arxiv: 2605.05947 · v1 · submitted 2026-05-07 · ✦ hep-ph · astro-ph.CO· hep-ex

Recognition: unknown

Kaon Portal to Freeze-in Dark Matter

Motoi Endo , Takumu Yamanaka

Authors on Pith no claims yet

Pith reviewed 2026-05-08 08:30 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-ex

keywords freeze-in dark matterkaon decaysflavor-changing operatorsreheating temperaturerare kaon decayslow-scale cosmologydark matter production

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The pith

Light dark matter can be produced by kaon decays and scatterings in low-reheating cosmologies through a flavor-changing operator.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines freeze-in production of light dark matter in a universe with reheating temperatures below the QCD crossover. Kaons, though Boltzmann-suppressed, generate the dark matter abundance via decays to a pion plus a dark matter pair and via kaon-pion scatterings. The same quark-level interaction that drives this production also induces rare kaon decays with missing energy. Lower reheating temperatures reduce the kaon population, so larger couplings are required to reach the observed dark matter density, placing the signal within the sensitivity of rare-decay searches.

Core claim

For reheating temperatures below the QCD crossover, the freeze-in production of light dark matter proceeds dominantly via kaon decays K to pi plus dark matter pairs and scatterings K pi to dark matter pairs induced by the operator (s-bar gamma_mu d)(chi-bar gamma^mu chi). This mechanism sets the dark matter relic abundance and simultaneously determines the branching fractions of the rare decays K+ to pi+ plus dark matter pair and K_L to pi0 plus dark matter pair.

What carries the argument

The flavor-changing operator (s-bar gamma_mu d)(chi-bar gamma^mu chi) that mediates both kaon-driven dark matter production and the rare kaon decays with missing energy.

If this is right

Lower reheating temperatures demand larger couplings to compensate for the reduced kaon abundance.
The predicted rates for the rare kaon decays become accessible to current and planned searches.
Kaon-mediated freeze-in supplies a concrete cosmological origin for the dark matter density that is tied directly to flavor physics.
The scenario remains viable only when the reheating temperature lies below the QCD crossover and the operator dominates production.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Analogous portals through other light mesons could operate in different temperature windows and warrant similar analyses.
Including possible entropy production after reheating would alter the required coupling and shift the predicted decay rates.
The mechanism suggests that non-standard early-universe histories can be probed indirectly through flavor-violating dark matter signatures.

Load-bearing premise

The dark matter abundance is produced solely by this kaon portal with no other significant contributions or entropy dilution effects.

What would settle it

An experimental upper bound on the branching ratio of K+ to pi+ plus invisible particles that lies below the value needed to produce the observed dark matter density at a given reheating temperature.

read the original abstract

We investigate freeze-in production of light dark matter through the quark flavor-changing operator $(\bar{s}\gamma_\mu d)(\bar{\chi}\gamma^\mu\chi)$ in a low-reheating cosmology. For reheating temperatures below the QCD crossover, kaon decays and scatterings generate the dark matter abundance through $K\to\pi\chi\bar{\chi}$ and $K\pi\to\chi\bar{\chi}$. The same interaction induces the rare kaon decays $K^+\to\pi^+\chi\bar{\chi}$ and $K_L\to\pi^0\chi\bar{\chi}$. 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper links low-reheating freeze-in dark matter through a kaon portal to NA62 and KOTO sensitivities, but the reach rests on kaons dominating over other hadronic channels.

read the letter

The main point is that in freeze-in scenarios with the operator (s-bar gamma d)(chi-bar gamma chi), reheating temperatures below the QCD crossover suppress the kaon abundance enough that larger couplings are needed to reach the observed relic density, pushing the branching ratios for K to pi chi chi into the range NA62 and KOTO can probe. The authors map this directly to the experimental limits on K+ to pi+ chi chi-bar and KL to pi0 chi chi-bar. That targeted connection between a cosmological parameter and existing decay searches is the concrete new element here. It takes the standard freeze-in logic and applies it to this specific low-T_R regime with a flavor-changing portal, which is not a routine extension of earlier work on either freeze-in or kaon decays. The paper does a clean job stating the logic: Boltzmann suppression at low T_R forces the coupling up, and the same operator sets the visible decay rates. For readers already working on hadronic portals or rare kaon physics, this gives a straightforward way to think about how T_R could be constrained experimentally. The soft spot is the assumption that kaon decays and scatterings dominate production once T_R drops below the QCD crossover, with no comparable yields from pions or etas and no late entropy injection. If other channels contribute or dilution occurs, the required coupling drops and the experimental signal weakens. The abstract does not show the Boltzmann equations or numerical scans, so the full paper needs to demonstrate that the kaon channel really carries the load and that the relic density calculation is stable under reasonable variations. This work is for people who already follow freeze-in models or kaon experiments and want to see one narrow but testable intersection. A reader outside those areas will not get much from it. It deserves a serious referee because the experimental tie-in is sharp and the underlying idea is well-defined, even if the dominance claim needs close checking. I would send it for review and ask the referees to focus on whether the production is truly kaon-dominated and how sensitive the results are to reheating details.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates freeze-in production of light dark matter via the dimension-6 flavor-changing operator (s-bar gamma_mu d)(chi-bar gamma^mu chi) in a low-reheating cosmology with T_R below the QCD crossover. It claims that DM production proceeds dominantly through kaon decays K to pi chi chi-bar and scatterings K pi to chi chi-bar due to Boltzmann suppression of the kaon density, directly linking the observed relic abundance to the branching ratios of the rare decays K+ to pi+ chi chi-bar and K_L to pi0 chi chi-bar. This makes the scenario testable at NA62, KOTO, and KOTO II, with the key result that lower T_R requires larger operator couplings to compensate for the suppressed kaon abundance.

Significance. If the calculations hold, the work establishes a direct, falsifiable connection between the reheating temperature and observable kaon decay branching ratios, allowing joint constraints on dark matter and early-universe cosmology from flavor experiments. A strength is the explicit focus on the low-T_R regime and the mapping to specific experimental sensitivities; this is a genuine advance over standard high-T_R freeze-in studies.

major comments (2)

[§3] §3 (DM production): The central claim that kaon channels dominate and force larger couplings at low T_R rests on the assumption that pion- and eta-mediated processes (which have higher number densities) contribute negligibly. The Boltzmann equations and yield comparisons must explicitly demonstrate this dominance, including the relative rates from the same operator; otherwise the required coupling and experimental reach are overstated.
[§4] §4 (relic density and entropy): The relic abundance calculation assumes no entropy dilution from late decays or reheating dynamics below the QCD crossover. If any such dilution is present, the DM yield decreases and the coupling needed to match Omega h^2 shrinks, removing the link to NA62/KOTO sensitivity. This assumption must be justified or included as a parameter scan.

minor comments (2)

[§2] The operator is written with a specific Lorentz structure; clarify whether other structures (e.g., scalar or pseudoscalar) are considered and why they are subdominant.
[Figure 2] Figure 2 (or equivalent) showing branching ratio vs T_R should include error bands from the numerical integration and from the kaon decay constants used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help clarify the robustness of our results on kaon-mediated freeze-in dark matter. We address each major comment point by point below.

read point-by-point responses

Referee: [§3] §3 (DM production): The central claim that kaon channels dominate and force larger couplings at low T_R rests on the assumption that pion- and eta-mediated processes (which have higher number densities) contribute negligibly. The Boltzmann equations and yield comparisons must explicitly demonstrate this dominance, including the relative rates from the same operator; otherwise the required coupling and experimental reach are overstated.

Authors: We agree that an explicit demonstration of kaon dominance is required for the central claim. In the revised manuscript, we will expand Section 3 to include the full set of Boltzmann equations incorporating pion-, eta-, and kaon-mediated processes from the same dimension-6 operator. We will add numerical yield comparisons as a function of temperature, showing that for T_R below the QCD crossover the kaon channels dominate due to the operator's flavor structure and the Boltzmann suppression of lighter mesons. New figures will display the relative contributions to the DM yield, confirming that the required couplings for the observed relic density remain accessible to NA62, KOTO, and KOTO II. These additions will directly address the concern and strengthen the mapping to experimental sensitivities. revision: yes
Referee: [§4] §4 (relic density and entropy): The relic abundance calculation assumes no entropy dilution from late decays or reheating dynamics below the QCD crossover. If any such dilution is present, the DM yield decreases and the coupling needed to match Omega h^2 shrinks, removing the link to NA62/KOTO sensitivity. This assumption must be justified or included as a parameter scan.

Authors: We acknowledge the importance of this assumption. Our baseline calculation adopts a standard low-reheating cosmology without late-time entropy injection, consistent with the minimal particle content of the model (only the dark matter and the flavor-changing operator). In the revised Section 4 we will add an explicit justification: below the QCD crossover the relevant degrees of freedom are the light mesons, and the model introduces no long-lived states capable of injecting entropy after reheating. To further address the referee's point we will include a brief discussion of how a hypothetical entropy dilution factor would rescale the required coupling upward, thereby preserving or strengthening the connection to rare kaon decay searches. A full parameter scan over arbitrary dilution is beyond the scope of this work as it would necessitate additional unspecified sectors, but the baseline results and their experimental implications hold under the stated minimal cosmology. revision: partial

Circularity Check

0 steps flagged

No circularity: relic density calculation yields independent predictions for rare kaon decays

full rationale

The paper solves the Boltzmann equation for DM production via the specified dimension-6 operator acting on Boltzmann-suppressed kaon number densities below the QCD crossover, equates the resulting yield to the observed relic density, and extracts the required coupling strength as a function of T_reh. This coupling then determines the branching ratios for K→πχχ̄ without any fitted parameter being renamed as a prediction or any self-citation closing the loop. The derivation remains self-contained against external benchmarks (standard freeze-in formalism and kaon abundance calculations) and does not reduce by construction to its inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The claim rests on the standard freeze-in Boltzmann equation, the assumption that the given dimension-6 operator is the only relevant portal, and the cosmological premise of reheating below the QCD crossover. No new particles beyond the dark matter chi are introduced, but the operator strength is a free parameter adjusted to match the observed relic density.

free parameters (2)

operator coupling strength
Adjusted to reproduce the observed dark matter abundance for each reheating temperature; appears as the central free parameter in the abstract.
reheating temperature T_R
Varied below the QCD crossover; lower values require larger couplings and are the key variable that changes experimental reach.

axioms (2)

domain assumption Freeze-in production is dominated by kaon decays and scatterings with no significant entropy injection or dilution after production.
Invoked to link the kaon abundance directly to the final dark matter density.
domain assumption The flavor-changing operator (s-bar gamma_mu d)(chi-bar gamma^mu chi) is the sole portal and does not induce other observable effects that would already be excluded.
Required for the kaon-decay signals to be the primary experimental signature.

invented entities (1)

light dark matter particle chi no independent evidence
purpose: The stable particle whose abundance is set by kaon processes.
Postulated as the dark matter candidate; no independent evidence such as a predicted mass or coupling is given beyond the operator.

pith-pipeline@v0.9.0 · 5441 in / 1590 out tokens · 30913 ms · 2026-05-08T08:30:39.121698+00:00 · methodology

discussion (0)

Reference graph

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