Antinuclei from Primordial Black Holes

Agnese Tolino; David Maurin; Fiorenza Donato; Lorenzo Stefanuto; Valentina De Romeri

REVIEW 2 major objections 5 minor 129 references

Antinuclei from Primordial Black Holes

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read AMS-02 antiproton data set upper bounds on the local density of evaporating primordial black holes, and any future antideuteron detection would be a new-physics signal only partly attributable to PBH evaporation.

desk verdict Solid, transparent update of PBH antinuclei constraints; the memory-burden caveat is the one thing a referee should push on. read the letter →

arxiv 2505.04692 v2 pith:QRFS2SEU submitted 2025-05-07 hep-ph astro-ph.HE

Valentina De Romeri , Fiorenza Donato , David Maurin , Lorenzo Stefanuto , Agnese Tolino This is my paper · ORCID

classification hep-phastro-ph.HE PACS 98.70.Sa95.35.+d04.70.Dy

keywords primordialblackholesHawkingevaporationantiprotonsantideuteronscosmicraysdarkmatterlognormalmassdistributionAMS-02

topics Dark Matter

open problems 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 of the Milky Way's dark matter could be made of light primordial black holes (PBHs) that are evaporating today, and answers with a tighter number using AMS-02 antiproton measurements. It computes the antiproton and antideuteron fluxes from Hawking evaporation for a lognormal PBH mass distribution, propagates them through Galactic transport models, and compares the result with the measured antiproton flux. The central result is an upper bound on the local PBH density: for a critical mass $\mu_c \simeq 5\times 10^{14}$ g, the allowed density ranges from about $3.5\times10^{-12}$ to $8.1\times10^{-11}$ GeV cm$^{-3}$, depending on the width $\sigma$ of the mass distribution. A second result is that all primary PBH antinuclei fluxes share a universal spectral shape, so a future antideuteron detection would not be attributable to PBH evaporation alone; it would be a signal of new physics whose PBH component is limited by the antiproton bounds.

What carries the argument

The central object is the evolved mass distribution of evaporating primordial black holes. The paper assumes semi-classical Hawking evaporation, $dM/dt = -\alpha(M)/M^2$, holds for the entire PBH lifetime, and shows that any extended distribution develops a common low-mass tail proportional to $M^2$ below about $10^{13}$ g; that tail, made of PBHs evaporating now, dominates antinucleus production. The source term factorizes as $Q(r,z,E) = q(E)\,\tilde{\rho}(r,z)$, separating the energy spectrum from the spatial density profile. Antideuteron formation is handled with a coalescence model based on the Wigner formalism, calibrated on collider data. The upper bounds come from a likelihood-ratio analysis of the antiproton data that treats the Galactic halo height as a nuisance parameter and uses a covariance matrix encoding experimental and theoretical uncertainties.

What would settle it

Detect antideuterons: the paper predicts a maximum antideuteron flux obtained by saturating the antiproton bound, so an observed rate above that maximum excludes PBH evaporation as the source, while a clear non-detection at the predicted peak energy would tighten the density bound. A second check is whether PBHs near $5\times10^{14}$ g still evaporate on the Universe's timescale; if memory-burden effects make them live longer, the predicted fluxes disappear.

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Extended reading notes

Core claim

The paper's central claim is that AMS-02 antiproton data set strong upper bounds on the local density of Galactic primordial black holes with a lognormal mass distribution, and that these bounds are comparable to or slightly stronger than constraints from other messengers. For the critical mass $M^* \simeq 5\times 10^{14}$ g, the mass of a PBH evaporating completely today, the maximum allowed density is $3.5\times10^{-12}$, $2.2\times10^{-11}$, $4.4\times10^{-11}$, and $8.1\times10^{-11}$ GeV cm$^{-3}$ for widths $\sigma = 0.1, 0.5, 1, 2$, respectively. Translated into a fraction of the local dark-matter density, the strongest limit is $f_{\mathrm{PBH}} < 10^{-11}$ at $\sigma = 0.1$ and $\mu_c = M^*$. The same calculation yields a universal spectral shape for every primary PBH antiproton and antideuteron flux, so the antiproton bound fixes the normalization of the antideuteron flux as $\mu_c$ and $\sigma$ vary. From this the authors conclude that a future antideuteron detection would clearly be a signal of new physics, but one that PBH evaporation alone cannot fully explain.

Load-bearing premise

The load-bearing premise is that black holes evaporate exactly as in the semi-classical Hawking calculation, with no quantum memory-burden back-reaction slowing the final stage; if evaporation is slower, the mass evolution, source spectra, and all derived density bounds would change.

Editorial extensions

If this is right

At $\mu_c = M^* \simeq 5\times10^{14}$ g and $\sigma=0.1$, the AMS-02 antiproton data exclude PBHs as the whole of local dark matter, with $f_{\mathrm{PBH}} < 10^{-11}$.
Because all primary fluxes share one spectral shape, the antiproton bounds translate directly into a maximum antideuteron flux: it exceeds the secondary background below a few GeV/n but stays near the sensitivity of upcoming detectors.
If an antideuteron is measured, the paper's conclusion is that it is a clear new-physics signal whose PBH component cannot account for the full event rate.
Fixing the lognormal distribution, the same bounds imply a local PBH explosion rate of at most about $7\times10^{-5}$ pc$^{-3}$ yr$^{-1}$, an improvement of more than two orders of magnitude over an earlier estimate.
Broader lognormal widths weaken the density bound but extend the reach to larger critical masses, probing the asteroid-mass region where PBHs could conceivably be all of the dark matter.

Reading between the lines

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

The universal spectral shape implies that a template search could extract the PBH component from low-energy antiproton data without fitting the full lognormal parameters, because only the normalization depends on the mass-distribution combination.
The same universality predicts exactly where to look: the antiproton peak sits near 1-2 GeV and the antideuteron peak near a few hundred MeV/n, so future sub-GeV measurements at solar minimum would either sharpen the bound or reveal residuals.
If the memory-burden effect slows evaporation as recent proposals suggest, the semi-classical assumption would break before the final stage; the predicted fluxes and bounds would shift, and an antideuteron detection would need a different interpretation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a careful, credible update of PBH antinuclei constraints. The genuinely new pieces are the lognormal mass distribution for antinuclei, the use of the 2021 AMS-02 antiproton sample with a covariance-based likelihood, and the explicit demonstration that all primary PBH antinuclei fluxes collapse to one spectral shape up to a normalization. That last point is more than a curiosity — it lets the AMS-02 antiproton bound be rescaled directly to antideuterons, which is why the forecast in Sec. V is as clean as this business gets. The central claim holds: within standard Hawking evaporation, AMS-02 antiprotons exclude PBHs as all of the local dark matter for the lognormal parameter space, and a future antideuteron detection would be mostly new physics beyond PBH evaporation.

The machinery is assembled honestly. BlackHawk, CosmiXs, and USINE are public; the propagation setup follows the recent AMS-02 antiproton analysis of Ref. [91]; the covariance matrix carries the main systematics. The paper flags its own caveats: no memory burden, the single-jet division for CosmiXs fragmentation functions, and the force-field solar modulation assumption. That is the right scientific posture.

Soft spots, in proportion. The memory-burden point is the main one. The low-mass tail that actually produces antinuclei is generated under dM/dt ∝ M^{-2} up to the Planck scale. If memory burden slows evaporation, that tail changes and the bounds could weaken by orders of magnitude. The paper mentions this but does not quantify it. Not fatal — the assumption is standard and clearly stated — but a referee should ask how the headline upper limits respond to a slowdown. The factor-two difference between the 2016 and 2021 AMS-02 datasets also deserves more comment; the reader should know which dataset is doing the heavy lifting. The custom convolution code is not released. Everything else is public, so this is minor, but the authors should be asked to share it.

Citation pattern is clean. Self-citations point to the actual propagation and antinuclei tools used, and the comparison with other messengers is properly qualified. The paper overstates nothing.

Who this is for: anyone in PBH dark matter, cosmic-ray antinuclei, or GAPS/AMS-02 science. It deserves a serious referee — send it out.

Referee Report

2 major / 5 minor

Summary. The paper computes Galactic antiproton and antideuteron fluxes from Hawking evaporation of primordial black holes (PBHs) with a lognormal initial mass distribution, using public codes (BlackHawk, CosmiXs, USINE) and state-of-the-art propagation models. It then compares the predicted antiproton flux to AMS-02 data using the likelihood framework of Ref. [91] and derives 95% CL upper limits on the local PBH density as a function of the lognormal peak mass and width. The authors find that AMS-02 antiproton data exclude PBH densities far below those probed by other messengers, translate the bounds into fractions of local dark matter and into a local PBH explosion rate, and argue that the primary PBH antinuclei fluxes share a universal spectral shape. They also compute the maximal antideuteron flux allowed by the antiproton bounds and conclude that a future AMS-02 or GAPS antideuteron detection would be a new-physics signal that could only partly be explained by PBH evaporation.

Significance. If the results hold, the paper provides competitive and robust constraints on PBH abundances from a single well-measured cosmic-ray channel, and it produces a falsifiable prediction: any detected antideuteron flux above the secondary background would require non-PBH new physics. The analysis is built on public, reproducible tools and follows an established statistical pipeline, which is a genuine strength. The claimed universal spectral shape of PBH antinuclei fluxes is a useful simplification that connects the antiproton bounds to antideuteron forecasts in a transparent way. The central claims are not circular: the PBH density limits come from AMS-02 data, and the antideuteron prediction imports those limits as an input.

major comments (2)

[Sec. II A (after Eq. (6)) and Sec. IV B] The headline constraints, including the values quoted in Sec. VI (rho_PBH < 3.5e-12, 2.2e-11, 4.4e-11, 8.1e-11 GeV/cm3 for sigma = 0.1, 0.5, 1, 2 at mu_c = M*), are derived from standard Hawking evolution dM/dt = -alpha(M)/M^2 assumed to hold for the entire PBH lifetime, and from the resulting universal M^2 low-mass tail shown in Fig. 1. The paper explicitly notes that memory-burden backreaction (Refs. [76-82]) could slow evaporation and extend PBH lifetimes, but it does not quantify the effect on Eq. (9), Eq. (12), the UL curves in Fig. 4, the explosion-rate bound in Eq. (21), or the antideuteron forecast in Sec. V. If memory burden is operative before PBHs of initial mass ~5e14 g complete evaporation, the low-mass tail that dominates antinuclei production would be suppressed and the quoted limits could be substantially weakened or shifted. I recommend adding a quantitative estimate, for example using a minimal memory-burden parametrization with a transition mass or occupation number as in Refs. [79-82], and/or stating prominently that the constraints apply only within standard Hawking evaporation and are not robust to memory-burden scenarios.
[Sec. IV A, Eq. (18) and footnote 4] The likelihood uses a covariance matrix C taken from the secondary-antiproton analysis of Ref. [96], with the justification that the PBH primary flux is subdominant. At the 95% upper limit, however, the primary flux is by construction large enough to be constrained, and its normalization inherits the modeling choices of footnote 4 (division by 2 for the single-jet treatment) as well as uncertainties in the Hawking spectra and fragmentation functions. A factor-2 error in the single-jet approximation would directly rescale all the upper limits in Fig. 4 by a factor of 2. Please quantify this systematic, or state the resulting uncertainty band on the quoted ULs, so that the comparison with other messengers in Fig. 5 is not read as more precise than the underlying source modeling allows.

minor comments (5)

[Sec. IV B, paragraph after Fig. 4] The text says that adding simulated GAPS data would 'increase the upper bounds by a factor 2', while the conclusions say GAPS 'should improve the above limits by a factor 2'; please clarify whether the combined AMS-02 + GAPS upper limit is larger or smaller.
[Sec. V, paragraph after Fig. 6] The sentence about 'fusion modeling of the antinuclei to for and antideuteron' appears garbled and should be rephrased.
[Footnote 4] The phrase 'we assume the second one not to escape the PBH' is unclear; it should be stated more precisely that one of the two jets is effectively reabsorbed and only a single jet contributes to the hadronization spectrum.
[Sec. V and Fig. 5] The text states the strongest f_PBH bound is at mu_c = M*, but the left panel of Fig. 5 starts at 1e15 g; please make the displayed range and the quoted value consistent.
[Eq. (18)] The symbol L is used both for the halo half-height and for the log-likelihood function, which makes the notation in Eq. (18) confusing; consider using a calligraphic symbol for the likelihood.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the PBH density bounds and antideuteron forecast are derived from external AMS-02 data and public codes, with no fitted quantity renamed as a prediction.

full rationale

Walking the derivation chain, the antinuclei source spectra are computed from the Hawking emission formulas (Eqs. 6-12) using public tools (BlackHawk, CosmiXs, USINE), without defining the signal in terms of the data being constrained. The only fitted parameter, rho_PBH, is constrained by a likelihood-ratio analysis (Eqs. 18-19) against external AMS-02 antiproton data, and the reported upper limits are outputs of that fit. The antideuteron flux in Sec. V is not fitted to antideuteron measurements; it is a projection obtained by inserting the antiproton-derived 95% CL upper limit on rho_PBH into the independently propagated model, which is a standard cross-channel forecast rather than a circular prediction. The reuse of the covariance matrix and secondary fluxes from Refs. [91,96] (some co-authored by the present authors) is not load-bearing circularity: those quantities are publicly documented, derived from AMS-02 data and the open USINE code, and they do not presuppose any PBH signal. The paper's explicit assumption that semi-classical Hawking evaporation holds for the entire PBH lifetime (Sec. II A) is a model assumption and a genuine correctness risk, especially in light of memory-burden back-reaction, but it is not a circular step: Eq. (6), the evolved-mass tail, and the derived bounds are not defined in terms of the AMS-02 data they constrain. Self-citations are frequent but do not reduce the central claim to their own assertions.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard Hawking evaporation, on the lognormal mass function as a phenomenological input, on the BIG propagation setup and covariance matrix from prior fits, and on the single-jet approximation for CosmiXs fragmentation. No new particles, forces, or entities are introduced. The main unvalidated ingredient is the absence of memory-burden effects, which the authors flag themselves.

free parameters (2)

lognormal peak mass mu_c = scanned over 1e10 to 1e20 g
Central mass of the lognormal PBH distribution, Eq. (2); bounds are presented as functions of it and it is scanned rather than fitted to the antiproton data.
lognormal width sigma = 0.1, 0.5, 1, 2
Width of the lognormal mass distribution; reference values chosen by hand; the UL on rho_PBH varies by orders of magnitude across these values.

assumptions (6)

domain assumption Semi-classical Hawking evaporation is valid throughout the PBH lifetime, without memory-burden back-reaction.
Used in Eqs. (5)-(8) and to evolve the mass distribution via Eq. (9). The paper explicitly notes this may be inconsistent and that memory burden effects are under debate (Sec. II A).
domain assumption CosmiXs fragmentation functions for annihilating DM of mass m_DM = E_i describe the hadronization of Hawking-emitted quarks and gluons, with the spectrum divided by 2 for a single jet.
Used in Sec. II B to compute source spectra; the factor-2 and single-jet assumption is an approximation acknowledged by the authors.
domain assumption The Galactic cosmic-ray propagation model BIG, and to a lesser extent SLIM and QUAINT, with parameters from fits to nuclear data, and the covariance matrix from Ref. [96], are applicable to primary antiprotons and antideuterons.
Used in Secs. III and IV; the transport model is inherited from previous analyses rather than re-fit here.
ad hoc to paper The PBH mass distribution is lognormal per Eq. (2), rather than power-law or monochromatic.
The main results are all for the lognormal form; the paper states it is a phenomenological description motivated by a symmetric peak in the inflationary power spectrum, but other production mechanisms give different forms.
domain assumption The local DM density rho_sun = 0.385 GeV cm^-3 and an NFW profile describe the Galaxy.
Used to normalize f_PBH and the source spatial distribution; the paper verifies percent-level changes for other profiles.
domain assumption Force-field solar modulation with potential <phi> = 731 MV applies to both antiprotons and antideuterons, with uncertainties absorbed in the covariance matrix.
Used in Secs. IV and V to convert interstellar to top-of-atmosphere fluxes; more detailed modulation models are discussed and deferred.

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Cite this review

Pith. "Pith review of Antinuclei from Primordial Black Holes." pith.science (2026). https://pith.science/paper/QRFS2SEU

@misc{pith2026250504692,
  author       = {Pith},
  title        = {Pith review of: Antinuclei from Primordial Black Holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QRFS2SEU}},
  note         = {Machine review of arXiv:2505.04692}
}

read the original abstract

Light primordial black holes (PBHs) may have originated in the early Universe, and could contribute to the dark matter in the Universe. Their Hawking evaporation into particles could eventually lead to the production of antinuclei, which propagate and arrive at Earth as cosmic rays with a flux peaked at GeV energies. We revisit here the antiproton and antideuteron signatures from PBH evaporation, relying on a lognormal PBH mass distribution, state-of-the-art propagation models, and an improved coalescence model for fusion into antideuterons. Our predictions are then compared with AMS-02 data on the antiproton flux. We find that the AMS-02 antiproton data severely constrain the Galactic PBH density, setting bounds that depend significantly on the parameters of the lognormal mass distribution, and that are comparable to or slightly stronger than bounds set from diverse messengers. We also discuss prospects for future detection of antideuterons. Given the bounds from AMS-02 antiproton data, we predict that if antideuterons were to be measured by AMS-02 or GAPS, since the secondary contribution is subdominant, they would clearly be a signal of new physics, only part of which could, however, be explained by PBH evaporation.

Figures

Figures reproduced from arXiv: 2505.04692 by the authors.

**Figure 2.** FIG. 2: The antiproton (top panels) and antideuteron (bottom panels) source spectra from [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** FIG. 3: Fluxes of top-of-atmosphere antiprotons: secondary flux (solid red line), primary flux from [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: as a function of µc, for different values of the lognormal parameter σ. The results strongly depend on the width of the lognormal distribution: they get stronger while σ spreads from 0.1 to 2. The maximum allowed ρPBH for µc ≃ 5 × 1014 g is about 3.5 × 10−12 , 2.2 × 10…

**Figure 5.** Figure 5: FIG. 5: Antiproton bounds on the fraction [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: FIG. 6: Fluxes of TOA antideuterons as due to secondary processes (solid red line) and to the [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

Discussion (0). Continue with ORCID to comment.

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The flux for TOA antideuteron of secondary origin (solid red line) is shown along with the one for PBHs for µc = 10 15 g, σ = 1 and ρPBH = 5.2× 10−11 GeV cm−3 (solid blue line), which is the upper limit allowed by antiproton data (see Sec. IV). The solar modulation potential is set to ⟨ϕ⟩ = 731 MV. The total flux given by the sum of the two components, is...

2022