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arxiv: 2606.29710 · v1 · pith:ZKWSHXPHnew · submitted 2026-06-29 · ✦ hep-ph · astro-ph.HE· hep-th

Size Dependence of the Sommerfeld Enhancement for Puffy Dark Matter

Wu-Long Xu , Jin Min Yang , Wen-Na Yang This is my paper

Pith reviewed 2026-06-30 05:48 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.HEhep-th
keywords Sommerfeld enhancementpuffy dark matterdark matter annihilationpartial wave analysisresonancesfinite size effectsnugget dark matter
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The pith

The finite size of dark matter particles affects the Sommerfeld enhancement in addition to low velocity.

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

This paper examines the effects of finite particle size on the Sommerfeld enhancement factor in puffy dark matter annihilation. It uses the partial-wave method for cases with only a charge density distribution to show that two dimensionless parameters describe the resonance structure. The analysis establishes finite size as another basic factor influencing the enhancement, separate from velocity. For nugget-type dark matter with internal structures, the factor displays resonant behavior akin to point-like cases. A reader would care as this refines how we calculate dark matter annihilation rates and signals.

Core claim

The partial-wave analysis demonstrates that the Sommerfeld enhancement for puffy dark matter depends on its finite size through two dimensionless parameters that characterize the resonance structure, making size a fundamental factor in addition to low velocity.

What carries the argument

Partial-wave method applied to puffy dark matter with a supplied charge density distribution, using two dimensionless parameters to map the resonance structure of the enhancement factor.

If this is right

  • Resonance structure is characterized by two dimensionless parameters.
  • Nugget dark matter shows resonant Sommerfeld enhancement similar to point particles.
  • Size effects must be accounted for in low-velocity annihilation calculations.
  • The approach allows characterization without specifying full internal structure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This size dependence may alter expected indirect detection signals from dark matter.
  • Similar methods could apply to other extended objects in particle physics.
  • Future work might derive constraints on dark matter size from annihilation data.

Load-bearing premise

The partial-wave method remains valid when applied to puffy dark matter using only a charge density distribution without specifying internal structure.

What would settle it

An explicit computation of the Sommerfeld factor for an extended charge distribution that shows identical enhancement to the point-particle limit at all velocities would falsify the size dependence claim.

read the original abstract

We examine the size effects in the Sommerfeld enhancement factor for puffy dark matter annihilation. First, we use the partial-wave method to study the case of puffy dark matter for which only a charge density distribution is given without specifying its internal structure. We find that by using two dimensionless parameters, we can provide a characterization of the resonance structure of the Sommerfeld enhancement. Using this approach, we demonstrate that the finite size of dark matter particle is another fundamental factor, in addition to low velocity, that affects the Sommerfeld enhancement. Then, as an example of puffy dark matter with nontrivial internal structures, we perform the analysis for the nugget-type dark matter, whose Sommerfeld enhancement factor is found to exhibit a resonant behavior similar to that of point-like particles.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that the finite size of dark matter particles is a fundamental factor (in addition to low velocity) affecting the Sommerfeld enhancement for puffy dark matter annihilation. It applies the partial-wave method to cases supplied only with a charge density distribution (no internal structure specified), reduces the problem to two dimensionless parameters, and uses them to characterize resonance structure. As an example with nontrivial internal structure, it analyzes nugget-type dark matter and reports resonant behavior similar to the point-like case.

Significance. If the central claim and the partial-wave reduction hold, the work would establish particle size as an independent control parameter for Sommerfeld-enhanced annihilation rates in composite dark matter models, with direct implications for indirect detection signals. The dimensionless-parameter characterization could provide a practical tool for scanning size effects across different density profiles.

major comments (2)
  1. [Abstract and the partial-wave analysis section] The central claim that finite size is 'another fundamental factor' (Abstract) rests on applying the partial-wave method to a static charge-density potential with no internal degrees of freedom specified. The manuscript provides no explicit test or justification that this decomposition remains complete when composite effects, back-reaction, or additional channels could modify the effective potential, which directly undermines the asserted independence from velocity and the reduction to two parameters.
  2. [Nugget-type dark matter analysis] In the nugget-type example, the reported similarity of resonant behavior to point-like particles is presented as supporting the size-dependence claim, yet no quantitative comparison (e.g., shift in resonance locations or widths as a function of the two dimensionless parameters) is given to show that the size effect survives once internal structure is restored.
minor comments (2)
  1. Notation for the two dimensionless parameters is introduced without an explicit equation linking them to the input charge density; adding this relation would clarify the claimed parameter-free character of the resonance characterization.
  2. Figure captions for the resonance plots should state the precise values of the two dimensionless parameters used and whether error bands or convergence checks with respect to partial-wave truncation are included.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major comments point by point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract and the partial-wave analysis section] The central claim that finite size is 'another fundamental factor' (Abstract) rests on applying the partial-wave method to a static charge-density potential with no internal degrees of freedom specified. The manuscript provides no explicit test or justification that this decomposition remains complete when composite effects, back-reaction, or additional channels could modify the effective potential, which directly undermines the asserted independence from velocity and the reduction to two parameters.

    Authors: The analysis in the partial-wave section is performed for the specific case in which only a static charge-density distribution is supplied and no internal degrees of freedom are specified, as stated in the abstract. Within this setup the effective potential is fully determined by the density, so the partial-wave decomposition of the two-body Schrödinger equation is complete. The two dimensionless parameters are constructed precisely to separate the finite-size effect from the velocity dependence, and the resonance structure is characterized in terms of these parameters. We agree that the manuscript would benefit from an explicit statement of this scope; we will add a clarifying paragraph in the discussion section delineating the regime of validity and noting that additional composite effects lie outside the present model. revision: partial

  2. Referee: [Nugget-type dark matter analysis] In the nugget-type example, the reported similarity of resonant behavior to point-like particles is presented as supporting the size-dependence claim, yet no quantitative comparison (e.g., shift in resonance locations or widths as a function of the two dimensionless parameters) is given to show that the size effect survives once internal structure is restored.

    Authors: The nugget-type section is presented as an example in which internal structure is incorporated through the effective density profile. The figures demonstrate that resonant features persist and are governed by the same two dimensionless parameters. We acknowledge that a direct quantitative comparison of resonance shifts or widths is not tabulated. We will add a short quantitative comparison (listing resonance locations for representative values of the two parameters) in the revised nugget subsection to make the survival of the size effect explicit. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation applies partial-wave method to supplied charge density to obtain two independent dimensionless parameters

full rationale

The paper's central result—that finite size is an additional factor affecting Sommerfeld enhancement—is obtained by applying the partial-wave method to a given charge-density distribution (without internal structure) and extracting two dimensionless parameters that characterize the resonance structure. These parameters are constructed directly from the input density and velocity, not fitted to reproduce any target resonance or enhancement value. The subsequent nugget example follows the same logic with added internal structure. No self-citations are load-bearing, no ansatz is smuggled, and no prediction reduces by construction to a fitted input. The derivation chain is therefore self-contained against the supplied density input.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract supplies insufficient detail to enumerate free parameters or invented entities; the two dimensionless parameters are presented as derived quantities rather than fitted constants.

axioms (1)
  • domain assumption Partial-wave method is applicable to puffy dark matter given only a charge density distribution without internal structure
    Invoked in the first part of the analysis to study the general puffy case.

pith-pipeline@v0.9.1-grok · 5661 in / 1102 out tokens · 26841 ms · 2026-06-30T05:48:08.559494+00:00 · methodology

discussion (0)

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