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Self-interacting dark matter from radiative bound-state-formation feedback

Marcos M. Flores, Kalliopi Petraki, Thomas Pignard

Oct 19, 2026arXiv:2610.27089v1
hep-phastro-ph.COastro-ph.GA
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Scorecard· 16/16
6.0/10 impact

Conceptually novel and technically careful mechanism for generating SIDM from unitarity feedback, but confined to a specific toy model with omitted contributions and unquantified inelastic constraints.

Abstract

Observations of galactic structure motivate sizable dark-matter self-interactions at low velocities, naturally realized through light force mediators. Such mediators can also make inelastic processes very efficient. Unitarity then requires their absorptive contributions to the two-particle self-energy kernel to be resummed, which in turn feeds back into both the elastic and inelastic scattering amplitudes. We study the feedback of radiative bound-state formation on elastic scattering and its implications for self-interacting dark matter. We focus on capture processes through emission of a charged scalar; such transitions are particularly efficient because the scattering and bound states are governed by different effective potentials, a feature also shared by radiative capture through emission of a non-Abelian gauge boson. We show that their feedback can generate sizable elastic scattering relevant for halo dynamics, even when the baseline elastic amplitude vanishes. Notably, the generated elastic cross section can grow toward low velocities, resembling long-range scattering. A companion paper examines the feedback from annihilation processes.

AI Impact Assessments

(1 model)

Core Contribution

The paper studies how radiative bound-state formation (BSF) through charged-scalar emission feeds back, via unitarity and the optical theorem, onto elastic scattering in self-interacting dark matter (SIDM). The model is a global-U(1) complex scalar X with a charge-2 mediator ϱ. Same-charge XX pairs have no baseline long-range potential, so the baseline elastic amplitude is zero. They can still capture into XX† bound states, because the scattering and bound states feel different potentials and the monopole transition is unsuppressed. Summing capture over the Coulombic tower of excited levels gives unbounded low-velocity growth that violates partial-wave unitarity. Resumming the absorptive BSF kernel, including the principal-value dispersive matrix W_ℓ, restores unitarity and generates a nonzero elastic cross section.

The main results are:

  • Analytic and numerical velocity scalings, e.g. σ_elas ∝ v^-12 at high velocity, v^-6 and then v^-4 at low velocity, and a finite-mediator-mass plateau.
  • A proof (Cauchy–Schwarz) that W_ℓ can only reduce the elastic cross section relative to the W_ℓ=0 approximation.
  • Kramers-like analytic sums for massive emission in the appendix.
  • A phenomenological scan showing that asymmetric DM can obtain SIDM-relevant cross sections purely from this feedback. The cross sections are cluster-safe, sizable at dwarf scales, and large at subhalo scales.

    • This is a conceptually novel route to SIDM: the elastic scattering comes from an absorptive kernel rather than from a potential.

    Methodological Rigor

    The framework builds on the authors' earlier unitarization papers (Flores–Petraki 2024, 2025, 2026). Within the stated approximations it is internally consistent, and the analytic derivations, including the unitarity bounds, the W_ℓ inequality and the scaling arguments, are careful. Approximations are stated openly:

  • Coulomb wavefunctions are used for the bound states, with a validity check on the Coulomb approximation, and the paper notes where it degrades (α_ϱ ≳ 0.2).
  • Contact-like XX elastic terms are neglected.
  • The direct Hermitian dispersive optical-potential contributions are omitted, and the authors flag that these could modify the results.
  • Real BSF energy loss, depletion and halo evolution are not treated.
  • The numerics are limited in places ("Numerical limit" regions), and antiresonances are hard to resolve.
  • Some scalings (viscosity exponents) are inferred only numerically.
  • The inelastic losses inside halos, which could exclude parts of the interesting parameter space, are not quantified.

    • There is no independent cross-check against a full field-theoretic calculation. The paper itself cites a complementary EFT approach (De Ros & Reig Navarro). The conclusions are therefore credible but model- and approximation-dependent.

    Potential Impact

    The conceptual point is that inelasticity necessarily generates elasticity, and that this can create a velocity-dependent SIDM scenario with no baseline long-range force. It matters for the following communities:

  • Dark-matter bound-state and unitarity researchers.
  • SIDM model builders, who gain a new class of velocity-dependent cross sections, especially for asymmetric DM.
  • Anyone using Sommerfeld/BSF calculations, who must now account for feedback.

    • Phenomenologically, the symmetric-DM result is largely negative: Yukawa scattering dominates, and the antiresonance regions do not open viable parameter space. The asymmetric-DM result is positive but sits in a specific model with a global U(1) and a contrived charge assignment. Real-world impact is limited by the unaddressed inelastic losses, indirect-detection constraints and cosmology. Adoption by the SIDM simulation community would require further work. The broader lesson (unitarity feedback on elastic scattering) generalizes, for example to non-Abelian BSF.

    Timeliness & Relevance

    SIDM is highly topical given recent strong-lensing hints (the paper cites several 2025–2026 works). Unitarity violation in BSF was recently identified (Beneke et al. 2025), and the unitarization program is active, so the paper addresses a live bottleneck. Its audience is narrow, though: a specialist hep-ph subcommunity.

    Strengths

  • A genuinely new mechanism with clear analytic understanding.
  • A transparent hierarchy of approximations, with bounds and scalings that make the physics interpretable.
  • A direct link to SIDM benchmarks and a discussion of cosmology and relic constraints.
  • Honest discussion of limits and omitted contributions.

    • Limitations

  • Heavy reliance on companion and prior papers, some "to appear".
  • A specific toy model, with a global symmetry and neglected contact terms.
  • Omitted Hermitian dispersive pieces, which could change the quantitative results.
  • No code or data release is mentioned, and the numerics are complex.
  • The symmetric-DM conclusion is largely a null result.
  • Relic density is treated by extrapolation.
  • Inelastic constraints, such as DM depletion and indirect detection, are not evaluated, so viable parameter space is only indicative.

    • Overall this is a solid, technically sophisticated, incremental-to-moderate advance within an active program. It is likely to be cited by the bound-state and SIDM theory community but is unlikely to reshape the broader field.

    Rating:6/ 10
    Significance 5.5Rigor 6.5Novelty 7Clarity 6.5

    Generated Oct 21, 2026

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