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ALP-Mediated Dark Matter at Low Reheating Temperature and the Belle II Excess

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Joel Jones-Pérez, Luca Merlo, Javier Silva-Malpartida

High Energy Physics - Phenomenology · Submitted 30 Sep 2026 · 136 references

Pith's verdict: Competent, honest reanalysis; the coldness worry the reader flagged does not land, and the real question is whether the relic-density branch that generates the headline shift is robust across the QCD transition.

T0 · AI review

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arXiv ID2610.00460 (version 1)
Pith ID4BCSRZU2, Pith's permanent record of this paper and its review
CitationJavier Silva-Malpartida, Joel Jones-P\'erez, Luca Merlo. "ALP-Mediated Dark Matter at Low Reheating Temperature and the Belle II Excess." arXiv:2610.00460 (2026). https://pith.science/paper/4BCSRZU2
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The paper

The paper claims

Low reheating removes the tension between the Belle II $B^+\to K^+$ invisible excess and ALP thermal dark matter: inflaton entropy dilutes freeze-out abundance, so smaller couplings match the relic density and the viable ALP mass rises…

The reading

The paper asks whether a single axion-like particle (ALP) can explain both the Belle II excess in $B^+\to K^+\nu\bar\nu$ — a $2.7\sigma$ deviation above the Standard Model prediction — and the observed dark matter abundance, and whether doing so forces abandoning the assumption of a standard cosmological history. Using a newly released mass-differential Belle II likelihood plus two visible-decay searches (an LHCb dimuon search and a Belle diphoton search) that earlier analyses omitted, the authors find that under standard cosmology the ALP-mediated dark matter scenario survives only in a narrow window. They then let dark matter freeze out during a low-temperature reheating era: the decaying inflaton injects entropy that dilutes the freeze-out abundance, so a smaller ALP coupling suffices to reach the observed relic density. This broadens the viable region and shifts it to larger ALP masses, up to $\gtrsim 1.2$ GeV at the lightest benchmark, into the $m_a \approx 2$ GeV range the excess favours. The message is that what reconciles the excess with a thermal dark matter origin is a change in the pre-BBN expansion history, not a change in the ALP couplings.

What carries the argument

The central object is the ALP portal: an effective Lagrangian in which the gauge-singlet pseudoscalar $a$ couples to electroweak gauge bosons (generating $B\to K^{(*)}a$ production and the diphoton decay) and derivatively to a Majorana dark matter fermion $\chi$ (controlling the invisible width and the $s$-channel annihilation $\chi\chi\to a^*\to\gamma\gamma$ that sets the relic density). The phenomenology is governed by the differing scalings of the two widths, $\Gamma(a\to\gamma\gamma)\propto g_{a\gamma\gamma}^2 m_a^3$ versus $\Gamma(a\to\chi\chi)\propto g_{a\chi\chi}^2 m_a m_\chi^2$, which decide whether the ALP decays visibly or invisibly and hence which of three searches — missing-energy, dimuon, or diphoton — binds. The cosmological machinery is the coupled system of Boltzmann equations for the oscillating inflaton (pressureless, $w_\phi=0$), the SM radiation bath, and the $\chi$ number density, solved with a temperature-dependent equation of state; during reheating, continuous entropy injection suppresses $n_\chi/T^3$, thereby shifting the couplings needed to hit $\Omega h^2\simeq 0.12$.

Extended reading notes

Core claim

The paper's central claim is that thermal freeze-out during a low-temperature reheating era removes the tension between the Belle II $B^+\to K^+$ + invisible excess and ALP-mediated thermal dark matter. Entropy injected as the inflaton decays dilutes the abundance that freeze-out would otherwise produce, so a smaller annihilation rate — hence a smaller ALP coupling — is enough to match the observed relic density. At the lightest benchmark, $m_\chi = 0.1$ GeV, the standard-history solution sits at $m_a \approx 0.2$ GeV, whereas the low-reheating solutions lie at $m_a \gtrsim 1.2$ GeV, in the region the excess favours and at couplings the flavour bounds leave open; a reheating temperature at the BBN floor $T_{\rm rh}\gtrsim 4$ MeV is enough to achieve this. Under standard cosmology, by contrast, the resonant condition $m_a\simeq 2m_\chi$ survives only in a narrow window, and the authors' combined missing-energy, dimuon and diphoton analysis excludes every benchmark point of the earlier resonant-annihilation interpretation at $Z_{\rm comb} > 2.8$.

Load-bearing premise

The load-bearing premise is that dark matter decoupling while still relativistic during a low-temperature reheating era nevertheless becomes cold enough by the time of structure formation, and this rests entirely on the cooling mechanism of Refs. [142,143], since the $m_\chi = 0.1$ GeV solutions that best fit the excess decouple at $x_{\rm fo}\sim 4$–10 while still relativistic.

Editorial extensions

If this is right

  • A reheating temperature as low as the BBN floor, $T_{\rm rh}\gtrsim 4$ MeV, suffices to move the relic-density solutions to larger ALP masses (up to $\gtrsim 1.2$ GeV at $m_\chi = 0.1$ GeV), into the $m_a\approx 2$ GeV region the Belle II excess favours, without tuning to the resonant funnel.
  • Under a standard thermal history the model is only marginally compatible with the excess, and the combined missing-energy, dimuon, and diphoton analysis excludes every benchmark point of the earlier resonant interpretation at $Z_{\rm comb} > 2.8$.
  • The low-reheating branch yields two solution families per $T_{\rm rh}$ (freeze-out at very different $x_{\rm fo}$), and for $m_\chi = 1$ GeV the late-reheating solution avoids the CMB late-injection bound while still crossing $m_a\approx 2$ GeV.
  • The overall picture is not qualitatively sensitive to the ratio $\rho_{EW}=g_{a\gamma\gamma}/g_{aWW}$ over $[0.23,5]$; taking $\rho_{EW}=0.23$ further improves overlap with the $\sim 2$ GeV excess region at the lightest benchmarks.
  • The newly opened coupling window lies within the projected sensitivity of a future 1 TeV $e^+e^- \to \gamma a (\to \chi\chi)$ search, so the scenario is falsifiable by near-future data.

Reading between the lines

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

  • The entropy-dilution mechanism is not specific to ALPs: the same low-reheating logic should open comparable windows for other light-mediator dark matter portals that try to explain low-energy anomalies, so the strategy generalises beyond this one realisation.
  • Because the viable window sits at couplings a future 1 TeV $e^+e^-$ collider is projected to reach, a null result there would simultaneously constrain the ALP couplings and the pre-BBN expansion history, since the viable region exists only if reheating completed near the BBN floor.
  • The compatibility claim inherits sensitivity to the cooling mechanism of Refs. [142,143]: if radiation-era cooling does not apply as assumed, the $m_\chi = 0.1$ GeV solutions that decouple while relativistic at $x_{\rm fo}\sim 4$–10 would likely be pushed against Lyman-$\alpha$ free-streaming bounds.
Original abstract

Belle II has reported a $2.7\sigma$ excess in $B^+\to K^+\nu\bar\nu$ over its Standard Model prediction, recently interpreted as arising from an axion-like particle mediating a thermal dark matter candidate. We reassess this interpretation using a new mass-differential measurement of the same data set and adding two visible-decay searches that earlier analyses omitted. The resulting bounds leave the predictions from a standard cosmological history only marginally compatible with the excess, viable in a narrow window of parameter space. Thus, we consider a situation where dark matter freezes out during a low-temperature reheating era, featuring entropy injection diluting the relic abundance. This requires smaller couplings compared to those in standard cosmology in order to match the observed dark matter density, opening a region of parameter space where the compatibility of the model with the Belle II excess is significantly improved.

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, 2026-10-02: 1 request, 4,372 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.65 · human participants 0.02 · controlled comparison 0.32 · randomized assignment 0.01 · states quantitative result 0.68 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Belle II has reported a $2.7\sigma$ excess in $B^+\to K^+\nu\bar\nu$ over its Standard Model prediction, recently interpreted as arising from an axion-like particle mediating a thermal dark matter candidate. We reassess this interpretation using a new mass-differential measurement of the same data set and adding two visible-decay searches that earlier analyses omitted. The resulting bounds leave the predictions from a standard cosmological history only marginally compatible with the excess, viable in a narrow window of parameter space. Thus, we consider a situation where dark matter freezes out during a low-temperature reheating era, featuring entropy injection diluting the relic abundance. This requires smaller couplings compared to those in standard cosmology in order to match the observed dark matter density, opening a region of parameter space where the compatibility of the model with the Belle II excess is significantly improved.

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 Belle II has reported a $2.7\sigma$ excess in $B^+\to K^+\nu\bar\nu$ over its Standard Model prediction, recently interpreted as arising from an axion-like particle mediating a thermal dark matter candidate. background 1.00 0.05 0.04 asserted 0.62
s1 We reassess this interpretation using a new mass-differential measurement of the same data set and adding two visible-decay searches that earlier analyses omitted. method 0.57 0.93 0.04 asserted 0.97
s2 The resulting bounds leave the predictions from a standard cosmological history only marginally compatible with the excess, viable in a narrow window of parameter space. result 0.94 0.89 0.29 asserted 0.75
s3 Thus, we consider a situation where dark matter freezes out during a low-temperature reheating era, featuring entropy injection diluting the relic abundance. contribution 0.66 0.31 0.12 asserted 0.61
s4 This requires smaller couplings compared to those in standard cosmology in order to match the observed dark matter density, opening a region of parameter space where the compatibility of the model with the Belle II excess is significantly improved. interpretation 0.54 0.67 0.55 asserted 0.95

What kind of paper the classifier reports this is: theoretical result 0.56 · evidence from analysis of existing data 0.97.

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. Missing-energy exclusion significance from Ref. [91] (colour map and cyan 2σ contour), with the LHCb B → Kµµ bound (green, hatched: excluded at > 2σ), the Belle B → K(∗)a(γγ) prompt-rate proxy of Eq. (2.19) (blue dashed, 2σ) and the ma = fa EFT cutoff (white dotted) overlaid, for mχ = 0.1 GeV and gaχχ = 10−3 , 10−1 GeV−1 (left to right). The red dash-dotted line corresponds to the projected ILC sensitivity [132]. consequences of having ma < 2mχ, which closes the a → χχ invisible decay channel. In this situation, the visible channels dominate the decay, and are crucial in the…
Figure 3. Left: Evolution of the normalised DM number density nχ/T3 as a function of x = mχ/T. Red curves correspond to standard cosmology, while blue curves show the scenario with Trh = 5 MeV. In both cases, the solid (dashed) curves correspond to gaγγ = 4 × 10−4 GeV−1 (2 × 10−5 GeV−1 ). The grey solid line denotes the equilibrium number density, while the horizontal dotted line indicates Ωχh 2 ≃ 0.12. Right: Ratio Γann/H = ⟨σv⟩neq/H for the same two couplings, considering only the Trh = 5 MeV scenario, with the same solid and dashed line conventions. The horizontal dotted line marks ⟨σv⟩neq…
Figure 4. Combined exclusion significance Zcomb of Eq. (2.20) (colour map and cyan 2σ contour) in the (ma, gaWW ) plane, for mχ = 0.1 GeV and gaχχ = 10−3 , 10−1 GeV−1 (left to right). The solid white line is the standard-cosmology relic-density solution; dashed lines show the same solution once entropy injection from a low reheating temperature is included (for Trh = 5, 6, 7, 9 MeV). The grey region is excluded by the cosmic microwave background (CMB) bound on late dark-matter energy injection. large gaWW , while on the right they reach a maximum around gaWW ∼ 5 × 10−4 GeV−1 . For this case,
Figure 6. Same as Figs. 4 and 5, for ρEW = 0.23 (gaγγ = 0.23 gaWW ) and a single gaχχ = 0.1 GeV−1 , for mχ = 0.1 (left) and 0.5 GeV (right). As in Figs. 4 and 5, only a sample of the available Trh values is shown: 5, 6, 7, 9 MeV. For very small gaWW the dashed lines are cut off, as DM does not reach thermal equilibrium. low-reheating branch, and the CMB-excluded grey band all rescale rigidly as gaWW → gaWW /ρEW, uniformly across all six panels: up by a factor ≃ 4.3 at ρEW = 0.23 and down by a factor 5 at ρEW = 5. The main result of this work, namely that a low reheating temperature reproduces…

Showing 4 of the paper's 6 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2610.00460 by the authors.

References

Discussion

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