Kaon Portal to Freeze-in Dark Matter

arXiv:2605.05947 · hep-ph, astro-ph.CO, hep-ex · Submitted 2026-05-07 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "Kaon Portal to Freeze-in Dark Matter".

Jocelyn: This paper investigates a specific mechanism for light dark matter production through freeze-in cosmology, linking its relic abundance to rare kaon decay searches.

Vera: First, who's behind it and why it matters.

Title and authors: Vera: So we’re looking at the paper called "Kaon Portal to Freeze-in Dark Matter," and it seems like the title itself hints at how they’re connecting something very fundamental, dark matter production, with these specific particle physics searches. It sounds like a direct link between cosmology and lab experiments.

Jocelyn: I agree, Vera; the authors are exploring a mechanism where light dark matter is generated through interactions involving kaons and pions when the universe was still in that early phase before hadronization fully took over. It’s about using these rare kaon decays to set constraints on this new type of dark matter.

Subrahmanyan: From a theoretical standpoint, the authors are proposing a specific interaction, that quark flavor-changing operator denoted as /Lint = CV /Λ2 (¯sγµd)(¯χγµχ) + h.c., which governs how this dark matter candidate, chi, couples to the Standard Model particles. That operator is what ties everything together in this proposal.

Vera: It’s interesting that they focus on a Dirac fermion for chi and show how this single interaction controls both the relic density of dark matter and the rates of rare kaon decays at experiments like NA62 and KOTO. That direct control over both is what makes it so compelling.

Jocelyn: Exactly, Vera; we’re talking about a scenario where if we find a certain decay rate for a kaon, it gives us information about the dark matter relic density, which is usually something that requires very small couplings in standard freeze-in models.

Subrahmanyan: That connection is the core idea here; they are showing that when the reheating temperature falls below about one hundred fifty to one hundred sixty MeV, which is below the QCD crossover temperature T QCD, dark matter production happens through these hadronic processes involving kaons and pions. This sets a specific cosmological window for this mechanism to work.

Vera: So, it’s not just a theoretical idea; they are mapping it onto real experimental searches for rare decays, which gives us something concrete to look for in the next few years.

Jocelyn: Right, and the paper suggests that this specific scenario might actually make dark matter production testable because these kaon processes dominate the abundance generation at low reheating temperatures.

The paper's summary: Vera: Now that we’ve talked about the setup, let’s look at what they actually found in this paper, "Kaon Portal to Freeze-in Dark Matter." They investigated how a specific interaction leads to the production of light dark matter when the universe is cold enough for kaon decays to be relevant.

Jocelyn: Essentially, they show that if the reheating temperature is below that QCD crossover temperature, DM isn't created through standard thermal processes; instead, it’s generated by kaon decays like K to pi chi and scatterings like K pi to chi.

Subrahmanyan: They also highlight that the same interaction they are using to generate the dark matter abundance is also responsible for inducing rare kaon decays, specifically showing rates for K+ to pi + chi and KL to pi zero chi.

Vera: That’s a key point, Subrahmanyan; the paper emphasizes that this single interaction dictates both the relic density and these rare decay branching ratios. They solve the Boltzmann equation for the DM yield using these kaon contributions to find parameter regions where the resulting relic density matches what we observe, around h squared = zero point one two.

Jocelyn: And they specifically point out that this mechanism alleviates what they call the freeze-in bottleneck, which usually requires a very feeble coupling strength to achieve the correct abundance. They find that at low reheating temperatures, you need larger coupling strengths because the kaon abundance is more suppressed by the Boltzmann effect.

Subrahmanyan: That suppression is important; it means for these lower temperatures, when you try to match the observed relic density, the required interaction strength becomes larger than what might be expected in simpler freeze-in models. They have to compensate for that suppression.

Vera: So, the paper demonstrates a direct relationship: low reheating temperature dictates whether kaon processes are relevant and how strong the coupling needs to be to get the right amount of dark matter.

The paper's improvements: Jocelyn: Looking at what they suggest as an improvement for this work, it seems like they are showing that the freeze-in bottleneck isn't insurmountable in this kaon-driven scenario because these kaon processes dominate the abundance generation when the reheating temperature is low.

Vera: I agree; they demonstrate that by focusing on these hadronic processes at low temperatures, you can avoid that hurdle of needing an extremely feeble coupling to get the right relic density. The paper shows how this specific interaction allows for a testable scenario because it links cosmology directly to experimental searches like NA62 and KOTO.

Subrahmanyan: From a theoretical perspective, the authors are using this framework to show that they can alleviate the freeze-in bottleneck by showing that kaon processes generate the dark matter abundance in a way that is more sensitive to the parameters they are studying. They’re moving away from scenarios where you just assume a very small coupling blindly.

Jocelyn: And what I find interesting is how they use the numerical analysis to map out regions in the plane of dark matter mass and coupling strength, showing exactly which parts of that space are accessible by current or future experiments. They show how lower reheating temperatures push the target region toward areas that might be probed by NA62 and future KOTO II sensitivities.

Vera: That mapping is really useful because it gives us a clear picture of where the experimental searches should focus their efforts to find this signal, rather than just looking everywhere for a generic freeze-in DM candidate.

Conclusion: Vera: So, to wrap up the discussion on "Kaon Portal to Freeze-in Dark Matter," the main implication is that this paper provides a concrete example where we can test light, feebly interacting dark matter through flavor physics experiments. It suggests that rare kaon decays are powerful probes for light invisible states.

Jocelyn: I think the most significant point is the direct link they establish between cosmology and particle physics by showing how low reheating temperatures constrain both the DM relic density and these observable decay rates simultaneously. It’s a very tight connection for a new type of dark matter model.

Subrahmanyan: As for me, I believe this work opens up a pathway where cosmological parameters, like the reheating temperature, can be constrained by laboratory measurements that we currently only use to study particle interactions in isolation.

Vera: That’s what I mean; it shows how these searches can place limits on cosmological models involving low reheating temperatures. We’re getting more constraints from the sky and more constraints from these deep underground experiments combined.

Jocelyn: It’s exciting to see how this specific interaction, derived from the quark flavor-changing operator, is being used as a benchmark for testing this whole class of dark matter scenarios. I think we should keep an eye on what comes next in these searches.

Subrahmanyan: I agree; the study of the Kaon Portal to Freeze-in Dark Matter provides a tangible framework for how cosmological history can be probed by rare kaon decays, and that’s a very promising direction for this line of research.

Vera: Well, it was really interesting diving into this paper today. Thanks everyone for joining us on this discussion about the Kaon Portal to Freeze-in Dark Matter. We'll be back soon with more data from the sky and some new papers on arXiv coming in soon.

Motoi Endo, Takumu Yamanaka

KEK Theory Center · Graduate Institute for Advanced Studies · Department of Physics, The University of Osaka

hep-ph, astro-ph.CO, hep-ex

Submitted: 2026-05-07

Updated: 2026-09-29

Comments: 15 pages, 3 figures, v2: published version

Journal ref: JHEP 09 (2026) 266

DOI: 10.1007/JHEP09(2026)266

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: This paper investigates a specific mechanism for light dark matter production through freeze-in cosmology, linking its relic abundance to rare kaon decay searches.

Key concepts

Freeze-in Cosmology: This is a mechanism for producing light dark matter where it is generated through interactions in the early universe rather than through standard thermal processes. In this paper, light dark matter is produced via kaon decays when the universe has a low reheating temperature.
Kaon Portal to Freeze-in Dark Matter: This paper explores a specific mechanism where light dark matter is created through interactions involving kaons and pions in the early universe. It links the relic abundance of this dark matter directly to rare kaon decay searches, providing a concrete link between cosmology and particle physics experiments.
Quark Flavor-Changing Operator: This is a specific interaction term, denoted as /Lint = CV /Λ2 (¯sγµd)(¯χγµχ) + h.c., proposed by the authors. This operator describes how a dark matter candidate, chi, couples to Standard Model particles and governs both the dark matter production and rare kaon decays.
Reheating Temperature: This parameter dictates the early universe conditions relevant to this model. The paper shows that if the reheating temperature falls below about 150 to 160 MeV (below the QCD crossover temperature), dark matter production shifts to these hadronic processes involving kaons and pions.

Terminology

Reheating — 49× in this paper · explained in 2 episodes
Abundance — 39× in this paper · explained in 1 episode
Boltzmann Equation — 12× in this paper · explained in 2 episodes
Standard Model — 4× in this paper
Benchmark — 3× in this paper · explained in 2 episodes
Core — 2× in this paper · explained in 2 episodes
Flavour Lattice Averaging Group — 1× in this paper
Tonne-Years of Exposure of the LUX-ZEPLIN — 1× in this paper

Summary

This paper investigates a specific mechanism for light dark matter production through freeze-in cosmology, linking its relic abundance to rare kaon decay searches. It proposes that for low reheating temperatures below the QCD crossover, dark matter is generated via hadronic processes involving kaons and pions, providing a testable connection between cosmological histories and experimental particle physics results.

The DM Production Mechanism

The study focuses on a Dirac fermion dark matter candidate, denoted as χ, which couples to the Standard Model (SM) through the quark flavor-changing operator:

/Lint = CV /Λ2 (¯sγµd)(¯χγµχ) + h.c., (1.1)

When the reheating temperature (TRH) falls below the QCD crossover temperature, DM production takes place in the hadronic bath through kaon decays and scatterings:

K → πχχ¯
Kπ → χχ¯

The same operator also induces rare kaon decays:

K+ → π + χχ¯
KL → π0χχ¯

These processes are crucial because the relic density and the rare decay branching ratios are controlled by this single interaction, establishing a direct connection between the low-reheating cosmology and laboratory searches.

The Role of Low Reheating Temperatures

A key finding is that the required coupling strength depends on TRH. The paper states: When TRH falls below the QCD crossover temperature TQCD ∼ 150–160 MeV [9, 10], DM production through this interaction takes place in the hadronic bath. Furthermore, it notes that for low reheating temperatures, the Boltzmann suppression of the initial-state particles requires a larger coupling to reproduce the observed relic abundance, which potentially brings the scenario within experimental reach. The analysis restricts itself to TRH < TQCD because, for these lower temperatures, the relevant degrees of freedom for freeze-in production are hadrons.

Linking Freeze-in to Rare Kaon Searches

The paper bridges a gap between cosmology and particle physics by showing that the interaction governing the DM abundance also governs rare kaon decays. The derived decay rates and cross sections are used to solve the Boltzmann equation for the DM yield, which is then compared against experimental limits:

/BR(K+ → π + νν¯)NA62 = 9.6 +1.9 −1.8 × 10−11 (2.7)

/BR(KL → π0νν¯)KOTO < 2.2 × 10−9 (90% C.L.) (2.12)

The results indicate that the freeze-in bottleneck, which usually requires a feeble coupling, can be alleviated in this scenario because the kaon processes dominate the abundance generation at low TRH, and these processes are simultaneously probed by NA62 and KOTO experiments.

Numerical Analysis and Testability

The numerical analysis solves the Boltzmann equation for the DM yield, using thermal distributions (Maxwell-Boltzmann approximations) for initial-state mesons. The final relic abundance is calculated as:

/omegah squared = 2mχs˜0Yχ(x = ∞)ρc,0 ≃ 5.49 × 108 GeV−1 × mχYχ(x = ∞), (3.18)

The study evaluates the parameter space in the plane of DM mass and coupling strength (Λ/pCV). Figure 2 demonstrates that lower reheating temperatures necessitate larger interaction strengths because the kaon abundance is more strongly Boltzmann suppressed, shifting the freeze-in target toward regions accessible by current NA62 and future KOTO II sensitivities. The differential missing-mass spectrum for KL → π0+invisible provides an additional handle, showing how the DM contribution turns on at q squared = 4m 2χ, with the shape of this excess being correlated with both mχ and TRH.

Conclusion

The paper concludes that kaon-driven freeze-in dark matter offers a concrete example where the cosmological origin of light, feebly interacting DM can be tested through flavor experiments. While the analysis is restricted to a vector-current operator as a benchmark, it suggests that other operators (like scalar ones) could lead to different decay spectra and freeze-in efficiencies. The core message is that rare kaon decays serve as powerful probes for light invisible states, and this work demonstrates how these searches can constrain cosmological models involving low reheating temperatures.

Improvements for AI systems

As a fastidious researcher, I have analyzed this paper, Kaon Portal to Freeze-in Dark Matter, and identified several high-impact areas where AI systems could be significantly improved or specialized.

Here are the specific improvements and the resulting capabilities of an enhanced AI system:

) 1. Specialized Physics Simulation Engine (SPS E) for Low-Temperature Cosmology

The paper relies on solving a coupled Boltzmann equation (Eq. 3.10) involving complex collision terms derived from hadronic scattering and decay rates, integrated over thermal distributions (Eqs. 3.12 - 3.17).

Specific Improvement: Develop a specialized numerical solver module capable of efficiently handling the non-trivial temperature dependencies of the effective degrees of freedom functions, such as the modified Bessel function in Eq. (3.12) and the Maxwell-Boltzmann distributions, while accurately accounting for resonant contributions (like the K∗(892) resonance in Eq. 3.5).
Improved AI System Capability: This SPS E could perform Virtual Cosmology Simulations. It would allow researchers to rapidly explore parameter spaces (TRH, mχ, coupling strength) to determine which combinations satisfy the relic density constraint without running computationally prohibitive full cosmological simulations. It could instantly map the freeze-in bottleneck regions in the parameter space.

) 2. Multi-Modal Experimental Signature Correlator (MESC)

The paper explicitly links a single theoretical interaction (the operator in Eq. 1.1) to multiple experimental observables: rare kaon decays at NA62 and KOTO, and the DM relic abundance constraint.

Specific Improvement: Implement a machine learning model trained on the differential decay spectra (Figure 3) and invariant mass distributions (Figure 2). This model must learn the subtle correlations between the DM signal shape (dependent on mχ) and the SM background shape, as well as how these shapes shift with different cosmological parameters like TRH.
Improved AI System Capability: The MESC could act as an Experimental Signature Predictor. Given a hypothetical dark matter mass and interaction strength, it could predict the specific observable signature (e.g., the expected excess in the KL → π0 + invisible spectrum) that should be searched for by NA62 or KOTO, effectively automating the design of future experimental analyses and reducing false positive rates.

) 3. Operator-to-Observable Mapping & Uncertainty Quantification (OOMUQ)

The paper notes that different operators (vector vs. scalar, e.g., Eq. 1.1 vs. Eq. 30) lead to different results for the relic density and decay spectra, and suggests a need for future investigation into scalar operators like (¯sd)(¯χχ).

Specific Improvement: Create an AI framework that maps fundamental particle physics operators (like the dimension-six operator in Eq. 1.1) directly onto the resulting cosmological relic density constraints and the predicted observable branching ratios. Crucially, this system must incorporate Bayesian uncertainty propagation to quantify how uncertainties in input parameters (like form factor parameters f+(0) or CP violation phase) propagate into both the DM abundance and the experimental bounds.
Improved AI System Capability: This OOMUQ system would serve as a Theoretical Risk Assessor. It could ingest new theoretical models (e.g., switching from vector to scalar operators) and instantly quantify the resulting impact on existing or projected experimental constraints, guiding theorists on which interaction channels are most promising for testing.

) 4. Automated Literature Synthesis and Gap Identification

The Introduction highlights a gap: studies connecting quark FCNC interactions to both DM abundance and rare meson observables.

Specific Improvement: Develop an AI agent capable of Cross-Domain Knowledge Retrieval. This agent would crawl the literature (using tools like those implied by the references) specifically looking for intersections between flavor physics, non-thermal cosmology, and rare meson decay phenomenology.
Improved AI System Capability: The Literature Agent could proactively suggest novel theoretical avenues or identify missing experimental probes that bridge the gap identified in Section 1 of this paper, essentially acting as a dedicated research assistant focused on synthesizing interdisciplinary knowledge relevant to the Kaon Portal scenario.

Abstract

We investigate freeze-in production of light dark matter through the quark flavor-changing operator (γ μd)(χγ μχ) in a low-reheating cosmology. For reheating temperatures below the QCD crossover, kaon decays and scatterings generate the dark matter abundance through K toπχ χ and Kπ toχ χ. The same interaction induces the rare kaon decays K+ toπ+χ χ and K L toπ 0χ χ. This links the freeze-in relic abundance to searches at NA62, KOTO, and KOTO II. We find that lower reheating temperatures require larger couplings to compensate for the Boltzmann-suppressed kaon abundance, making kaon-driven freeze-in dark matter testable at rare kaon decay experiments.