Prospects for K_L → π ^0ν ν ̅, K_S→ μ ^+μ ^-, K_L→ π ^0 ℓ ^+ℓ ^- and ε '/ε after the new K^+ → π ^+ν ν ̅…

Abstract

The recently announced NA62 measurement of the K⁺ → π ⁺ν ν ̅ K + → π + ν ν ¯ branching ratio, based on 2016–2024 data, is fully consistent with its very accurate Standard Model (SM) prediction. While it is not excluded that the final result based on 2016–2026 data will deviate from the SM prediction, the question arises whether a similar fate awaits the K_L → π ⁰ν ν ̅ K L → π 0 ν ν ¯ decay. This decay is currently being searched for by the KOTO experiment, with the present upper bound roughly two orders of magnitude above its very precise SM prediction. The proposed KOTO II experiment aims to provide the first discovery of the K_L → π ⁰ν ν ̅ K L → π 0 ν ν ¯ decay and measure its branching ratio. Building on the findings of several previous papers we demonstrate that in the presence of suitably chosen large new complex phases and of a small amount of new right-handed s̅ d s ¯ d couplings, in addition to the left-handed ones, the K_L → π ⁰ν ν ̅ K L → π 0 ν ν ¯ branching ratio can still be enhanced by one order of magnitude with respect to the SM prediction while keeping both K⁺ → π ⁺ν ν ̅ K + → π + ν ν ¯ and ε _K ε K SM-like. Simultaneously the decays K_S→ μ ⁺μ ^- K S → μ + μ - , studied by LHCb, and K_L→ π ⁰ℓ ⁺ℓ ^- K L → π 0 ℓ + ℓ - , searched for by KOTO II, can be strongly enhanced and the anomaly in the ratio ε '/ε ε ′ / ε , as claimed by Dual QCD, removed. We illustrate this with an example of a specific Z^′ Z ′ scenario.

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Prospects for K_L→π⁰νν̅, K_S→μ⁺μ^-, K_L→π⁰ ℓ⁺ℓ^- and ε^′/ε after the new K⁺→π⁺νν̅ result from NA62PreprintarXiv · 10.48550/arxiv.2607.19055

Prospects for K_L→π⁰νν̅, K_S→μ⁺μ^-, K_L→π⁰ ℓ⁺ℓ^- and ε^′/ε after the new K⁺→π⁺νν̅ result from NA62
Monika Blanke, Andrzej J. Buras, Cristina Lazzeroni +1
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BibTeX

@article{blanke2026prospects,
  title = {{Prospects for $$K_L \rightarrow \pi ^0\nu \bar\nu $$, $$K_S\rightarrow \mu ^+\mu ^-$$, $$K_L\rightarrow \pi ^0 \ell ^+\ell ^-$$ and $$\varepsilon '/\varepsilon $$ after the new $$K^+ \rightarrow \pi ^+\nu \bar\nu $$ result from NA62}},
  author = {Monika Blanke and Andrzej J. Buras and Cristina Lazzeroni and Joel C. Swallow},
  journal = {The European Physical Journal C},
  year = {2026},
  month = oct,
  doi = {10.1140/epjc/s10052-026-16418-0},
  url = {https://link.springer.com/10.1140/epjc/s10052-026-16418-0},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Prospects for K_L → π ^0ν ν ̅, K_S→ μ ^+μ ^-, K_L→ π ^0 ℓ ^+ℓ ^- and ε '/ε after the new K^+ → π ^+ν ν ̅ result from NA62
AU  - Monika Blanke
AU  - Andrzej J. Buras
AU  - Cristina Lazzeroni
AU  - Joel C. Swallow
PY  - 2026
DA  - 2026/10/13
JO  - The European Physical Journal C
DO  - 10.1140/epjc/s10052-026-16418-0
UR  - https://link.springer.com/10.1140/epjc/s10052-026-16418-0
AB  - The recently announced NA62 measurement of the K^+ → π ^+ν ν ̅ K + → π + ν ν ¯ branching ratio, based on 2016–2024 data, is fully consistent with its very accurate Standard Model (SM) prediction. While it is not excluded that the final result based on 2016–2026 data will deviate from the SM prediction, the question arises whether a similar fate awaits the K_L → π ^0ν ν ̅ K L → π 0 ν ν ¯ decay. This decay is currently being searched for by the KOTO experiment, with the present upper bound roughly two orders of magnitude above its very precise SM prediction. The proposed KOTO II experiment aims to provide the first discovery of the K_L → π ^0ν ν ̅ K L → π 0 ν ν ¯ decay and measure its branching ratio. Building on the findings of several previous papers we demonstrate that in the presence of suitably chosen large new complex phases and of a small amount of new right-handed s̅ d s ¯ d couplings, in addition to the left-handed ones, the K_L → π ^0ν ν ̅ K L → π 0 ν ν ¯ branching ratio can still be enhanced by one order of magnitude with respect to the SM prediction while keeping both K^+ → π ^+ν ν ̅ K + → π + ν ν ¯ and ε _K ε K SM-like. Simultaneously the decays K_S→ μ ^+μ ^- K S → μ + μ - , studied by LHCb, and K_L→ π ^0ℓ ^+ℓ ^- K L → π 0 ℓ + ℓ - , searched for by KOTO II, can be strongly enhanced and the anomaly in the ratio ε '/ε ε ′ / ε , as claimed by Dual QCD, removed. We illustrate this with an example of a specific Z^′ Z ′ scenario.
SN  - 1434-6044
SN  - 1434-6052
ER  -

Prospects for K_L → π ⁰ν ν ̅, K_S→ μ ⁺μ ^-, K_L→ π ⁰ ℓ ⁺ℓ ^- and ε '/ε after the new K⁺ → π ⁺ν ν ̅ result from NA62

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