Minimal Axiogenesis Overview

• Minimal axiogenesis is a class of axion-driven baryogenesis models that uses axion rotation to generate baryon asymmetry via Standard Model sphaleron processes.
• Different models minimize various elements such as low-energy operators, field content, or cosmological conditions, leading to distinct theoretical and experimental predictions.
• Key tensions include balancing successful baryogenesis with dark matter overproduction and maintaining high-quality PQ symmetry despite necessary explicit breaking.

Minimal axiogenesis is the class of axion-driven baryogenesis scenarios that tries to explain the baryon asymmetry with the smallest possible additional structure, but the literature uses “minimal” in more than one sense. In the original QCD-axion proposal, axiogenesis means baryogenesis sourced by a rotating axion background, with $\theta \equiv a/f_a$, a nonzero $\dot\theta$ acting as an effective chemical potential, and Standard Model QCD and electroweak sphaleron transitions converting the resulting charge bias into baryon number (Co et al., 2019). Later papers use the same label for a low-energy effective theory containing only the PQ sector, the Standard Model, and the Weinberg operator (Co et al., 2020), for a single-field cosmological construction with Hubble-induced and Planck-suppressed PQ-breaking terms (Co et al., 2023), and, by contrast, for analyses concluding that the truly minimal one-axion realization is not self-consistent without extra dissipation or extra axionic structure (Asadi et al., 19 Nov 2025).

1. Terminological scope and core definitions

At the level common to the literature, axiogenesis is baryogenesis from axion rotation. Once the radial mode has settled, the PQ charge density is

$n_{\rm PQ}=\dot\theta\, f_a^2,$

and the baryon yield is often written in the compact form

$$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$

with $T_{\rm EW}\simeq 130~{\rm GeV}$ in the electroweak-sphaleron realization (Co et al., 2019, Badziak et al., 2023). In the fuller treatment of the QCD-anomaly chain, the target value emphasized for successful electroweak-era baryogenesis is

$\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$

which is presented as the central benchmark for any realization of axiogenesis (Asadi et al., 19 Nov 2025).

The phrase “minimal axiogenesis” is therefore not a single model name but a family resemblance. Different papers minimize different ingredients.

Sense of “minimal”	Representative paper	Minimal ingredient set
Truly minimal QCD-axion axiogenesis	(Co et al., 2019)	One QCD axion, SM sphalerons, early explicit PQ breaking
Minimal EFT lepto-axiogenesis	(Co et al., 2020)	PQ field, Standard Model, Weinberg operator
Minimal single-field cosmology	(Co et al., 2023)	One complex PQ field, Hubble-induced terms, Planck-suppressed PQ breaking
Minimal SUSY KSVZ realization	(Kawamura et al., 2021)	One PQ field, KSVZ vector-like fields, type-I seesaw
Minimal gauge extension	(Harigaya et al., 2021)	QCD axion plus $SU(2)_R$ sphalerons
Minimal standard axion sector with fine-tuned magnetogenesis	(Co et al., 2022)	DFSZ/KSVZ axion sector, CPI/helical hypermagnetic fields

This suggests that “minimality” is being applied to distinct layers: low-energy operator content, visible-sector field content, cosmological initial conditions, or the amount of extension needed to rescue the original one-field picture.

2. The original one-axion construction

The original proposal “Axiogenesis” formulates the minimal scenario as a standard PQ sector plus the Standard Model, supplemented by an early-universe source of explicit PQ breaking that torques the PQ field and initiates rotation (Co et al., 2019). The complex PQ-breaking scalar is written as

$P=\frac{1}{\sqrt{2}}(S+f_a)\, e^{i a/f_a},$

with $S$ the radial mode and $a$ the axion. In the concrete toy realization, the radial potential is

$\dot\theta$0

and the rotation is generated by a higher-dimensional PQ-breaking operator

$\dot\theta$1

that is important when $\dot\theta$2 is large and becomes negligible later (Co et al., 2019).

The baryogenesis module is intentionally spare. The PQ asymmetry stored in the rotation is communicated to the plasma through QCD and electroweak sphalerons, giving

$\dot\theta$3

with $\dot\theta$4 in the supplement-level discussion summarized in the paper’s details (Co et al., 2019). In this strict version, no extra baryon-violating sector is required, and no extra axion-like field is invoked.

The same paper already identifies the central cosmological tension. The rotation needed for successful baryogenesis tends to delay QCD-era trapping and enhance the axion relic abundance. Its parametric estimate is

$\dot\theta$5

so the original minimal picture works most easily only at very small $\dot\theta$6, with the paper stressing the hadronic-window region around $\dot\theta$7, or else with an enhanced $\dot\theta$8 or a raised sphaleron-freeze-out temperature $\dot\theta$9 (Co et al., 2019).

3. Why the truly minimal QCD-axion picture is now regarded as obstructed

The sharpest critique is given in “Axiverse Baryogenesis,” which defines the minimal QCD axion scenario as one axion that simultaneously solves strong CP, provides the rotating background at the electroweak epoch, and later constitutes the dark matter (Asadi et al., 19 Nov 2025). In that analysis, the anomaly chain is explicit: the QCD chiral anomaly ties the rolling axion to QCD topological transitions, electroweak $n_{\rm PQ}=\dot\theta\, f_a^2,$0 sphalerons convert the induced asymmetry into baryon number, and the same topological transitions feed back into the axion equation of motion as friction. Yet the resulting Standard Model friction is parametrically too weak: their figure shows $n_{\rm PQ}=\dot\theta\, f_a^2,$1 in the SM is orders of magnitude below unity, so the QCD axion’s rotation is not appreciably damped between $n_{\rm PQ}=\dot\theta\, f_a^2,$2 and the QCD epoch (Asadi et al., 19 Nov 2025).

The paper’s most concrete conclusion is that if the axion velocity is large enough at electroweak freeze-out to generate the observed baryon asymmetry, then “this same motion overproduces axion dark matter by two to three orders of magnitude” (Asadi et al., 19 Nov 2025). The corresponding diagnosis is stated directly: in the minimal QCD axion scenario, consistent axiogenesis cannot be achieved, and the one-field setup “either underproduces baryons or overproduces dark matter” (Asadi et al., 19 Nov 2025).

A second obstruction is the sharpened PQ-quality problem. In the one-axion kinetic-misalignment implementation, the initial angular velocity requires explicit PQ breaking large enough to spin up the field after inflation, but the same symmetry must remain sufficiently exact today to solve strong CP. The paper phrases the tension as follows: “the initial velocity necessary for kinetic misalignment demands explicit PQ breaking, reintroducing the axion quality problem, generating an unacceptably large effective QCD $n_{\rm PQ}=\dot\theta\, f_a^2,$3 parameter today” (Asadi et al., 19 Nov 2025).

A third obstruction appears when one tries to repair overclosure with a single extra confining sector coupled to the same axion. The paper argues that a new confining gauge group generally has its own $n_{\rm PQ}=\dot\theta\, f_a^2,$4, so the total potential becomes a sum of misaligned periodic terms and generically shifts the vacuum away from the CP-conserving point, spoiling the strong-CP solution (Asadi et al., 19 Nov 2025).

This negative reassessment is reinforced, from a different angle, by “Baryogenesis from Decaying Magnetic Helicity in Axiogenesis.” That analysis keeps the standard QCD axion sector and kinetic misalignment, but shows that the induced fermion asymmetries or direct hypercharge couplings typically generate helical hypermagnetic fields. If the chiral plasma instability is fully efficient, the paper estimates

$n_{\rm PQ}=\dot\theta\, f_a^2,$5

far above the observed $n_{\rm PQ}=\dot\theta\, f_a^2,$6, so the minimal scenario survives only on a finely tuned boundary where the CPI is marginal rather than fully efficient (Co et al., 2022). In that sense, minimality can be preserved, but only as a “minimal, albeit fine-tuned” setup (Co et al., 2022).

4. Lepto-axiogenesis and single-field cogenesis as alternative minimalities

A different branch of the literature preserves minimality by changing the asymmetry-conversion channel rather than insisting on the original weak-scale electroweak-sphaleron implementation. “Lepto-Axiogenesis” formulates a low-energy effective picture in which the rotating PQ condensate supplies the CP-violating source and out-of-equilibrium dynamics, while the only explicit $n_{\rm PQ}=\dot\theta\, f_a^2,$7-violating ingredient is the Weinberg operator

$n_{\rm PQ}=\dot\theta\, f_a^2,$8

The resulting sequence is PQ rotation $n_{\rm PQ}=\dot\theta\, f_a^2,$9 Higgs and lepton-chirality asymmetries $$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$0 Weinberg-operator conversion into $$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$1 $$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$2 electroweak sphaleron conversion into baryon number (Co et al., 2020). In the quadratic/SUSY regime, the baryon asymmetry becomes largely controlled by the PQ soft mass scale,

$$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$3

which the paper presents as a particularly predictive sense of minimal axiogenesis (Co et al., 2020).

“Axion cogenesis without isocurvature perturbations” adopts yet another notion of minimality. Its irreducible ingredients are one complex PQ field, Hubble-induced mass terms, Planck-suppressed explicit PQ breaking active only when the PQ field sits near $$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$4, and standard reheating with at most a mild assumption about thermalization (Co et al., 2023). In that model the PQ field is Planckian during inflation, the angular mode is heavy with $$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$5 or larger, isocurvature is exponentially damped, and the dangerous post-inflationary “roulette”-type domain-wall problem is avoided (Co et al., 2023). The same initial rotation can produce dark matter and baryogenesis, but the paper finds that ordinary electroweak-scale axiogenesis lies mostly outside the viable QCD-axion band, whereas lepto-axiogenesis is more efficient and leads to the advertised prediction that the QCD axion mass must exceed $$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$6, corresponding to

$$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$7

for successful cogenesis (Co et al., 2023).

A concrete supersymmetric realization of this alternative minimality is “Lepto-axiogenesis in minimal SUSY KSVZ model.” Its claim to minimality is that only one PQ chiral superfield and one pair of KSVZ vector-like fields are added to the MSSM, together with the type-I seesaw sector. The PQ field is stabilized radiatively, not by introducing extra PQ-sector stabilizers, and the same field stores the PQ charge and sources lepto-axiogenesis (Kawamura et al., 2021). The paper’s headline result is that the observed baryon asymmetry is reproduced for

$$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$8

with viable $$Y_B = c_B \left(\frac{T_{\rm EW}}{f_a}\right)^2 Y_{\rm PQ}, \qquad Y_{\rm PQ}=\frac{\dot\theta\, f_a^2}{s},$$9 around $T_{\rm EW}\simeq 130~{\rm GeV}$0 (Kawamura et al., 2021).

5. Minimal extensions that repair efficiency or dissipation

One way to salvage axiogenesis without abandoning the basic one-rotation logic is to modify the baryon-violating epoch. “Axiogenesis from $T_{\rm EW}\simeq 130~{\rm GeV}$1 phase transition” keeps the QCD axion rotation and kinetic misalignment, but raises the freeze-out temperature by replacing the electroweak bottleneck with $T_{\rm EW}\simeq 130~{\rm GeV}$2 sphalerons (Harigaya et al., 2021). The paper derives the characteristic relation

$T_{\rm EW}\simeq 130~{\rm GeV}$3

and therefore a corresponding prediction for $T_{\rm EW}\simeq 130~{\rm GeV}$4 as a function of $T_{\rm EW}\simeq 130~{\rm GeV}$5 (Harigaya et al., 2021). However, it also shows that the purely minimal left-right matter content is insufficient, because $T_{\rm EW}\simeq 130~{\rm GeV}$6 sphalerons violate only $T_{\rm EW}\simeq 130~{\rm GeV}$7, and the resulting asymmetry is washed out by $T_{\rm EW}\simeq 130~{\rm GeV}$8 sphalerons unless extra chiral or vector-like fermions are added (Harigaya et al., 2021). The construction is thus minimal at the gauge level, but not in absolute matter content.

A second repair strategy is to keep baryogenesis unchanged and add a dissipative sink for the post-baryogenesis axion rotation. “Dark Matter and Baryon Asymmetry from Monopole-Axion Interactions” explicitly describes its novelty in those terms: the baryogenesis part is “standard minimal axiogenesis,” while the modification is a post-baryogenesis dissipation mechanism based on dark monopoles and dyonic level transitions (Co et al., 13 Nov 2025). The key anomalous interaction is

$T_{\rm EW}\simeq 130~{\rm GeV}$9

and the dissipation rate is summarized by

$\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$0

In benchmark cases the dissipation temperature is estimated as

$\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$1

and the final conclusion is that successful baryogenesis plus acceptable dark matter prefers

$\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$2

(Co et al., 13 Nov 2025). The paper is explicit that this is a minimal extension of minimal axiogenesis, not a minimal field-content completion.

The hypermagnetic-helicity scenario occupies an intermediate position. “Baryogenesis from Decaying Magnetic Helicity in Axiogenesis” does not add a dedicated baryogenesis sector; instead it argues that the axion-induced chiral asymmetries generically seed CPI-driven helical hypermagnetic fields, which then dominate baryogenesis at the electroweak transition (Co et al., 2022). Because fully efficient CPI vastly overproduces baryons, the successful region is a narrow boundary where the instability is only marginally efficient, and in supersymmetric realizations this fixes the radial PQ mass or the soft SUSY-breaking scale rather sharply (Co et al., 2022).

6. Astrophobic and axiverse reformulations

A distinct attempt to rescue the original low-$\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$3 window is the “Naturally astrophobic QCD axion” model. Its premise is that minimal axiogenesis requires a decay constant below the standard astrophysical lower bounds, so the relevant visible couplings must be suppressed. The paper argues that appropriate PQ charges can suppress couplings to nucleons, electrons, and muons, that a reanalysis of next-to-leading-order nucleon and photon couplings allows

$\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$4

and that if the electromagnetic anomaly satisfies $\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$5, the photon coupling is suppressed enough to permit

$\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$6

so that minimal axiogenesis works (Badziak et al., 2023). At the same time, the paper is explicit that its minimal model has

$\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$7

and is not compatible with minimal axiogenesis; viability requires non-minimal charge assignments giving, for example, $\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$8 or $\dot\theta(T_{\rm EW}) \simeq 5~\mathrm{keV},$9 (Badziak et al., 2023). In this regime the QCD axion mass is above $SU(2)_R$0, and direct detection via axion absorption becomes the relevant experimental picture (Badziak et al., 2023).

The most systematic non-minimal resolution is “Axiverse Baryogenesis.” Its core claim is that the obstacles found in the strict one-axion scenario are not intrinsic to axiogenesis as such but to forcing one axionic degree of freedom to solve strong CP, be spun up, and be efficiently damped at once (Asadi et al., 19 Nov 2025). The proposed cure is an axiverse with multiple axion-like fields and multiple PQ symmetries, so that the physical QCD axion is a linear combination of fields. In the toy model,

$SU(2)_R$1

with $SU(2)_R$2 providing the baryogenesis-driving rotation and coupling to a dark confining sector that later supplies strong friction (Asadi et al., 19 Nov 2025). The QCD-like state $SU(2)_R$3 can then remain high-quality and contribute subdominant or dominant dark matter, with a preferred scale $SU(2)_R$4 around $SU(2)_R$5–$SU(2)_R$6 and masses up to about $SU(2)_R$7 highlighted as experimentally interesting (Asadi et al., 19 Nov 2025). The paper’s conceptual conclusion is that the tensions are tensions of minimality, not of axiogenesis itself.

7. Status of the subject

The current literature does not support a single, unqualified statement that minimal axiogenesis is either established or excluded. What is much better supported is a more differentiated picture.

The strict one-axion QCD-axion realization introduced in the original “Axiogenesis” remains the cleanest formulation of the idea that a rotating QCD axion can source the baryon asymmetry using only Standard Model anomalous processes (Co et al., 2019). However, later analyses argue that this truly minimal implementation is not generically self-consistent once the baryon yield, the dark-matter abundance, and the PQ-quality requirement are imposed simultaneously (Asadi et al., 19 Nov 2025). This is the strongest current negative result.

At the same time, several nearby notions of minimality remain viable. If “minimal” means minimal low-energy operator content, then lepto-axiogenesis with the Weinberg operator remains a particularly economical framework (Co et al., 2020). If it means a single-field cosmological construction with Hubble-induced terms and transient Planck-scale PQ breaking, then axion cogenesis without isocurvature perturbations provides a viable and sharply predictive alternative, especially in the lepto-axiogenesis branch (Co et al., 2023). If it means minimal extensions of the original weak-scale scenario, then the literature offers several concrete repair mechanisms: raised sphaleron freeze-out from $SU(2)_R$8 (Harigaya et al., 2021), hypermagnetic-helicity baryogenesis on a fine-tuned CPI boundary (Co et al., 2022), post-baryogenesis damping by dark monopoles (Co et al., 13 Nov 2025), or a multi-axion axiverse in which the jobs of quality, rotation, and dissipation are separated (Asadi et al., 19 Nov 2025).

A common misconception is therefore that “minimal axiogenesis” denotes one settled model. In the arXiv literature it instead denotes a contested program with several internal meanings. The most stable technical lesson is that the benchmark

$SU(2)_R$9

remains central across realizations, but the viability of the mechanism depends sensitively on what exactly is being minimized: the visible-sector field content, the low-energy operator basis, the cosmological initial-condition sector, or the amount of new structure added to cure dark-matter overproduction and PQ-quality tensions (Asadi et al., 19 Nov 2025, Co et al., 2020, Co et al., 2023).