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$B^{+} \to K^{+} ν \bar{ν}$ excess and DM semi-annihilation

Jongkuk Kim ^1,2,3,* and Pyungwon Ko ^2,4,†

¹Department of Physics, Chung-Ang University, Seoul 06974, Republic of Korea
²Excellence Cluster ORIGINS, Boltzmannstraße 2, D-85748 Garching, Germany
³Division of Liberal Studies, Kangwon National University, Samcheok 25913, Republic of Korea
⁴School of Physics, Korea Institute for Advanced Study, 85 Hoegi-ro, Seoul 02455, Republic of Korea

^*Contact author: jongkukkim@cau.ac.kr
^†Contact author: pko@kias.re.kr

Phys. Rev. D 113, 075023 – Published 17 April, 2026

DOI: https://doi.org/10.1103/5ygk-bswh

Abstract

In 2023, the Belle II Collaboration announced the observation of the $B^{+} \to K^{+} ν \bar{ν}$ decay channel for the first time. This decay channel provides a clean signal with high precision in theoretical calculations. However, we encounter a $2.8 σ$ deviation from the Standard Model prediction. To resolve this excess, we study a scalar dark matter model with local discrete $Z_{3}$ symmetry. Assuming dark $U (1)_{X} \equiv U (1)_{L_{μ} - L_{τ}}$ symmetry, this $U (1)_{L_{μ} - L_{τ}}$ symmetry is spontaneously broken into local discrete $Z_{3}$ by nonzero vacuum expectation value of dark Higgs boson. Considering a dark Higgs mass is 2 GeV, we can explain the recent $Br (B^{+} \to K^{+} ν \bar{ν})$ excess reported from the Belle II Collaboration and relic abundance at the same time.

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Article Text

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Phys. Rev. D 113, 075023– Published 17 April, 2026

Vol. 113, Iss. 7 — 1 April 2026

Received 3 December 2025
Accepted 5 March 2026

DOI: https://doi.org/10.1103/5ygk-bswh

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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$B^{+} \to K^{+} ν \bar{ν}$ excess and DM semi-annihilation

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$B^{+} \to K^{+} ν \bar{ν}$ excess and DM semi-annihilation