times10^{-5}$, a high enough rate that a future Tera-Z factory should be able to confront it.
  • The $\Lambda_b\to\Lambda^\ast\nu\bar{\nu}$ mode remains several orders of magnitude rarer, with branching ratios around $10^{-9}$ to $10^{-8}$, so its observation would demand very large integrated luminosity.
  • The hadronic forward-backward asymmetry $A_{h,\mathrm{FB}}$ in the $\Lambda$ mode is the discriminating observable: its $q^2$-shape separates the Standard Model from lepton-flavor-universal, lepton-flavor-universality-violating, and lepton-flavor-violating new physics.
  • The ratios $R_\Lambda$ and $R_{\Lambda^\ast}$ can reach about 1.4 and 1.7 respectively relative to the Standard Model, giving concrete enhancement targets for future measurements.
  • If the Belle-II anomaly disappears with more data, the same expressions reduce to the Standard Model predictions in Table I, so these modes double as a null test of the SM in the neutrino sector.

Reading between the lines

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

  • A natural extension would be a global fit allowing all $C^{ij}_{AB}$ to vary simultaneously; this could shrink the allowed band for $\mathrm{Br}(\Lambda_b\to\Lambda\nu\bar{\nu})$ and test whether the lepton-flavor-universal framework survives correlations.
  • If the new-physics picture is right, the near-universal $F_L^{\Lambda^\ast}\simeq 2/3$ means the $\Lambda^\ast$ mode is of limited use for identifying the operator structure, so the experimental effort should concentrate on $A_{h,\mathrm{FB}}$ and the two branching ratios.
  • The form-factor reliability restriction ($q^2\ge 16.3$ GeV$^2$ for the $\Lambda^\ast$ mode) suggests that improved lattice calculations at lower $q^2$, if they become available, would sharpen the predictions and potentially expose new discriminators in the $\Lambda^\ast$ channel.
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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

4 major / 5 minor

Summary. The paper assumes the Belle-II B+ -> K+ nu nubar excess (R_K = 5.4 +/- 1.6) is due to new physics in b -> s nu nubar and studies the baryonic decays Lambda_b -> Lambda(-> p pi) nu nubar and Lambda_b -> Lambda*(-> N Kbar) nu nubar. Working in a low-energy effective field theory with light right-handed neutrinos, it computes differential branching ratios, longitudinal polarization fractions, and hadronic forward-backward asymmetries, and uses the Belle-II R_K and R_K* constraints to set bounds on the Lambda_b observables in three NP scenarios: lepton-flavor-universal (LFU), lepton-flavor-universality-violating (LFUV), and lepton-flavor-violating (LFV).

Significance. The paper addresses a timely topic and provides concrete, phenomenologically useful predictions for baryonic b -> s nu nubar modes at future Tera-Z factories. Its strengths include the use of lattice form factors, the explicit EFT setup with right-handed neutrinos, and the observation that the hadronic forward-backward asymmetry can discriminate among NP scenarios. However, the LFU scenario is not implemented as described, the LFV branching-ratio formula contains an internal inconsistency, and the Lambda* branching ratios are only partial; these issues must be corrected before the numerical bounds can be trusted.

major comments (4)
  1. [Section IV, Tables II-III] The scenario labeled "Lepton Flavor Universal new physics" is not actually flavor universal. As stated after Table II, C_LL^ii and C_RL^ii are varied for one lepton flavor while the other two flavors remain SM-like. In a true LFU scenario the same coefficient applies to all three flavors, so the sums in Eqs. (13), (33), and (34) acquire an extra factor of three in both the linear and quadratic terms, which changes the Belle-II constraint on the coefficients and hence the bounds in Tables II and III. Please either relabel this scenario as single-flavor NP or redo the analysis with genuinely flavor-universal coefficients.
  2. [Section III, Eq. (27) vs Eq. (25) and Table I] The LFV total branching ratio for Lambda_b -> Lambda nu nubar starts with a SM term (6.09 +/- 0.78) x 10^-6, whereas the SM branching ratio in Eq. (25) and Table I is (7.84 +/- 0.94) x 10^-6. Since LFV NP contributes incoherently, the total branching ratio cannot fall below the SM value. The B_Lambda upper limits in Table VI (e.g., 6.83 x 10^-6) are therefore suspect and must be recomputed once this inconsistency is resolved.
  3. [Section III, Table I and Tables II-VI] The Lambda_b -> Lambda* nu nubar branching ratios are only partial, integrated over q^2 >= 16.3 GeV^2 as stated for Table I. This qualifier is absent from the abstract, Section V, and the captions of Tables II-VI, where the entries are presented simply as branching ratios. The claimed bounds on B(Lambda_b -> Lambda* nu nubar) should be explicitly labeled as partial branching ratios in every place they appear.
  4. [Section IV, Tables II-VI and Figures 2-4] The procedure used to produce the tables is not documented. It is unclear how the Wilson coefficients are scanned (ranges, distributions, real vs complex), how the Belle-II constraints R_K = 5.4 +/- 1.6 and R_K* < 2.7 or 1.9 are imposed and at what confidence level, and how the theory uncertainties are propagated into the quoted upper and lower limits. Please provide the details needed to reproduce Tables II-VI.
minor comments (5)
  1. [Table III caption] There is a typo: "wheile" should be "while"; similar typos such as "hadronis" appear in Appendix A.
  2. [Equation (4)] The R_K* upper limit is given as "<2.7 or 1.9"; please specify which value is actually used in the numerical scans.
  3. [Section III] The sentence "our numerical estimates of Lambda_b -> Lambda*(->p pi) nu nubar" should read Lambda*(-> N Kbar), since the Lambda* decays strongly to N Kbar rather than p pi.
  4. [Table II] The R_Lambda and R_Lambda* rows contain eight entries for four sign combinations; please clarify whether these are lower and upper bounds and how they correspond to the table columns.
  5. [Figures 2-4] The color coding and the benchmark choices are not described in the captions; please define these so the figures can be interpreted independently.

Circularity Check

0 steps flagged · score 0.0 of 10

Derivation is self-contained: Belle-II B->K nu nubar data constrain Wilson coefficients, and Lambda_b observables are independent predictions.

full rationale

The derivation chain is: (i) Belle-II measures Br(B+ -> K+ nu nubar), giving R_K^nu nu = 5.4 +/- 1.6 (Eq. 4); (ii) the paper writes an EFT Hamiltonian (Eq. 5) with NP Wilson coefficients C_AB^ij; (iii) it expresses the Lambda_b -> Lambda(-> p pi) nu nubar and Lambda_b -> Lambda* nu nubar observables in terms of C_-, C_+, and C' (Eqs. 9-13, 17-18); (iv) it uses the B-meson constraints R_K^nu nu and R_K*^nu nu (Eqs. 33-34) to bound those coefficients; and (v) it converts the bounds into predicted Lambda_b branching ratios and ratios using Eqs. (25)-(32). No Lambda_b observable is used to fit anything; the Wilson coefficients are constrained solely from the B-meson inputs. The predicted R_Lambda in Eq. (29) is a different combination of the same coefficients, but the coefficients themselves are fixed externally, so the prediction is not forced by construction. The paper explicitly states its premise: 'Under this assumption, we study the hadronic Lambda_b -> Lambda(...) nu nubar decays'; this is an assumption, not a circular step. The angular-distribution formulas taken from the authors' earlier works [21-23, 28] are parameter-free and do not incorporate the Belle-II result, so those self-citations are not load-bearing. One noted issue is that the 'LFU' scenario in Tables II-III actually varies Wilson coefficients for one lepton flavor while keeping the other two SM-like, which is a labeling/implementation inconsistency rather than circularity. Overall, the central claim derives from external B-meson data applied to independent Lambda_b observables; no reduction of a prediction to its input is present.

Assumptions & free parameters 2 free parameters · 4 assumptions · 1 invented entities

The calculation relies on external lattice form factors, an assumed NP interpretation of Belle-II data, and an EFT with light right-handed neutrinos. The only free parameters are the NP Wilson coefficients, which are scanned rather than fitted. No invented entities beyond the right-handed neutrinos.

free parameters (2)
  • NP Wilson coefficients C_LL^ij, C_RL^ij, C_LR^ij, C_RR^ij = scanned within Belle-II R_K and R_K* constraints; no best-fit quoted
    These are the free couplings of the dimension-six operators in Eq. (5). They are varied in Tables II-VI and in the random scans in Figs. 2-4 subject to R_K = 5.4 +/- 1.6 and R_K* limits.
  • Benchmark points in figures = not specified (chosen for visibility)
    Figures 2-4 use random scans with 'benchmark points chosen for better distinguishability', which are arbitrary and not reproducible.
assumptions (4)
  • domain assumption The Belle-II excess in B+ -> K+ nu nubar is due to new physics in b -> s nu nubar.
    The whole analysis is conditional on this assumption, stated in the abstract and Section I. If the excess is a fluctuation, the bounds on Lambda_b observables do not apply.
  • domain assumption Low-energy EFT with dimension-six operators and light right-handed neutrinos describes all NP contributions.
    Eq. (5) postulates this operator basis. No matching from a specific ultraviolet model is provided.
  • domain assumption Lattice QCD form factors from Refs. [29-31] are reliable, with Lambda* parametrizations valid only for q^2 >= 16.3 GeV^2.
    Used in Section III and Appendix A. The high-q^2 restriction is stated, but the extension to the full range is not available.
  • domain assumption The approximations for R_K and R_K* in Eqs. (33,34) from Refs. [32,33] are valid.
    These formulas are used to translate Belle-II data into constraints on Wilson coefficients.
invented entities (1)
  • Light right-handed neutrinos
    purpose: Allow new physics operators with right-handed chiralities (O_AB with B=R) that contribute to the invisible final state in b -> s nu nubar.
    The paper does not propose a mass, mixing, or any signature beyond the decay rates themselves. The right-handed neutrinos are not detectable in this process, so there is no falsifiable handle outside the paper.

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Cite this review

Pith. "Pith review of $\Lambda_b \to \Lambda^{(\ast)}\nu\bar{\nu}$ decays and the recent Belle-II $B^+\to K^+\nu\bar{\nu}$ data." pith.science (2026). https://pith.science/paper/LBATQY5L

@misc{pith2026250701863,
  author       = {Pith},
  title        = {Pith review of: $\Lambda_b \to \Lambda^(\ast)\nu\bar\nu$ decays and the recent Belle-II $B^+\to K^+\nu\bar\nu$ data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LBATQY5L}},
  note         = {Machine review of arXiv:2507.01863}
}
abstract

The Belle-II experiment has recently reported the first measurement of $B^+ \to K^+ \nu\bar{\nu}$ decay which exceeds the Standard Model prediction by approximately 2.7$\sigma$. The deviation may indicate the presence of new physics beyond the Standard Model in the $b\to s\nu\bar{\nu}$ sector. Under this assumption, we study the hadronic $\Lambda_b \to \Lambda(\to p\pi)\nu\bar{\nu}$ and $\Lambda_b \to \Lambda^\ast(\to N\!\bar{K})\nu\bar{\nu}$ decays within both the Standard Model and beyond. We work in a low energy effective field theory framework with additional light right-handed neutrinos. We calculate the differential branching ratios of these decay modes and explore the implications of the Belle-II results through various observables.

Figures

Figures reproduced from arXiv: 2507.01863 by the authors.

Figure 1
Figure 1. FIG. 1: Standard Model prediction for Λ [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The observables [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The observables [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The observables [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

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Forward citations

Cited by 4 Pith papers

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

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  3. Probing Signatures of Right-Handed Neutrinos via $b \to s \nu \bar\nu$ Decays

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    Model-independent constraints on dimension-six vector operators with right-handed neutrinos from Belle II B to K nu nubar data, predicting enhanced rates in related decays and sensitivity via K* polarization.

  4. $\Lambda_b\to\Lambda^{(*)}\nu{\bar\nu}$ and $b\to s$ $B$ decays

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