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Constraints on Asymmetric Dark Matter Self Annihilation Cross Sections

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Pith's one-line read Asymmetric dark matter's allowed self-annihilation cross section shifts upward in a faster-expanding shear-dominated early universe and downward in a slower Gauss-Bonnet braneworld, relative to standard cosmology.

desk verdict Useful, clearly argued extension of ADM self-annihilation constraints to two non-standard cosmologies, but the headline cross-section limits are compromised by a g* inconsistency and a convention-dependent asymmetry benchmark. read the letter →

arxiv 2505.04056 v1 pith:4BCRDAV6 submitted 2025-05-07 hep-ph

Qiquan Li , Hoernisa Iminniyaz , Fangyu Liu This is my paper · ORCID
classification hep-ph
keywords asymmetricdarkmatterself-annihilationrelicdensityshear-dominateduniverseGauss-BonnetbraneworldBoltzmannequationwinomassfreeze-out
topics Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks how much asymmetric dark matter (ADM) may self-annihilate without erasing the particle–antiparticle asymmetry that sets its relic density, in two nonstandard early-universe cosmologies. It finds that a shear-dominated universe, whose Hubble rate is enhanced over the standard one, freezes out the asymmetry-washout process earlier and permits s-wave self-annihilation cross sections up to about twenty to a hundred times larger than in standard cosmology. A Gauss-Bonnet braneworld, with a weakened Hubble rate, delays freeze-out and forces cross sections several times smaller. These shifts translate into wino-mass lower limits for sneutrino and higgsino ADM that are lower in the shear case and higher in the Gauss-Bonnet case. The paper also gives approximate analytic formulas that reproduce the numerical freeze-out constraints.

What carries the argument

The engine is the asymmetry variable $\Delta_- = Y_\chi - Y_{\bar\chi}$ and its evolution equation $d\Delta_-/dx = -(\lambda/(x^2 A_{s,g}))\langle\sigma_{\chi\chi} v\rangle \Delta_+^{eq}(\Delta_- - \Delta_-^{eq})$, where $A_s = \sqrt{1+x_e^2/x^2}$ for the shear-dominated cosmology and $A_g = (x/x_t)^{2/3}$ for the Gauss-Bonnet braneworld modify the standard Boltzmann rate. $A_s > 1$ slows the washout of the asymmetry, while $A_g < 1$ speeds it up, producing the opposite shifts in the cross-section limits. The companion approximate formulas give the freeze-out point $x_{fw}$ and the surviving asymmetry ratio $R$ in closed form, and the paper shows these reproduce the numerical solution at $R=0.1$ with $R_{\text{approx}} = 0.10$–$0.12$.

What would settle it

A measurement or calculation that fixes the transition temperatures $T_e$ (shear) and $T_t$ (Gauss-Bonnet) relative to the freeze-out temperature $T_{fw}$ would settle the claim: if either transition occurred before freeze-out, the corresponding cross-section and $M_2$ bounds would revert to standard values rather than shift as reported.

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Extended reading notes

Core claim

Under the requirement that the ratio of final asymmetry to initial asymmetry satisfies $R > 0.1$, the paper reports that standard cosmology allows an s-wave self-annihilation cross section $a \lesssim 4.37\times10^{-16}$; the shear-dominated universe allows $a \lesssim 8.84\times10^{-15}$ at $x_e=130$ and $a \lesssim 4.20\times10^{-14}$ at $x_e=630$, while the Gauss-Bonnet braneworld only allows $a \lesssim 1.14\times10^{-16}$ at $x_t=50$ and $a \lesssim 4.57\times10^{-17}$ at $x_t=200$. For the same $R$, the lower limit on the wino mass $M_2$ in the s-wave case shifts from $M_2 \gtrsim 3.5\times10^6$ GeV in standard cosmology to $M_2 \gtrsim 8.3\times10^5$ GeV at $x_e=130$ and $M_2 \gtrsim 3.8\times10^5$ GeV at $x_e=630$ in the shear case, and to $M_2 \gtrsim 7.2\times10^6$ GeV at $x_t=50$ and $M_2 \gtrsim 1.1\times10^7$ GeV at $x_t=200$ in the Gauss-Bonnet case. The same direction of shift holds for p-wave self-annihilation, with similar numerical values.

Load-bearing premise

The nonstandard expansion histories are assumed to last through the entire asymmetry-washout era, switching abruptly at a single transition temperature; if the shear or Gauss-Bonnet phase ended before freeze-out, or transitioned gradually, all quoted limits would shift.

Editorial extensions

If this is right

  • For $R>0.1$, the shear-dominated universe raises the maximum s-wave self-annihilation cross section by a factor of about 20 at $x_e=130$ and about 96 at $x_e=630$ relative to standard cosmology.
  • The Gauss-Bonnet braneworld lowers the same limit by factors of about 3.8 at $x_t=50$ and about 9.6 at $x_t=200$.
  • The wino-mass lower limit for sneutrino and higgsino ADM drops by roughly an order of magnitude in the strongest shear case and rises by roughly a factor of three in the strongest Gauss-Bonnet case.
  • The approximate freeze-out equations give essentially the same cross-section bounds as the full numerical integration, so the constraints do not depend on solving the complete Boltzmann system.
  • Both velocity-independent (s-wave) and velocity-suppressed (p-wave) self-annihilation shift in the same direction, making the qualitative conclusion insensitive to the partial-wave structure.

Reading between the lines

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

  • If the shear-dominated or Gauss-Bonnet phase ended before the asymmetry freeze-out temperature, the quoted bounds would relax back toward standard values; the paper's numbers therefore presuppose that the modified era spans the entire wash-out epoch.
  • Because the direction of the shift is controlled by whether the modified Hubble rate is above or below the standard one, the same two equations can be applied to any cosmology with a known expansion history, giving a quick estimate of whether it loosens or tightens ADM self-annihilation bounds.
  • The $M_2$ bounds around $10^5$–$10^7$ GeV fall in a range where electroweak gaugino searches at colliders could eventually probe them; this is not tested in the paper, but follows from the mass scales it constrains.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper studies the evolution of the relic density of asymmetric dark matter (ADM) when self-annihilation processes are included, in two non-standard cosmological scenarios: a shear-dominated Bianchi type I universe and a Gauss-Bonnet braneworld. Using the Hubble rates of Eqs. (2) and (3), the authors derive the asymmetry evolution equation (11) and solve it both numerically and with a sudden-freeze-out approximation. They find that, for the same final-to-initial asymmetry ratio R, the shear-dominated universe (enhanced H) permits a larger self-annihilation cross section than standard cosmology, while the Gauss-Bonnet braneworld (weakened H) requires a smaller one. They then translate these cross-section bounds into lower limits on the wino mass M2 for sneutrino and higgsino ADM, quoted in Eqs. (16) and (17). The central qualitative ordering is physically transparent and robust to the numerical details.

Significance. If the numerical results are correct, the paper provides concrete, model-dependent constraints: for R > 0.1, the standard-cosmology s-wave limit a ≲ 4.37e-16 is raised to a ≲ 8.84e-15 (xe=130) and a ≲ 4.20e-14 (xe=630) in the shear-dominated universe, and lowered to a ≲ 1.14e-16 (xt=50) and a ≲ 4.57e-17 (xt=200) in the Gauss-Bonnet braneworld. The corresponding M2 lower limits in Eqs. (16)-(17) extend earlier ADM analyses to these non-standard histories. The derivation of Eq. (11) from the coupled Boltzmann equations is clear, and the approximate solution of Eqs. (12)-(13) is a useful check once the g* inconsistency is resolved. The main strength is that the ordering of limits follows directly from A_s > 1 > A_g in Eq. (11), so the qualitative claim does not depend on disputed numerical details.

major comments (4)
  1. [Sec. 2.2, Figs. 1-3] The numerical constraints quoted in the text are not reproducible as written because Fig. 1 fixes g* = 20 while the consistency check in Sec. 2.2 (xfw = 5.86 at a = 4.37e-16 and Rapp = 0.11) and Fig. 3 use g* = 90. With g* = 20, solving Eq. (12) at the quoted standard value a = 4.37e-16 gives xfw ≈ 6.6 rather than 5.86, and Eq. (13) then gives Rapp ≈ 0.06, not the claimed 0.10-0.12. Since the headline limits and the M2 bounds in Eqs. (16)-(17) are read from Fig. 1, this inconsistency affects all quantitative results and must be resolved by recomputing with one stated g* and correcting the figure captions and the consistency check accordingly.
  2. [Sec. 2.2, initial conditions] The initialization Delta_-in = Delta_-eq(1) with mu/T = 1e-9 means that the reported ratio R is dominated by the Boltzmann suppression of the equilibrium asymmetry at freeze-out rather than by the survival of an independently specified input asymmetry. Consequently, the absolute limits such as a ≲ 4.37e-16 are convention-dependent; a different choice of mu/T or xin would shift them, even though the relative ordering between cosmologies would remain. The authors should either justify this initialization as physical or demonstrate how the cross-section and M2 limits change with the initial condition.
  3. [Sec. 2.2, benchmark R > 0.1] The choice R > 0.1 is arbitrary and no sensitivity study is provided. All quoted limits in Sec. 2.2 and Eqs. (16)-(17) use this threshold, so the quantitative constraints depend on an unmotivated criterion. The authors should motivate a physically meaningful minimum R (for example, one consistent with the observed DM asymmetry) or present R-dependent results so that readers can assess how the limits vary with the assumed preserved fraction.
  4. [Eqs. (2)-(3) and Sec. 2.2] The modified Hubble rates are assumed to hold throughout the entire asymmetry-washout epoch, with an abrupt transition to the standard radiation-dominated rate at x_e or x_t. If the shear-dominated or Gauss-Bonnet phase ended before the washout process froze out, or if the transition were gradual, the cross-section and M2 limits would shift. The paper should state the assumed duration of the modified phase relative to the freeze-out point and, ideally, test sensitivity to the transition; otherwise the quoted upper limits are conditional on this unquantified assumption.
minor comments (3)
  1. [Below Eq. (2)] The quantity T_e appearing in x_e = sqrt(g*/g_e^*) m/T_e is not defined precisely; it should be stated explicitly that T_e is the temperature at which the shear energy density equals the radiation energy density.
  2. [Sec. 2.2, near Eq. (13)] There is a typo in the sentence beginning 'When R = 0.1, we fnd...' ('fnd' should be 'find'). The claim that the constraints on a and 6b/x 'must be same' should be phrased more precisely: at fixed R, Eq. (13) fixes xfw and Eq. (12) then fixes the combination ⟨sigma v⟩, which for s-wave and p-wave gives equal effective cross sections at that xfw.
  3. [Fig. 4 and Eqs. (16)-(17)] The M2 limits in Eqs. (16)-(17) are quoted with little explanation of the input spectrum; specifying M1 = M2/2 and tan^2 theta_W = 0.3 in the text is helpful, but the resulting values would benefit from a brief comparison with existing constraints in the standard cosmological case to anchor the non-standard results.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the cross-section and M2 limits are obtained by directly solving a Boltzmann equation with externally specified Hubble rates and fixed inputs; the only self-citation supplies a non-load-bearing approximate method.

full rationale

The central derivation is self-contained. Equation (11) is integrated numerically with fixed inputs (m = 10 GeV, g = 2, mu/T = 1e-9, xe/xt, and the imported Hubble rates of Eqs. (2)-(3)); none of the output cross-section bounds or M2 limits is used as an input, and no parameter is fitted to the target quantities. The qualitative ordering (shear-dominated expansion allows a larger self-annihilation cross section, Gauss-Bonnet braneworld requires a smaller one) follows directly from A_s > 1 > A_g in Eq. (11). Eq. (12), whose method is taken from the authors' previous work Ref. [21], is used only for an approximate consistency check and for a model-independent remark, not to generate the quoted numerical bounds. Eq. (13) is the standard freeze-out estimate of the asymmetry ratio and is not a fitted input. No self-definitional, fitted-input-called-prediction, or uniqueness-importing step is present. The apparent g* = 20 versus g* = 90 discrepancy between Fig. 1 and Fig. 3 is a numerical-consistency concern, not a circularity.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central calculation rests on the standard relic-density formalism plus the two modified Hubble rates imported from prior literature. The free parameters are the scenario parameters (g*, m, xe, xt), the chosen initial condition μ/T, and the order-unity constant ξ. No new entities are introduced. The main weight falls on the assumption that the non-standard Hubble rates apply throughout the washout epoch.

free parameters (8)
  • chemical potential to temperature ratio μ/T at x_in=1 = 1e-9
    Set as the initial condition for the numerical solution of Eq. (11) in Sec. 2.2. R is normalized to the initial asymmetry, so the cross-section limits are insensitive to this choice, but it is still a chosen input.
  • freeze-out constant ξ = 1
    Order-unity numerical constant in the approximate freeze-out condition Eq. (12), taken as ξ=1.
  • effective relativistic degrees of freedom g* = 20 (Fig. 1) and 90 (Figs. 2-4)
    Input governing λ and the expansion rate. The paper uses g*=20 in Fig. 1 and g*=90 in Figs. 2-4. Changing g* shifts the quoted cross-section limits.
  • ADM mass m = 10 GeV
    Dark matter mass used in all numerical examples (m=10 GeV); chosen for illustration and affects λ and the x scaling.
  • shear factor xe = 130, 630
    Shear factor in Eq. (2), scanned over the values 130 and 630 from prior work. The cross-section upper limits are quoted for each value.
  • Gauss-Bonnet transition xt = 50, 200
    Transition parameter in Eq. (3), scanned over 50 and 200. The cross-section upper limits are quoted for each value.
  • wino-bino mass ratio M1/M2 = 1/2
    Assumed to be 1/2 in Sec. 2.3 to convert the sneutrino/higgsino cross-section formulas into wino mass constraints.
  • tan^2 θ_W = 0.3
    Taken as 0.3 in Sec. 2.3, a standard electroweak input, to evaluate the wino mass constraints.
assumptions (6)
  • domain assumption ADM particles and antiparticles are in thermal and kinetic equilibrium during the washout epoch, so the equilibrium densities and Δ+ ≈ Δ_eq+ hold.
    Used to reduce Eq. (9) to Eq. (11) in Sec. 2.2. Standard sudden-freeze-out and equilibrium assumptions for relic density calculations.
  • domain assumption The shear-dominated Hubble rate Hs = H sqrt(1 + x_e^2/x^2) describes the expansion during the ADM freeze-out epoch.
    Eq. (2), cited from Refs. [26,27]. This is the key input that changes the freeze-out time relative to standard cosmology.
  • domain assumption The Gauss-Bonnet braneworld Hubble rate Hg = H (x/x_t)^(2/3) describes the expansion during the ADM freeze-out epoch.
    Eq. (3), cited from Ref. [31]. The weakened Hubble rate relative to standard cosmology produces the opposite shift in cross-section limits.
  • domain assumption The self-annihilation cross sections of particles and antiparticles are equal, ⟨σχχ v⟩ = ⟨σχ̄χ̄ v⟩.
    Stated in Sec. 2.1 below Eq. (4). Used to write the single equation for Δ-.
  • domain assumption The sudden-freeze-out approximation for the washout process: R ≈ Δ_eq^-(x_fw)/Δ_eq^-(1) = x_fw^(3/2) e^(-x_fw)/e^(-1).
    Eq. (13), adapted from Ref. [21]. Used for the analytic estimates of freeze-out points and for translating cross-section limits to M2 constraints.
  • standard math The thermally averaged cross-section can be expanded as ⟨σv⟩ = a + 6b/x for non-relativistic particles.
    Eq. (7), standard partial-wave expansion for s-wave and p-wave annihilation.

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Pith. "Pith review of Constraints on Asymmetric Dark Matter Self Annihilation Cross Sections." pith.science (2026). https://pith.science/paper/4BCRDAV6

@misc{pith2026250504056,
  author       = {Pith},
  title        = {Pith review of: Constraints on Asymmetric Dark Matter Self Annihilation Cross Sections},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4BCRDAV6}},
  note         = {Machine review of arXiv:2505.04056}
}
abstract

We investigate the evolution of the relic density for asymmetric dark matter incorporating self annihilation processes in both the shear-dominated universe and Gauss-Bonnet braneworld. Under the same conditions where the ratio of final asymmetry to the initial asymmetry $ R \equiv \Delta_{-\infty}/\Delta_{\text{in}} $ is identical, the shear-dominated universe, due to its enhanced Hubble expansion rate, leads to an earlier freeze-out point of wash-out asymmetry process and allows a higher upper limit on the self annihilation cross section. Conversely, the Gauss-Bonnet braneworld, with a weakened Hubble expansion rate, delays the freeze-out point and permits a lower upper limit on the self annihilation cross section. We further constrain the wino mass $M_2$ for sneutrino and higgsino asymmetric dark matter in both scenarios, showing that, compared to the standard model, the lower limit of $M_2$ is smaller in the shear-dominated universe but higher in the Gauss-Bonnet braneworld.

Figures

Figures reproduced from arXiv: 2505.04056 by the authors.

Figure 1
Figure 1. The ratio of final asymmetry to the initial asymmetry R = ∆−∞/∆in as a function of a and b for the shear-dominated universe and Gauss-Bonnet braneworld. Here, (a) and (c) correspond to s-wave annihilation, while (b), (d) represent p-wave annihilation and m = 10 GeV, g = 2, g∗ = 20. From Eq. (7) and above conditions, we present in [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. The ratio of final asymmetry to the initial asymmetry R = ∆−∞/∆in as a function of a for the shear-dominated universe and Gauss-Bonnet braneworld. Here m = 10 GeV, g = 2, g∗ = 90. (c) and (d) correspond to those in the Gauss-Bonnet braneworld. In [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. The inverse-scaled freeze-out point xfw as a function of a and b. Here m = 10 GeV, g = 2, g∗ = 90. the shear-dominated universe and Gauss-Bonnet braneworld can be derived as xfw = ln 0.29 ξλghσχχvi g∗x 1/2As,g [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The ratio of final asymmetry to the initial asymmetry R = ∆−∞/∆in as a function of the wino mass M2. Here m = 10 GeV, g = 2, g∗ = 90. conditions M1 ≃ M2/2, tan2 θW ≈ 0.3, and Eq. (11), we present the function relationship between the wino mass M2 and R in [PITH_FULL_I…

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