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Light dark-matter window constrained by $K^{+} \to π^{+} + E$

Xiao-Gang He^1,2,*, Xiao-Dong Ma ^3,4,†, Jusak Tandean ^1,2,‡, and German Valencia ^5,§

¹State Key Laboratory of Dark Matter Physics, Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 201210, China
²Key Laboratory for Particle Astrophysics and Cosmology (MOE) and Shanghai Key Laboratory for Particle Physics and Cosmology, Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 201210, China
³State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China
⁴Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science, Guangzhou 510006, China
⁵School of Physics and Astronomy, Monash University, Wellington Road, Clayton, Victoria 3800, Australia

^*Contact author: hexg@sjtu.edu.cn
^†Contact author: maxid@scnu.edu.cn
^‡Contact author: jtandean@yahoo.com
^§Contact author: german.valencia@monash.edu

Phys. Rev. D 112, 055025 – Published 17 September, 2025

DOI: https://doi.org/10.1103/qppt-g39h

Abstract

We explore the constraints on new physics from the recent NA62 observation of the kaon decay $K^{+} \to π^{+} + E$ with missing energy $E$ in the context of a dark-matter (DM) scenario recently used to accommodate the Belle II finding of an enhanced rate of the $b$ -meson decay $B^{+} \to K^{+} + E$ compared to the standard-model expectation. Specifically, assuming that a light real scalar boson $ϕ$ plays the role of DM and working in an effective field-theory framework, we study model independently the impact of operators involving $ϕ$ and ordinary quarks on the aforementioned transitions over the kaon mode’s kinematical mass region of $m_{ϕ} < (m_{K} - m_{π}) / 2 = 177 MeV$ . Such a DM particle is subject to significant restrictions from the observed relic abundance and from DM direct-detection experiments incorporating the Migdal effect, as well as from indirect searches in cosmic microwave background data and collider experiments, except when its mass is between 110 and 146 MeV. We demonstrate that $K^{+} \to π^{+} ϕ ϕ$ can saturate the new-physics window in the NA62 result if $m_{ϕ}$ lies in the 110–130 MeV portion of the range left by the DM constraints, thus providing a complementary constraint on this scenario. Improved data from future Belle II and NA62 measurements and DM quests can test it more stringently. In particular, expanding the NA62 signal window into the region that is now removed due to three-body decay background modes could further explore the remaining mass window for this type of invisible particle, $130 < m_{ϕ} < 177 MeV$ .

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Phys. Rev. D 112, 055025– Published 17 September, 2025

Vol. 112, Iss. 5 — 1 September 2025

Received 30 June 2025
Accepted 1 September 2025

DOI: https://doi.org/10.1103/qppt-g39h

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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Light dark-matter window constrained by $K^{+} \to π^{+} + E$

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Light dark-matter window constrained by K+→π++E

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Physics Subject Headings (PhySH)

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References (62)

Light dark-matter window constrained by $K^{+} \to π^{+} + E$