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arxiv: 2606.18335 · v1 · pith:3GHCSDK7new · submitted 2026-06-16 · ✦ hep-ph · astro-ph.CO

Weak corrections to Minimal Dark Matter annihilations

Dario Buttazzo , Mateusz Duch , Pier Paolo Giardino , Alessandro Strumia This is my paper

Pith reviewed 2026-06-26 23:44 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords Minimal Dark Matterweak correctionsannihilation cross sectionrelic abundanceinfrared divergencesSudakov correctionsSommerfeld enhancementfermionic multiplets
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The pith

One-loop weak corrections to fermionic minimal dark matter annihilation reach the 5% level for the most motivated multiplets.

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

The paper calculates the one-loop corrections arising from weak interactions to the annihilation cross sections of fermionic dark matter candidates that transform as multiplets under the electroweak gauge group. Infrared divergences cancel in the velocity-independent s-wave channel that controls the thermal relic abundance after freeze-out. The magnitude of the corrections increases with the dimension of the multiplet. A reader would care because these shifts directly change the predicted dark matter density that must match cosmological observations.

Core claim

We compute the one-loop weak corrections to the annihilation cross sections of fermionic Minimal Dark Matter multiplets. Infrared divergences cancel in the dominant s-wave combination relevant for the thermal relic abundance. Instead, infrared-enhanced corrections affect velocity-suppressed rates, through a Sudakov/Sommerfeld interplay. The corrections grow with the multiplet size and are at the 5% level in the most motivated cases: the Higgsino-like doublet, the wino-like triplet, the stable quintuplet.

What carries the argument

One-loop electroweak corrections to the annihilation cross sections of fermionic Minimal Dark Matter multiplets, with infrared divergences canceling in the s-wave combination.

If this is right

  • The thermal relic abundance for these multiplets must incorporate the one-loop corrections to achieve percent-level accuracy.
  • Velocity-suppressed annihilation channels receive additional infrared-enhanced corrections from the Sudakov/Sommerfeld interplay.
  • The size of the effect scales upward with larger multiplet dimension.
  • The doublet, triplet, and quintuplet cases each receive shifts at the five percent level.

Where Pith is reading between the lines

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

  • Relic density constraints derived from cosmic microwave background data would shift when these corrections are included in parameter scans.
  • Comparable one-loop electroweak corrections may be required for scalar minimal dark matter candidates or for co-annihilation processes.
  • Full resummation of Sudakov logarithms could extend the precision beyond the one-loop result for even larger multiplets.
  • The separation into infrared-safe and enhanced channels suggests similar techniques could apply to other early-universe processes involving electroweak multiplets.

Load-bearing premise

The one-loop weak corrections extracted after isolating the infrared-safe s-wave combination remain accurate without higher-order or non-perturbative effects altering the result at the quoted five percent level.

What would settle it

A two-loop or non-perturbative calculation of the annihilation cross section for the wino-like triplet or stable quintuplet that differs from the one-loop result by substantially more than five percent.

Figures

Figures reproduced from arXiv: 2606.18335 by Alessandro Strumia, Dario Buttazzo, Mateusz Duch, Pier Paolo Giardino.

Figure 1
Figure 1. Figure 1: One loop EW, QCD and top Yukawa corrections to the annihilation cross sections of a Minimal DM n-plet of SU(2)L. The δ corrections are computed with respect to the tree level cross section σ ∼ α 2 2 /M2 X written in terms of the pole mass MX and of α2 renormalized at µ¯ = 2MX . The correction to the total cross section includes the extra I = 3, 7 channels and approximate Sommerfeld factors. The thermal mas… view at source ↗
Figure 2
Figure 2. Figure 2: The continuous curves show the tree level values of the velocity-suppressed cross sections divided by the total rate obtained by naively summing the s-wave cross sections in eq. (2). The dashed curves include the IR-enhanced EW corrections. δσvff,HH ¯ † I=3,ℓ=0,S=1 = σv ff,HH ¯ † I=3  − n 2 − 1 3 − 2(n 2 − 4) 3  L−, (40d) δσvWW I=5,ℓ=0,S=0 = σvWW I=5 (7 − n 2 )L−, (40e) δσvffW,HH ¯ †W I=5,ℓ=1,S=1 = σv ff… view at source ↗
read the original abstract

We compute the one-loop weak corrections to the annihilation cross sections of fermionic Minimal Dark Matter multiplets. Infrared divergences cancel in the dominant $s$-wave combination relevant for the thermal relic abundance. Instead, infrared-enhanced corrections affect velocity-suppressed rates, through a Sudakov/Sommerfeld interplay. The corrections grow with the multiplet size and are at the $5\%$ level in the most motivated cases: the Higgsino-like doublet, the wino-like triplet, the stable quintuplet.

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

0 major / 3 minor

Summary. The paper computes the one-loop weak corrections to the annihilation cross sections of fermionic Minimal Dark Matter multiplets. Infrared divergences cancel in the dominant s-wave combination relevant for the thermal relic abundance. Infrared-enhanced corrections affect velocity-suppressed rates through a Sudakov/Sommerfeld interplay. The corrections grow with the multiplet size and reach the 5% level for the Higgsino-like doublet, wino-like triplet, and stable quintuplet.

Significance. If the central result holds, the work supplies a concrete, parameter-free improvement to the annihilation rates entering thermal relic calculations for Minimal Dark Matter. The explicit isolation of the IR-safe s-wave projector and the reported size of the corrections for the three most motivated multiplets constitute a useful update to existing MDM phenomenology. The direct perturbative nature of the expansion, with no fitted parameters or ad-hoc entities, strengthens the result.

minor comments (3)
  1. The abstract states that corrections 'grow with the multiplet size' but does not quantify the growth or list the representations beyond the three examples; a brief table or sentence in §2 or §3 would clarify the pattern.
  2. The interplay between Sudakov logarithms and Sommerfeld enhancement is mentioned for velocity-suppressed rates; a short paragraph or equation showing the leading logarithmic structure would help readers reproduce the separation of scales.
  3. No numerical values or plots are referenced in the provided abstract; if the manuscript contains them, they should be cited explicitly in the text when the 5% figure is stated.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation of minor revision. The report accurately summarizes our computation of one-loop weak corrections to fermionic Minimal Dark Matter annihilation cross sections, including the cancellation of infrared divergences in the s-wave channel and the size of the corrections for the doublet, triplet, and quintuplet cases.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper performs an explicit one-loop perturbative computation of weak corrections to fermionic Minimal Dark Matter annihilation cross sections. The key technical step is the demonstration that infrared divergences cancel exactly in the s-wave projector relevant to thermal freeze-out, after which the remaining finite corrections are evaluated directly for the doublet, triplet and quintuplet cases. No equation or result is obtained by fitting a parameter to a subset of the same data, by renaming a known empirical pattern, or by invoking a load-bearing self-citation whose content is itself unverified; the derivation chain consists of standard QFT Feynman rules and cancellation identities that are independent of the final numerical percentages quoted.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on standard perturbative QFT methods and the definition of Minimal Dark Matter multiplets; no free parameters, ad-hoc axioms, or invented entities are visible from the abstract.

pith-pipeline@v0.9.1-grok · 5605 in / 1079 out tokens · 18266 ms · 2026-06-26T23:44:50.805127+00:00 · methodology

discussion (0)

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Reference graph

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