Feasibility Study of Lepton Number Violation in Rare $B$ and $K$ Meson Decays

TL;DR

The paper investigates lepton-number-violating interactions at dimension seven within the Standard Model EFT that contribute to $B\to K\,\nu\nu$ and $K\to \pi\,\nu\nu$ decays. It develops a detailed framework connecting dim-7 LNV operators to semileptonic meson decays, baryon-number washout in the early Universe, and neutrinoless double beta decay, including two-loop neutrino masses and Weinberg-operator effects. The study finds that observable meson-decay excesses are highly sensitive to the lepton-flavor structure and to the suppression of first-generation couplings, with viable regions typically requiring a low cutoff $\Lambda$ or partial decoupling to avoid washout and $0\nu\beta\beta$ bounds. It highlights that the Weinberg operator can coexist with the dim-7 LNV terms without spoiling baryogenesis, while UV completions (e.g., leptoquarks) may be necessary to realize these operators. The work thus maps out the conditions under which future measurements at Belle II and KOTO II could reveal LNV effects in rare meson decays while remaining consistent with cosmological and low-energy constraints.

Abstract

We study lepton-number-violating interactions at dimension seven in the Standard Model effective field theory that contribute to the meson decays $B \to K νν$ and $K \to πνν$. Such interactions could washout the baryon asymmetry of the Universe and also contribute to the neutrinoless double beta decay, even though the interactions involve a change in down-type quark flavors. We clarify conditions under which excesses in meson decay rates over the Standard Model predictions can be successfully observed. We also show that, although these interactions contribute to neutrino masses at the two-loop level, the Weinberg operator can be introduced consistently without spoiling the scenario.

Figures (13)

• Figure 1: Left: The temperature dependence of $\eta_B$. The blue, green, red, and black curves correspond to $c^{pr,rp}_{\alpha \beta} = 10^{-8}$, $10^{-7}$, $10^{-6,5}$, and $10^{-6}$, respectively. Right: The LNV coupling dependence of $\eta_B$. The lepton-flavor structures are diagonal (blue), mixing (orange), and first-generation decoupled (green) cases, respectively.
• Figure 3: Diagram at the tree level.
• Figure 4: Diagrams at the one-loop level.
• Figure 6: Left (right): The results for varying $C^{sb}_{\alpha \beta}$ and $C^{bs}_{\alpha \beta}$ in Scenario 1 (Scenario 2). The blue solid (dash-dotted) lines show the current bound (future projection) of the $B^+ \to K^+ \nu \nu$ decay. The black lines are the constraints from the $0 \nu \beta \beta$ decay. The primordial baryon asymmetry is washed out by the LNV operators, and the corresponding regions for $\eta_B = 6.14 \times 10^{-10}$ are denoted by the green lines. In the right plot, the red line represents the case when the neutrino masses are explained only by the dim. 7 LNV operators.
• Figure 7: Left: Same as figure \ref{['fig:scenario1and2']} in Scenario 3 with $r = 10^{-1}$ (solid), $r=10^{-3}$ (dashed), and $r=10^{-5}$ (dotted). Right: the contour plot of $\eta_B$ in the $r$-$\Lambda$ plane. The orange line shows $\eta_B = 6.14 \times 10^{-10}$.