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$\mu$DM: a new mechanism for the baryon-dark matter coincidence

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Wen Yin

High Energy Physics - Phenomenology · Submitted 27 Aug 2026 · 99 references

Pith's verdict: The μDM mechanism is largely sound as a parametric framework, and the real question is whether the burst-production benchmark can be closed.

T0 · AI review

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arXiv ID2608.26709 (version 1)
Pith IDYVUJ5XIN, Pith's permanent record of this paper and its review
CitationWen Yin. "$\mu$DM: a new mechanism for the baryon-dark matter coincidence." arXiv:2608.26709 (2026). https://pith.science/paper/YVUJ5XIN
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The paper

The paper claims

A single relation ties dark matter mass to the baryon chemical potential, explaining their coincident abundances.

The reading

The paper proposes a new class of dark matter, called chemical-potential-matched dark matter (μDM), in which the dark-matter mass $m_X$ is comparable to the baryon-number chemical potential $|\mu_B|$ established just after weak-sphaleron freeze-out. If this relation holds, the thermal-scale relic abundance of dark matter automatically yields the observed ratio $\Omega_{\rm DM}/\Omega_b \simeq 5.4$, eliminating the need to fine-tune the dark-matter mass or couplings. The key mechanism is that a rotating complex scalar field (an Affleck–Dine field) generates the chemical-potential bias via spontaneous baryogenesis while its excitations constitute the dark matter. A concrete realization using right-handed neutrinos shows that the relation can be natural over a broad parameter space, and that the dark-matter mass is forced into the eV–keV range unless late entropy dilution intervenes. If correct, the mystery of why dark matter and baryons have similar energy densities is reduced to order-one numbers of degrees of freedom and an integer charge.

What carries the argument

The central object is the rotating Affleck–Dine field $P = (R/\sqrt{2}) e^{i\theta}$ with an approximately quadratic potential $V(P) \simeq m_R^2 |P|^2$. Its angular velocity $\dot\theta \simeq m_R$ drives the spontaneous-baryogenesis bias $\mu_{\rm bias} = c \dot\theta \simeq c m_R$, which sets the frozen baryon density and hence $\mu_B$. The excitations of $P$ (radial and phase modes) are produced from a thermal plasma with a cold momentum distribution via Bose-enhanced stimulated emission, achieving the thermal-scale abundance $\kappa_X \simeq 0.09 g_{\chi2}$ that enters the coincidence formula. The relation $|\mu_B| \sim m_R$ then cancels the dark-matter mass from the ratio $\Omega_X/\Omega_b$, leaving only order-one numbers of degrees of freedom and the integer charge $n$ that appears in the Majorana coupling $y_P P^n \nu_{R,1}^c \nu_{R,1}$.

Extended reading notes

Core claim

The central claim is that the baryon–dark matter coincidence follows directly from two ingredients: (i) a relativistically decoupled thermal relic with number density $n_X \sim T^3$ and (ii) a frozen baryon asymmetry parametrized by $|n_B| \sim |\mu_B| T_{\rm sph}^2$. When the dark-matter mass equals the magnitude of the baryon-number chemical potential, $|\mu_B| \sim m_X$, the present-day energy-density ratio becomes independent of $m_X$ and of microscopic couplings, yielding $\Omega_X/\Omega_b \simeq 5.4 \, (11 g_{\chi2}/n)\, (g_{*s}(T_{\rm sph})/g_{*s}(T_p))\, (T_{\rm sph}/131.7~{\rm GeV})\, (0.94~{\rm GeV}/m_N)$. The paper demonstrates this relation explicitly for an Affleck–Dine field $P$ whose rotating phase $\dot\theta \simeq m_R$ sources the chemical-potential bias $\mu_{\rm bias} \simeq c m_R$, while the excitations of $P$ (radial and phase modes) are produced at thermal abundance via Bose-enhanced stimulated emission and constitute the dark matter. A neutrino-portal model with a pseudo-Dirac sterile pair realizes the required coupling without excessive thermal corrections to the $P$ potential.

Load-bearing premise

The benchmark relies on the premise that a light boson produced from a hot plasma via Bose-enhanced stimulated emission reaches an attractor number density $\kappa_X \approx 0.09 g_{\chi2}$ while remaining cold; this attractor result is imported from prior simulations and is not verified for the specific neutrino-coupled model in this paper.

Editorial extensions

If this is right

  • If the μDM mechanism is correct, the dark-matter mass must lie in the eV–keV range (absent entropy dilution), providing a sharp target for direct and indirect detection experiments such as JWST/NIRSpec, X-ray telescopes, and WISP searches.
  • The coincidence is reduced to a handful of dimensionless parameters—degrees of freedom and an integer charge $n$—making it testable: any measurement that fixes these numbers predicts the observed ratio exactly.
  • The Affleck–Dine realization ties dark matter to the seesaw mechanism for neutrino masses, so that neutrino physics experiments (e.g., searches for sterile neutrinos or $P \to \nu\nu$ decay) can probe the mechanism.
  • The same rotating field that sources the baryon asymmetry also produces dark matter, implying that baryogenesis and dark-matter production share a common origin and cannot be treated independently.
  • The burst production via stimulated emission creates a cold momentum distribution, which avoids structure-formation constraints on light dark matter; this prediction can be checked with high-redshift Lyman-$\alpha$ or 21-cm observations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • This mechanism provides a new organizing principle for model building: any theory in which $|\mu_B| \sim m_{\rm DM}$ with a thermal-scale relic abundance automatically explains the coincidence, regardless of the detailed particle physics. This suggests that the coincidence is not an accident but a consequence of a generic attractor in the early Universe.
  • The requirement that the dark matter be cold via stimulated emission ties the mechanism to a specific non-thermal production regime. Experimental confirmation of a sub-keV dark-matter particle with suppressed free-streaming would strongly support the μDM class, whereas detection of a warmer spectrum would rule out the baseline attractor.
  • If future observations find the baryon-to-dark-matter ratio to deviate from $\sim 5.4$ at the percent level, the μDM framework would require an independent tuning of the integer $n$—a discrete parameter—which is arguably more natural than a continuous fine-tuning.
Original abstract

For a relativistically decoupled thermal relic, the dark-matter energy-to-entropy ratio scales as $\rho_{\rm DM}/s\sim 10^{-3}m_{\rm DM}$. This is the familiar hot-dark-matter abundance relation. Immediately after weak-sphaleron freeze-out, the baryon asymmetry can be parametrized as $\rho_{\rm baryon}/s\sim 10^{-4}|\mu_B|$. Here $\mu_B$ is the baryon-number chemical potential. We propose a new class of models, called chemical-potential-matched dark matter ($\mu$DM), in which $|\mu_B|\sim m_{\rm DM}$, thereby providing a new route to the baryon-dark matter coincidence. As a concrete example of $\mu$DM, we consider an Affleck-Dine field whose excitations constitute dark matter. We also briefly discuss spontaneous electroweak baryogenesis associated with axion-like-particle walls. In the absence of entropy dilution, this coincidence mechanism generically points to dark matter in the eV-keV mass range. Its momentum distribution can nevertheless be cold if thermal production is dominated by Bose-enhanced stimulated emission. Alternatively, entropy dilution after both the dark-matter and baryon yields are fixed allows masses up to the MeV scale.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,521 input tokens.

What the abstract itself states, as probabilities: claims first 0.12 · states limitation 0.68 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.87 · compares with prior results 0.63 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

For a relativistically decoupled thermal relic, the dark-matter energy-to-entropy ratio scales as $\rho_{\rm DM}/s\sim 10^{-3}m_{\rm DM}$. This is the familiar hot-dark-matter abundance relation. Immediately after weak-sphaleron freeze-out, the baryon asymmetry can be parametrized as $\rho_{\rm baryon}/s\sim 10^{-4}|\mu_B|$. Here $\mu_B$ is the baryon-number chemical potential. We propose a new class of models, called chemical-potential-matched dark matter ($\mu$DM), in which $|\mu_B|\sim m_{\rm DM}$, thereby providing a new route to the baryon-dark matter coincidence. As a concrete example of $\mu$DM, we consider an Affleck-Dine field whose excitations constitute dark matter. We also briefly discuss spontaneous electroweak baryogenesis associated with axion-like-particle walls. In the absence of entropy dilution, this coincidence mechanism generically points to dark matter in the eV-keV mass range. Its momentum distribution can nevertheless be cold if thermal production is dominated by Bose-enhanced stimulated emission. Alternatively, entropy dilution after both the dark-matter and baryon yields are fixed allows masses up to the MeV scale.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 For a relativistically decoupled thermal relic, the dark-matter energy-to-entropy ratio scales as $\rho_{\rm DM}/s\sim 10^{-3}m_{\rm DM}$. background 1.00 0.08 0.04 asserted 1.00
s1 This is the familiar hot-dark-matter abundance relation. background 0.99 0.05 0.02 asserted 1.00
s2 Immediately after weak-sphaleron freeze-out, the baryon asymmetry can be parametrized as $\rho_{\rm baryon}/s\sim 10^{-4}|\mu_B|$. background 0.99 0.12 0.05 asserted 0.66
s3 Here $\mu_B$ is the baryon-number chemical potential. background 0.99 0.10 0.02 asserted 0.98
s4 We propose a new class of models, called chemical-potential-matched dark matter ($\mu$DM), in which $|\mu_B|\sim m_{\rm DM}$, thereby providing a new route to the baryon-dark matter coincidence. contribution 1.00 0.82 0.78 asserted 0.73
s5 As a concrete example of $\mu$DM, we consider an Affleck-Dine field whose excitations constitute dark matter. contribution 0.70 0.83 0.06 asserted 0.96
s6 We also briefly discuss spontaneous electroweak baryogenesis associated with axion-like-particle walls. contribution 0.94 0.65 0.03 unclear 0.58
s7 In the absence of entropy dilution, this coincidence mechanism generically points to dark matter in the eV-keV mass range. result 0.52 0.66 0.28 hedged possibility 0.61
s8 Its momentum distribution can nevertheless be cold if thermal production is dominated by Bose-enhanced stimulated emission. interpretation 0.52 0.52 0.05 hedged possibility 0.62
s9 Alternatively, entropy dilution after both the dark-matter and baryon yields are fixed allows masses up to the MeV scale. result 0.76 0.58 0.11 asserted 0.55

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from argument 0.68.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Parameter region in the (yR,eff (Tsph), yν) plane for Tsph = 131.7 GeV, M = 10 GeV, R(Tsph) = 104 GeV, and mR = 230 eV. The chemical-equilibration boundaries are obtained by equating the QKE transfer rate derived in Appendix B to the Hubble rate. The black solid, dashed, and dotted curves correspond to n = 1, 10, and 100, respectively. The out-of-chemical-equilibrium region and the region with excessively large thermal corrections are also shown. The purple band, yν > 2.6 × 10−4 , is excluded by the DELPHI active–sterile-mixing limit. B. Explaining the coincidence through the…
Figure 2. Numerical evolution of the homogeneous QKE in Eq. (B13) at the overdamped point
Figure 3. The Yukawa norm y2 required to reproduce the two nonzero light-neutrino masses as a function of yν, for M = 10 GeV. The solid and dashed curves show nor￾mal and inverted ordering, respectively; the narrow bands use the NuFIT 6.1 online update 3σ ranges of the mass splittings [93]. The markers denote yν = 10−5 , for which y2 = 9.72 × 10−10 (normal ordering) or 1.63 × 10−9 (in￾verted ordering). With the flavor directions in Eq. (C4), every point on the curves reproduces the PMNS matrix. The purple line indicates the illustrative DELPHI limit on yν used in the main text. We next exami
Figure 4. Thermal-force upper envelopes of the complex-

Figures reproduced from arXiv:2608.26709 by the authors.

References
How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 81 sentences without a confident label

Uses the method or tool of 5 papers
Uses data or values from 4 papers
Cites as background 17 papers
  • We characterize the frozen asymmetry parametrically by the baryon-number chemical potential $μ_B$, [equation] This relation does not specify how the asymmetry was generated: the frozen baryon density may arise, for example, from a pre-existing $B-L$ asymmetry or from a time-dependent bias acting before freeze-out [ref] .

    Baryon and lepton number violation rates across the electroweak crossover · Baryon asymmetry and the baryon-number chemical potential · 0.85

  • In asymmetric-dark-matter scenarios, this relation typically points to a dark-matter mass near the nucleon mass if the two number asymmetries are comparable [ref] .

    Asymmetric Dark Matter: Theories, Signatures, and Constraints · Introduction · 0.90

  • In asymmetric-dark-matter scenarios, this relation typically points to a dark-matter mass near the nucleon mass if the two number asymmetries are comparable [ref] .

    Dark Matter from Baryon Asymmetry · Introduction · 0.90

Discussion

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