pith. sign in

arxiv: 2606.00830 · v1 · pith:SVVHOOEQnew · submitted 2026-05-30 · ✦ hep-ph

n to Kell and the baryon asymmetry of the universe

Carolina Arbel\'aez , Juan Carlos Helo , Martin Hirsch , Toshihiko Ota This is my paper

Pith reviewed 2026-06-28 18:07 UTC · model grok-4.3

classification ✦ hep-ph
keywords nucleon decayB-L violationbaryon asymmetrySMEFTdimension seven operatorskaon lepton final state
0
0 comments X

The pith

Observing n to K lepton decays without other modes would indicate B-L violation.

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

The paper shows that in the Standard Model Effective Field Theory an observation of a nucleon decaying to a kaon plus charged lepton can signal violation of B minus L conservation even if the lepton charge sign is unknown. This holds because the mode n to K plus lepton minus appears already at dimension seven while any (B-L) conserving counterpart n to K minus lepton plus needs dimension ten operators. Those higher-dimension operators would necessarily produce lower-dimension (B plus L) violating decays such as proton to pion zero lepton plus. Therefore an isolated n to K lepton signal would point to B-L violation, which is strongly constrained by the observed baryon asymmetry of the universe.

Core claim

In SMEFT the decay n → K⁺ℓ⁻ arises at dimension seven while the (B-L)-conserving decay n → K⁻ℓ⁺ requires dimension-ten operators that would be accompanied by lower-dimensional (B+L)-violating decay modes. An observation of n → Kℓ in the absence of other modes such as p → π⁰ℓ⁺ would therefore strongly suggest that (B-L) is violated.

What carries the argument

Differing minimal operator dimensions in SMEFT for (B-L)-violating versus (B-L)-conserving n → Kℓ decays.

If this is right

  • An isolated n → Kℓ signal would indicate that B-L is violated.
  • Such a signal would carry direct implications for the origin of the baryon asymmetry.
  • It would constrain the scale and structure of any (B-L)-violating interactions.

Where Pith is reading between the lines

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

  • The argument supplies an experimental handle on B-L violation that does not require charge identification of the lepton.
  • It links nucleon decay searches to cosmological constraints on the baryon asymmetry through a single observable channel.
  • Similar operator-dimension comparisons could be applied to other rare decay final states in effective field theory.

Load-bearing premise

That no dimension-seven or dimension-eight operators allow a (B-L)-conserving n → K⁻ℓ⁺ decay without accompanying lower-dimensional (B+L)-violating modes.

What would settle it

Observation of n → Kℓ accompanied by modes such as p → π⁰ℓ⁺ would remove the indication that B-L is violated.

Figures

Figures reproduced from arXiv: 2606.00830 by Carolina Arbel\'aez, Juan Carlos Helo, Martin Hirsch, Toshihiko Ota.

Figure 1
Figure 1. Figure 1: d = 10 operator ∂uuddsℓ¯ generated from the d = 8 operator O (1) LQudW and a SM gauge interaction. H sR uR L uR dR dR sR uR eR uR dR dR ∂ [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Two simple examples of d = 10 operators that can generate the B−L-conserving decay process n → K−ℓ +. The operator on the right contains a derivative. for the current paper, however, is that none of these operators generates n → K−ℓ + either. We stated above that d = 8 SMEFT operators do not directly generate new two-body final states. There is, however, a subtlety in this statement that should be made exp… view at source ↗
Figure 3
Figure 3. Figure 3: Examples of “black-box” diagrams for the d = 10 operators, shown in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example diagrams for the two possible tree-level decompositions of the effective operator OLdddH. Lagrangian as cLdddH Λ3 = ˜cd=7 µ˜ Λ4 , (3.3) where in the effective field theory limit we assume, as usual, mF = mSi = Λ and c˜d=7 = ydsS · yF dS† · yLF H, µ˜ = mF , for Class-I, c˜d=7 = ydsS1 · yLdS2 , µ˜ = µ, for Class-II. (3.4) Note that the parameter µ in class-II could, in principle, be much smaller than… view at source ↗
Figure 5
Figure 5. Figure 5: Contours of Γ = H in the plane Λ-T for two different choices of ˜µ and ˜cd=7. Within the shaded regions Γ > H and thus, the (B −L)-violating process ds ↔ ¯dLH† is in thermal equilibrium. The two vertical lines correspond to the life-times of τ (n → K+e −) of 3.2 × 1031 and 1035 yr. estimate whether the process is in thermal equilibrium. Here, g∗ denotes the number of effective degrees of freedom, with g∗ ≃… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison between the contours of Γ = H and the lifetime of n → K+e −, with the assumption of ˜µ = Λ. choosing for example ˜µ = 10−2Λ and ˜cd=7 = 1 leads to the same plot as in [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
read the original abstract

The observed baryon asymmetry (BAU) of the universe puts strong constraints on any $(B-L)$-violating interaction. An observation of a $(B-L)$-violating nucleon decay channel would therefore have profound implications for our understanding of the BAU. Here we point out that the observation of the final state with a kaon and a charged lepton in a future nucleon decay experiment would hint at $(B-L)$ violation even if the charge of the lepton is not determined experimentally. In SMEFT, this follows from the fact that $n \to K^+\ell^-$ arises already at dimension seven, while the $(B-L)$-conserving decay $n \to K^-\ell^+$ requires dimension-ten operators that, in addition, would be accompanied by lower-dimensional $(B+L)$-violating decay modes. An observation of $n \to K\ell$ in the absence of other modes such as $p \to \pi^0\ell^+$, would then strongly suggest that $(B-L)$ is violated.

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

1 major / 0 minor

Summary. The paper claims that in SMEFT, the decay mode n → K⁺ℓ⁻ is generated by dimension-7 operators, whereas the (B-L)-conserving mode n → K⁻ℓ⁺ requires dimension-10 operators that necessarily induce lower-dimensional (B+L)-violating channels such as p → π⁰ℓ⁺. Consequently, an experimental observation of n → Kℓ (without charge identification) in the absence of those other modes would indicate (B-L) violation, with implications for the baryon asymmetry of the universe.

Significance. If the dimension assignments and completeness of the operator list hold, the result offers a practical experimental handle on (B-L) violation relevant to baryogenesis without requiring lepton charge measurement. The argument rests on standard SMEFT power counting and operator classification, which is a strength when the underlying basis is complete.

major comments (1)
  1. [Abstract] Abstract (and the SMEFT analysis paragraph): the central claim that (B-L)-conserving n → K⁻ℓ⁺ first appears at dimension 10 (accompanied by lower-dimensional (B+L)-violating modes) and that no dimension-7 or -8 operators permit this channel without those modes is asserted without an explicit operator basis, field-content counting, or symmetry argument demonstrating the absence of ΔB=1, ΔL=−1 operators with the required flavor structure below dimension 10. This assumption is load-bearing for the implication that n → Kℓ without accompanying modes signals (B-L) violation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for greater explicitness in the SMEFT operator analysis. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the SMEFT analysis paragraph): the central claim that (B-L)-conserving n → K⁻ℓ⁺ first appears at dimension 10 (accompanied by lower-dimensional (B+L)-violating modes) and that no dimension-7 or -8 operators permit this channel without those modes is asserted without an explicit operator basis, field-content counting, or symmetry argument demonstrating the absence of ΔB=1, ΔL=−1 operators with the required flavor structure below dimension 10. This assumption is load-bearing for the implication that n → Kℓ without accompanying modes signals (B-L) violation.

    Authors: We agree that the manuscript would be strengthened by an explicit demonstration. In the revised version we will add a dedicated appendix that (i) lists all possible ΔB=1 SMEFT operators up to dimension 9 with the relevant field content and hypercharge assignments, (ii) shows why none of these operators can produce the (B-L)-conserving n → K⁻ℓ⁺ final state without simultaneously generating lower-dimensional (B+L)-violating channels such as p → π⁰ℓ⁺, and (iii) identifies the lowest-dimensional operators that do allow n → K⁻ℓ⁺ (which appear at dimension 10 and necessarily induce the accompanying modes). This will rest on standard SMEFT power counting and the requirement that the operators respect the SM gauge symmetries and the flavor structure needed for the kaon-lepton final state. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim rests on external SMEFT operator counting

full rationale

The paper states that its implication for (B-L) violation follows from the established fact in SMEFT that n → K⁺ℓ⁻ appears at dimension seven while n → K⁻ℓ⁺ requires dimension-ten operators accompanied by lower-dimensional (B+L)-violating modes. No equations, fitted parameters, self-definitions, or load-bearing self-citations are present in the provided text; the dimension counting is an external mathematical result about effective operators that can be verified independently of this paper. The derivation chain does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The argument rests on the standard SMEFT framework and the assumption that the listed dimension assignments and accompanying modes are exhaustive at each order.

axioms (2)
  • domain assumption SMEFT provides the complete low-energy description of nucleon decays up to the relevant dimensions.
    Invoked throughout the abstract for classifying (B-L) violating and conserving operators.
  • ad hoc to paper No additional operators at dimension seven or eight permit (B-L)-conserving n → K⁻ℓ⁺ without also generating lower-dimensional (B+L)-violating modes.
    This completeness assumption is required for the claim that dim-10 is the lowest order for the conserving channel.

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discussion (0)

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