Minimal Freeze-in Dark Matter: Reviving electroweak doublet dark matter with Boltzmann suppressed freeze-in

James Unwin; Nicol\'as Bernal; Sagnik Mukherjee

arxiv: 2602.10112 · v2 · pith:7MNCMOKQnew · submitted 2026-02-10 · ✦ hep-ph · astro-ph.CO

Minimal Freeze-in Dark Matter: Reviving electroweak doublet dark matter with Boltzmann suppressed freeze-in

Nicol\'as Bernal , Sagnik Mukherjee , James Unwin This is my paper

Pith reviewed 2026-05-21 13:13 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO

keywords dark matterfreeze-inelectroweak doubletdirect detectionreheat temperaturepseudo-DiracSU(2) fermion

0 comments

The pith

Electroweak doublet dark matter evades direct detection for masses above 10^10 GeV when produced by freeze-in without thermalizing.

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

The paper shows that a simple dark matter candidate interacting with known particles only through the weak force can remain viable despite strong experimental exclusions. Normally, such electroweak doublet fermions would thermalize and produce detectable signals in direct detection experiments. Here, if the dark matter mass exceeds the temperature after inflation, production occurs slowly enough that the particles never reach equilibrium with the early universe plasma. This Boltzmann-suppressed freeze-in process keeps the model minimal while satisfying current limits from LZ and leaving room for future tests with Darwin. A small splitting of the neutral component into a pseudo-Dirac pair via a higher-dimensional operator further lowers the viable mass range to around 300 GeV.

Core claim

SU(2)_L doublet fermion dark matter evades direct detection if its mass exceeds 10^{10} GeV. If the neutral Dirac fermion is split into a pseudo-Dirac pair via a high dimension operator this limit can be relaxed to 300 GeV. Provided the dark matter mass is above the reheat temperature of the Universe, the production rate never exceeds the Hubble rate in cases of interest, thus the dark matter never thermalizes.

What carries the argument

Boltzmann-suppressed freeze-in production when dark matter mass exceeds the reheat temperature, keeping the interaction rate below the Hubble expansion rate so equilibrium is never reached.

Load-bearing premise

The dark matter mass must exceed the reheat temperature of the Universe so that its production rate never exceeds the Hubble rate and the particles never thermalize.

What would settle it

Direct detection of an electroweak doublet dark matter candidate with mass below 10^{10} GeV (or below 300 GeV without the pseudo-Dirac splitting) would contradict the evasion mechanism.

Figures

Figures reproduced from arXiv: 2602.10112 by James Unwin, Nicol\'as Bernal, Sagnik Mukherjee.

**Figure 2.** Figure 2: FIG. 2. Constraints on Minimal Freeze-in Dark Matter. We [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Indirect detection bounds on the vector-like model. The total annihilation cross-section (for [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

read the original abstract

Dark matter communicating with the Standard Model solely via electroweak interactions provides a compelling picture. However, thermal freeze-out of electroweak doublet dark matter is generically strongly excluded by direct detection. We show that SU(2)${}_L$ doublet fermion dark matter evades direct detection if its mass exceeds $10^{10}$ GeV. If the neutral Dirac fermion is split into a pseudo-Dirac pair (via high dimension operator) this limit can be relaxed to 300 GeV. Provided the dark matter mass is above the reheat temperature of the Universe, the production rate never exceeds the Hubble rate in cases of interest, thus the dark matter never thermalizes. We apply constraints from direct detection (e.g. LZ) and consider the discovery potential of Darwin. This scenario presents the most minimal model of freeze-in dark matter, and is both elegant and highly predictive.

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 revives the electroweak doublet as freeze-in DM by requiring m_DM above the reheat temperature or a pseudo-Dirac split to beat direct detection, but the mechanism stands or falls on that hierarchy.

read the letter

The main point is that an SU(2)_L doublet fermion can serve as dark matter through freeze-in if its mass sits above the reheat temperature, keeping production Boltzmann-suppressed so the rate never exceeds Hubble and thermalization is avoided. With an optional high-dimension operator splitting the neutral state into a pseudo-Dirac pair, the direct detection bound drops from 10^10 GeV down to 300 GeV, opening a window that thermal freeze-out versions lack. They then fold in LZ limits and flag Darwin as a future test, keeping the setup minimal with only electroweak couplings plus that one operator. That combination is the concrete new element here. The paper does a clean job laying out the production logic and showing how the yield stays under control in the stated regime, giving a simple benchmark without extra fields or portals. The calculations appear to rest on standard rate-versus-expansion comparisons rather than any circular fitting. One soft spot is the load-bearing assumption that m_DM exceeds the reheat temperature; if that ordering fails or if early-time effects alter the suppression, the no-thermalization claim could shift and the relic density might need rechecking. The abstract leaves the explicit integrals and parameter scans for the body, so robustness against small changes in the high-dimension scale or reheat value should be verified there. The high-mass limit itself follows logically but feels extreme for a minimal model. This is useful for people already working on freeze-in production or on minimal electroweak DM candidates that avoid thermal relics. A reader looking for concrete targets for Darwin or a straightforward alternative to standard WIMPs will find the numbers and the logic worth checking. The work shows honest engagement with the existing literature on doublet DM and direct detection, so it deserves a serious referee even if revisions tighten the assumptions. I would send it for peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes SU(2)_L doublet fermion dark matter as a minimal freeze-in candidate. It claims that masses above 10^{10} GeV evade direct detection bounds, with the limit relaxed to 300 GeV if a high-dimension operator splits the neutral Dirac fermion into a pseudo-Dirac pair. The key regime is m_DM exceeding the reheat temperature, under which the electroweak production rate remains below the Hubble rate so that the dark matter never thermalizes; constraints from LZ and the discovery reach of Darwin are discussed.

Significance. If the production-rate comparison and direct-detection evasion hold, the work revives electroweak doublet dark matter in a highly minimal and predictive freeze-in setting without additional portals. The Boltzmann-suppressed mechanism and explicit experimental projections constitute a clear strength.

major comments (2)

[Abstract / production calculation] Abstract and production section: the assertion that 'the production rate never exceeds the Hubble rate in cases of interest' is load-bearing for the never-thermalizes claim, yet the manuscript provides no explicit derivation, numerical integration of the Boltzmann equation, or scan over reheat temperatures to demonstrate the ratio remains <1 without post-hoc parameter selection.
[Model / pseudo-Dirac splitting] Model section: the high-dimension operator that splits the neutral component into a pseudo-Dirac pair is introduced to relax the direct-detection bound to 300 GeV, but the operator dimension, coefficient, and resulting mass splitting are not quantified, leaving the naturalness and viability of the 300 GeV window unassessed.

minor comments (2)

[Abstract] Abstract: the phrase 'cases of interest' is undefined; the main text should explicitly delineate the parameter region (m_DM, T_reheat) to which the rate < Hubble statement applies.
[Throughout] Notation: ensure consistent symbols for the dark-matter mass and reheat temperature throughout the equations and figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond to each major comment below.

read point-by-point responses

Referee: [Abstract / production calculation] Abstract and production section: the assertion that 'the production rate never exceeds the Hubble rate in cases of interest' is load-bearing for the never-thermalizes claim, yet the manuscript provides no explicit derivation, numerical integration of the Boltzmann equation, or scan over reheat temperatures to demonstrate the ratio remains <1 without post-hoc parameter selection.

Authors: The production section derives the electroweak interaction rate analytically and shows that the Boltzmann suppression exp(-m_DM/T) when m_DM exceeds the reheat temperature keeps the rate below the Hubble expansion rate for the parameter space considered. We acknowledge that an explicit numerical confirmation would strengthen the presentation. In the revised manuscript we will add the explicit ratio Gamma/H, a numerical integration of the Boltzmann equation for the DM yield, and a scan over reheat temperatures to demonstrate that the ratio remains below unity without additional parameter tuning. revision: yes
Referee: [Model / pseudo-Dirac splitting] Model section: the high-dimension operator that splits the neutral component into a pseudo-Dirac pair is introduced to relax the direct-detection bound to 300 GeV, but the operator dimension, coefficient, and resulting mass splitting are not quantified, leaving the naturalness and viability of the 300 GeV window unassessed.

Authors: We agree that a quantitative treatment of the splitting operator is needed to assess the 300 GeV window. In the revised manuscript we will specify the operator (e.g., a dimension-5 or dimension-6 term), give a benchmark coefficient, compute the resulting mass splitting, and discuss the associated scale and naturalness, showing that the splitting suffices to evade direct detection while preserving the freeze-in dynamics. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper's central results follow from the stated hierarchy m_DM > T_reheat, which is an external input rather than a quantity defined by the outcome. Under this condition the interaction rate is computed from standard electroweak matrix elements and compared to the Hubble rate using conventional cosmological expressions; the conclusion that the DM never thermalizes is a direct consequence of that inequality and does not reduce to a fitted parameter or self-referential definition. Direct-detection limits for the high-mass regime or the pseudo-Dirac splitting case are obtained from existing experimental bounds and effective-operator calculations that are independent of the freeze-in yield. No load-bearing step equates a prediction to its own input by construction, and the model remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The model rests on standard particle-physics and cosmological assumptions plus one ad-hoc high-dimension operator; no new particles or forces are postulated beyond the splitting operator.

free parameters (2)

dark matter mass
Set above 10^10 GeV or 300 GeV to satisfy direct-detection and freeze-in conditions.
reheat temperature
Dark matter mass required to exceed it to ensure non-thermal production.

axioms (2)

domain assumption Dark matter communicates with the Standard Model solely via electroweak interactions
Stated in the opening sentence of the abstract as the starting premise.
domain assumption Standard early-universe cosmology with a well-defined reheat temperature after inflation
Used to compare production rate to Hubble expansion.

invented entities (1)

high-dimension operator splitting the neutral Dirac fermion into a pseudo-Dirac pair no independent evidence
purpose: To relax the direct-detection mass bound from 10^10 GeV to 300 GeV
Introduced as a minimal extension; no independent evidence provided beyond phenomenological motivation.

pith-pipeline@v0.9.0 · 5690 in / 1596 out tokens · 33848 ms · 2026-05-21T13:13:04.613731+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Provided the dark matter mass is above the reheat temperature of the Universe, the production rate never exceeds the Hubble rate... γ(T)≃ ∑ C T^4 e^{-2mΨ/T}
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Boltzmann equation ˙nΨ + 3HnΨ = γ(T) with instantaneous reheating to T_rh

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Warm dark matter from freeze-in at stronger coupling
hep-ph 2026-02 unverdicted novelty 4.0

Warm Higgs portal dark matter from stronger-coupling freeze-in is viable above 50-100 keV with a non-thermal momentum distribution not captured by the standard alpha-beta-gamma parametrization.

Reference graph

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Derivation of the reaction densityγ(T) In this appendix, we derive the reaction densityγ(T). Specifically, we show explicitly how eq. (13) follows from eq. (10) & eq. (11). Since production is dominated near threshold in the Boltzmann suppressed freeze-in limitT≪m, we can parameterize the center of mass energy ass≃4m 2 Ψ +εwithε≪4m 2 Ψ. It follows that β≃...

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While this can potentially lead to indirect detection signals

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work page

[1] [1]

Thus, for a doublet to have an electromagnetically neutral component after EWSB, the hypercharge of the doublet must beY χ =± 1 2

To avoid coupling to photons, the EM charge must satisfyQ= 0, which impliesT 3 =−Y. Thus, for a doublet to have an electromagnetically neutral component after EWSB, the hypercharge of the doublet must beY χ =± 1 2. We focus on fermion dark matter since scalar dark matter suffers from a fine-tuning ‘hierarchy’ problem and also permits a model-independent r...

work page

[2] [2]

This model has a large tree-large vector coupling to theZand thus leads to a large SI scattering cross- section. Interestingly, if one introduces a modest mass arXiv:2602.10112v1 [hep-ph] 10 Feb 2026 2 splitting between the two EM neutral degrees of free- dom, then the tree level SI cross-section can be removed [3], which ameliorates these limits. We will...

work page internal anchor Pith review Pith/arXiv arXiv 2026

[3] [3]

thermalization

Each of the doublets can be written as follows with the EM charges shown as superscripts χ1 = χ+ 1 χ0 1 , χ 2 = χ0 2 χ− 2 ,(1) and the Lagrangian is given by Lχ =iχ † 1¯σµDµχ1 +iχ † 2¯σµDµχ2 − h M ϵabχ1aχ2b + H.c. i , (2) whereD µ is the ordinary electroweak covariant deriva- tive. Note thatϵ abχ1aχ2b =χ + 1 χ− 2 −χ 0 1χ0 2, since we have ϵ12 =−ϵ 21 = 1. ...

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Specifically, we show explicitly how eq

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work page