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arxiv: 2604.20340 · v1 · submitted 2026-04-22 · ✦ hep-ph · hep-ex

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Baryon-Meson Sum Rule for b to s νbarν

Teppei Kitahara , Manas Kumar Mohapatra , Kota Sasaki
Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:37 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords sum ruleb to s nu nuLambda b decaysB meson decaysnew physicsbranching fractionsleft-handed neutrinoseffective Hamiltonian
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0 comments X

The pith

A sum rule exactly relates the branching fractions of Λb to Λ νν̄ and B to K(*) νν̄ for left-handed neutrinos.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes an exact sum rule connecting the branching fractions of the baryonic decay Λb → Λ νν̄ and the mesonic decays B → K(*) νν̄. This holds despite the effective Hamiltonian allowing 18 independent Wilson coefficients for new physics. The numerical coefficients in this relation match those in a similar sum rule for b → c τν̄ decays involving Λb and B mesons. If the sum rule is correct, measuring the B decay rate determines the Λb rate in a model-independent way for scenarios with only left-handed neutrinos. This approach can help discriminate new physics models using combined baryon and meson observables in rare b to s neutrino transitions.

Core claim

We derive a robust sum rule among the branching fractions of Λb → Λ νν̄ and B → K(*) νν̄, assuming right-handed neutrinos are decoupled. Despite the presence of 18 independent Wilson coefficients in the effective Hamiltonian, this relation remains exact. The coefficients of this baryon-meson sum rule are numerically identical to those of the b→c semileptonic sum rule among the branching fractions of Λb → Λc τν̄ and B → D(*) τν̄. Once the decay rate of B → K* νν̄ is measured, the decay rate of Λb → Λ νν̄ can be determined in a model-independent manner for new-physics scenarios involving only left-handed neutrino interactions.

What carries the argument

The exact baryon-meson sum rule for branching fractions in b → s νν̄ transitions, which is preserved due to the left-handed neutrino structure in the effective theory.

Where Pith is reading between the lines

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

  • Deviations from the sum rule in future measurements could indicate the presence of right-handed neutrinos or other effects beyond the assumption.
  • The numerical match with the b to c sum rule hints at shared form factor relations or heavy quark symmetry between the two processes.
  • This sum rule approach could extend to additional observables like angular distributions to further constrain new physics.
  • Combining data from both baryonic and mesonic channels at experiments like LHCb or Belle II would provide independent tests of left-handed new physics models.

Load-bearing premise

Right-handed neutrinos are decoupled and do not contribute to the decays.

What would settle it

A precise measurement showing that the combination of branching fractions for Λb → Λ νν̄ and B → K(*) νν̄ does not satisfy the predicted sum rule relation would falsify the claim under the left-handed neutrino assumption.

Figures

Figures reproduced from arXiv: 2604.20340 by Kota Sasaki, Manas Kumar Mohapatra, Teppei Kitahara.

Figure 2
Figure 2. Figure 2: FIG. 2. Prediction of the sum rule using the Belle II re [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

We derive a robust sum rule among the branching fractions of $\Lambda_b \to \Lambda \nu \bar\nu$ and $B \to K^{(\ast)} \nu\bar\nu$, assuming that right-handed neutrinos are decoupled. Despite the presence of 18 independent Wilson coefficients in the effective Hamiltonian, this relation remains exact. Remarkably, it is found that the coefficients of this baryon-meson sum rule are numerically identical to those of the $b\to c$ semileptonic sum rule among the branching fractions of $\Lambda_b \to \Lambda_c \tau \bar\nu$ and $B \to D^{(\ast)}\tau\bar{\nu}$. Once the decay rate of $B \to K^{\ast} \nu \bar\nu$ is measured, the decay rate of $\Lambda_b \to \Lambda \nu\bar\nu$ can be determined in a model-independent manner for new-physics scenarios involving only left-handed neutrino interactions. This clearly demonstrates that observables in baryonic and mesonic $b \to s \nu \bar{\nu}$ transitions will serve as a powerful probe for discriminating among new-physics scenarios.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims to derive an exact sum rule relating the branching fractions of Λ_b → Λ νν-bar to those of B → K νν-bar and B → K* νν-bar. It asserts that a linear combination of these rates is independent of all 18 Wilson coefficients in the b → s νν effective Hamiltonian once right-handed neutrinos are decoupled, and that the numerical coefficients in the sum rule are identical to those appearing in the b → c semileptonic sum rule for Λ_b → Λ_c τν-bar and B → D(*) τν-bar. This would allow model-independent extraction of the baryonic rate from a measurement of the mesonic rate in left-handed neutrino scenarios.

Significance. If the claimed exact cancellation holds, the result would provide a useful model-independent consistency relation for new-physics searches in rare b decays, linking baryonic and mesonic channels and potentially discriminating among scenarios with only left-handed neutrinos. The reported numerical coincidence with the b → c sum rule is noteworthy and, if rigorously established, could point to a structural feature of the decay rates. The paper correctly flags the right-handed neutrino decoupling assumption as essential.

major comments (2)
  1. [§3] §3 (sum-rule derivation): The assertion that the linear combination eliminates dependence on all 18 Wilson coefficients for arbitrary values requires explicit demonstration that the q²-integrated hadronic matrix elements for each operator (vector, axial-vector, scalar, pseudoscalar, tensor) satisfy the same numerical ratios between the Λ_b → Λ and B → K(*) channels as in the b → c case. No such operator-by-operator cancellation or table of ratios is provided, and the independence of form factors for different Dirac structures makes this non-trivial.
  2. [Abstract and §4] Abstract and §4 (comparison to b → c): The claim that the coefficients are 'numerically identical' to the b → c semileptonic sum rule is stated without showing the explicit numerical values, the integration limits used, or an argument why the coincidence extends beyond the SM vector-axial operators to the full set of 18 coefficients.
minor comments (2)
  1. [§2] The effective Hamiltonian in §2 should explicitly list the 18 operators and their Wilson coefficients to make the counting and decoupling assumption transparent.
  2. Notation for branching fractions (e.g., Br(Λ_b → Λ νν-bar)) should be used consistently throughout to avoid ambiguity with differential rates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We appreciate the positive assessment of the potential utility of the sum rule for new-physics searches. We address the major comments point by point below and will revise the manuscript to incorporate additional explicit demonstrations and details as requested.

read point-by-point responses

  1. Referee: §3 (sum-rule derivation): The assertion that the linear combination eliminates dependence on all 18 Wilson coefficients for arbitrary values requires explicit demonstration that the q²-integrated hadronic matrix elements for each operator (vector, axial-vector, scalar, pseudoscalar, tensor) satisfy the same numerical ratios between the Λ_b → Λ and B → K(*) channels as in the b → c case. No such operator-by-operator cancellation or table of ratios is provided, and the independence of form factors for different Dirac structures makes this non-trivial.

    Authors: We agree that an explicit operator-by-operator verification strengthens the presentation. The derivation in §3 proceeds by writing each differential decay rate as a linear combination of the 18 Wilson coefficients multiplied by the corresponding q²-dependent hadronic functions for the baryonic and mesonic channels. The same numerical coefficients that cancel the b → c semileptonic rates are then applied; because the q²-integrated ratios of these hadronic functions between Λ_b → Λ and B → K(*) turn out to be identical to those in the b → c case for every Dirac structure, the linear combination cancels all contributions independently of the Wilson coefficients (provided right-handed neutrinos are decoupled). Although the form factors for different Lorentz structures are independent, the integrated ratios coincide due to the common kinematic prefactors and the analogous parameterization of the matrix elements. In the revised manuscript we will add a table in §3 (or a short appendix) listing the explicit integrated ratios for the vector, axial-vector, scalar, pseudoscalar, and tensor operators, thereby demonstrating the cancellation for arbitrary values. revision: yes

  2. Referee: Abstract and §4 (comparison to b → c): The claim that the coefficients are 'numerically identical' to the b → c semileptonic sum rule is stated without showing the explicit numerical values, the integration limits used, or an argument why the coincidence extends beyond the SM vector-axial operators to the full set of 18 coefficients.

    Authors: We accept that the manuscript would be clearer with these details supplied. The numerical coefficients are identical because the sum rule employs the identical linear combination of branching fractions that was previously shown to cancel the b → c rates; the b → s νν-bar channels possess the same relative normalizations of the integrated hadronic matrix elements for each operator. The integration is performed from the minimum neutrino-pair invariant-mass squared (essentially zero for massless neutrinos) up to the kinematic maximum set by the parent and daughter hadron masses. Because the cancellation is linear and holds separately for each of the five Dirac structures, it extends automatically to any linear combination of the 18 Wilson coefficients. In the revised version we will quote the explicit numerical coefficients in §4, state the integration limits used, and add a concise paragraph explaining why the identity holds for the complete operator basis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in effective Hamiltonian

full rationale

The paper derives the baryon-meson sum rule directly from the general effective Hamiltonian for b→s νν̄ (with right-handed neutrinos decoupled), showing exact cancellation in a linear combination of branching fractions for arbitrary Wilson coefficients. No step reduces by construction to a fitted input, self-defined quantity, or load-bearing self-citation; the numerical match to the b→c coefficients is presented as an output of the same operator structure rather than an imported premise. The analysis relies on the explicit operator basis and hadronic matrix elements as written, remaining independent of external benchmarks or prior results by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard effective-field-theory parameterization of b->s nu nubar transitions together with the explicit decoupling assumption; no additional free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Right-handed neutrinos are decoupled
    Explicitly required for the sum rule to remain exact independent of the Wilson coefficients.
  • standard math Effective Hamiltonian for b->s nu nubar contains 18 independent Wilson coefficients
    Standard parameterization of possible new-physics operators in the effective theory.

pith-pipeline@v0.9.0 · 5508 in / 1484 out tokens · 33452 ms · 2026-05-10T00:37:20.393268+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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