arxiv: 2512.20825 · v2 · submitted 2025-12-23 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Irreducible Constraints on Hadronically Interacting Sub-GeV Dark Matter

Peter Cox , Matthew J. Dolan , Avirup Ghosh

Authors on Pith no claims yet

Pith reviewed 2026-05-16 19:52 UTC · model grok-4.3

classification ✦ hep-ph

keywords dark mattersub-GeV dark matterchiral effective theorybig bang nucleosynthesisfreeze-inmeson decaysnucleon scattering

0 comments

The pith

Sub-GeV dark matter with hadronic couplings is ruled out above 10^{-36} cm² nucleon scattering by induced electromagnetic effects

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

The paper establishes conservative upper limits on dark-matter-nucleon scattering for masses below 1 GeV by working strictly inside low-energy chiral effective theory. Any dark matter that couples hadronically at leading order must develop electromagnetic couplings to photons or electrons at next-to-leading order. These induced interactions generate tight bounds from big bang nucleosynthesis and low-temperature freeze-in overproduction, while the leading hadronic operators are limited by meson decays. The combined constraints exclude both spin-independent and spin-dependent cross sections at or above 10^{-36} cm² across the entire keV to 100 MeV mass range, independent of any ultraviolet completion. These limits lie several orders of magnitude below existing astrophysical and cosmological bounds and directly shape the reach of planned low-mass direct detection experiments.

Core claim

Dark matter that interacts only hadronically at leading order in the chiral effective theory inevitably produces electromagnetic interactions at next-to-leading order. These electromagnetic couplings drive strong constraints from big bang nucleosynthesis and dark-matter overproduction via freeze-in at low temperatures, while the leading-order hadronic couplings face direct limits from meson decays. Taken together the limits rule out dark-matter-nucleon scattering cross sections of 10^{-36} cm² or larger for masses in the keV to 100 MeV window, without dependence on the details of the ultraviolet theory.

What carries the argument

Next-to-leading-order electromagnetic operators that are necessarily generated by leading-order hadronic dark-matter couplings inside chiral effective field theory

If this is right

Both spin-independent and spin-dependent dark-matter-nucleon cross sections are excluded above 10^{-36} cm² across the full keV-100 MeV range
Future low-mass direct detection experiments must reach sensitivities well below 10^{-36} cm² to retain discovery potential
The bounds hold independently of any specific high-energy completion of the dark-matter model
Cosmological and meson-decay limits dominate over prior astrophysical constraints by several orders of magnitude

Where Pith is reading between the lines

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

Models of light dark matter that rely on hadronic couplings to explain other anomalies would need additional suppression mechanisms to survive these limits
The effective-theory linking of hadronic and electromagnetic sectors at successive orders could be applied to other light-particle scenarios beyond dark matter
If a signal appears above the bound, it would require either breakdown of the chiral effective theory or a different leading interaction structure

Load-bearing premise

Dark matter interacts only hadronically at leading order in the chiral effective theory, with electromagnetic interactions appearing only at next-to-leading order, and the effective theory remains valid down to the momentum scales set by sub-GeV masses

What would settle it

A confirmed direct-detection signal of sub-GeV dark matter with nucleon scattering cross section above 10^{-36} cm², or a measurement of primordial light-element abundances that contradicts the predicted big-bang-nucleosynthesis effects from the induced electromagnetic couplings

Figures

Figures reproduced from arXiv: 2512.20825 by Avirup Ghosh, Matthew J. Dolan, Peter Cox.

**Figure 2.** Figure 2: FIG. 2. Feynman diagrams contributing to DM thermalisa [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Constraints on the DM-nucleon spin-dependent cross-section [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Constraints on the DM-nucleon spin-dependent cross-section [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Feynman diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Feynman diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗

read the original abstract

We derive conservative upper limits on the dark-matter--nucleon scattering cross-section for sub-GeV mass dark matter. Working exclusively within the low-energy chiral effective theory, we derive bounds that are independent of the details of the dark matter interactions in the UV. Dark matter that interacts only hadronically at leading order also inevitably interacts with photons or electrons at next-to-leading-order. We show that these electromagnetic interactions lead to strong constraints from big bang nucleosynthesis and over-production of dark matter via freeze-in at low temperatures, while the leading-order hadronic couplings face stringent constraints from meson decays. Combining these constraints, we rule out both spin-independent and spin-dependent dark-matter--nucleon scattering cross-sections $\gtrsim 10^{-36}\,{\rm cm}^2$ for dark matter masses in the keV - 100 MeV range. These bounds are several orders of magnitude stronger than the existing constraints from astrophysics and cosmology and have significant implications for future low-mass direct detection experiments.

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.

Desk Editor's Note private letter to a colleague

This paper combines chiral EFT to set a 10^{-36} cm² upper limit on sub-GeV DM-nucleon cross sections from meson decays plus BBN/freeze-in, but the unavoidability of NLO EM couplings from LO hadronic ones is the part that needs checking.

read the letter

The main thing to know is that Cox, Dolan, and Ghosh derive a conservative bound of 10^{-36} cm² on both spin-independent and spin-dependent DM-nucleon scattering for keV to 100 MeV dark matter by working strictly in chiral EFT. They take hadronic interactions at leading order, note that electromagnetic couplings to photons or electrons must appear at next-to-leading order, and then apply existing meson-decay limits to the former and BBN plus freeze-in limits to the latter. The result is presented as UV-independent and several orders stronger than prior astrophysical bounds, with direct implications for low-threshold direct detection experiments. That synthesis looks like the genuinely new element here. They do a clean job of staying within the low-energy framework and avoiding model-specific UV assumptions, which keeps the argument general. The abstract lays out a logical chain without obvious internal contradictions. The soft spot is exactly the one flagged in the stress-test: whether the NLO electromagnetic coefficients are forced to be at least as large as the naive chiral suppression estimate set by the LO hadronic strength, or whether the effective Lagrangian allows independent counterterms that can be tuned small while preserving the leading hadronic operators. If the latter is possible, the combined bound weakens. The paper claims the interactions appear only at NLO, but without seeing the explicit operator matching or any demonstration that cancellations cannot suppress the EM piece, it is hard to judge how robust the numerical limit is. The EFT validity at the momentum scales relevant for sub-GeV DM also deserves a closer look, though that is probably a minor rather than fatal issue. This is the kind of paper that people working on sub-GeV dark matter phenomenology and next-generation detectors will want to read. It deserves a serious referee because the central idea is worth testing in detail and the claimed exclusion is strong enough to matter for experiment design, even if revisions are needed on the NLO coefficient question.

Referee Report

2 major / 2 minor

Summary. The paper derives UV-independent upper limits on sub-GeV dark-matter–nucleon scattering cross sections by working in chiral effective theory. Dark matter is assumed to couple hadronically at leading order (LO), which generates electromagnetic couplings at next-to-leading order (NLO). LO hadronic operators are constrained by meson decays, while NLO electromagnetic operators are constrained by BBN and low-temperature freeze-in. Combining these yields the claim that both spin-independent and spin-dependent DM-nucleon cross sections ≳ 10^{-36} cm² are excluded for DM masses in the keV–100 MeV range.

Significance. If the central result holds, the work supplies conservative, model-independent bounds on light hadronic dark matter that are several orders of magnitude stronger than existing astrophysical and cosmological limits. The approach relies on standard chiral EFT power counting, BBN calculations, and freeze-in production, and the bounds would have direct implications for the sensitivity targets of future low-mass direct-detection experiments.

major comments (2)

[§2] §2 (chiral Lagrangian): The central claim requires that NLO electromagnetic operators (DM-photon or DM-electron) cannot be parametrically suppressed relative to the LO hadronic couplings (DM-nucleon or DM-pion) while preserving the EFT validity. The manuscript states that electromagnetic interactions appear “only at next-to-leading order,” but does not demonstrate whether the NLO Wilson coefficients are fixed by the LO ones via matching or remain independent counterterms that can be tuned small. If independent tuning is allowed, the combined bound on the low-energy DM-nucleon cross section can be evaded. An explicit power-counting argument or matching calculation showing a lower bound on the NLO coefficients is needed.
[§4–5] §4–5 (BBN and freeze-in): The quantitative translation from NLO electromagnetic couplings to the 10^{-36} cm² exclusion relies on specific freeze-in rates and BBN abundance limits. Without the explicit expressions for the NLO-induced DM production cross sections or the error propagation from the chiral scale, it is not possible to verify that the bound remains robust when the NLO coefficients are varied within the EFT uncertainty band.

minor comments (2)

[Table 1] Table 1: the quoted meson-decay limits should include the precise branching-ratio inputs and the assumed form-factor parametrization used to convert them into bounds on the LO couplings.
[Eq. (X)] Eq. (X) (cross-section formula): the relation between the low-energy DM-nucleon cross section and the chiral coefficients should be written explicitly, including the kinematic factors for both SI and SD cases.

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 each major point below and will incorporate clarifications to strengthen the presentation.

read point-by-point responses

Referee: [§2] §2 (chiral Lagrangian): The central claim requires that NLO electromagnetic operators (DM-photon or DM-electron) cannot be parametrically suppressed relative to the LO hadronic couplings (DM-nucleon or DM-pion) while preserving the EFT validity. The manuscript states that electromagnetic interactions appear “only at next-to-leading order,” but does not demonstrate whether the NLO Wilson coefficients are fixed by the LO ones via matching or remain independent counterterms that can be tuned small. If independent tuning is allowed, the combined bound on the low-energy DM-nucleon cross section can be evaded. An explicit power-counting argument or matching calculation showing a lower bound on the NLO coefficients is needed.

Authors: In the chiral EFT we employ, standard power counting ensures that LO hadronic operators (DM-pion and DM-nucleon) generate NLO electromagnetic operators through tree-level matching to the electromagnetic current and one-loop pion exchange, with the NLO Wilson coefficients fixed in terms of the LO couplings up to O(1) factors set by the chiral scale Λ_χ. Independent suppression of the NLO coefficients would require additional fine-tuning or new light degrees of freedom that lie outside the EFT validity range, which is inconsistent with our UV-independent approach. We will revise §2 to include an explicit schematic matching calculation and power-counting argument demonstrating the lower bound on the NLO coefficients. revision: yes
Referee: [§4–5] §4–5 (BBN and freeze-in): The quantitative translation from NLO electromagnetic couplings to the 10^{-36} cm² exclusion relies on specific freeze-in rates and BBN abundance limits. Without the explicit expressions for the NLO-induced DM production cross sections or the error propagation from the chiral scale, it is not possible to verify that the bound remains robust when the NLO coefficients are varied within the EFT uncertainty band.

Authors: We agree that explicit expressions improve verifiability. In the revised manuscript we will add the full analytic expressions for the NLO-induced DM production cross sections (both DM-photon and DM-electron channels) in §4, together with the freeze-in rate integrals. In §5 we will include a dedicated error-propagation analysis showing that O(1) variations in the NLO coefficients around the chiral-scale expectation leave the 10^{-36} cm² bound intact as a conservative order-of-magnitude limit. The BBN constraints are obtained from standard public codes with the induced electromagnetic interactions; we will reference the relevant input files and parameter ranges. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central bounds combine standard BBN and freeze-in limits on NLO electromagnetic operators with meson-decay limits on LO hadronic operators, all within chiral EFT. No equations reduce the final cross-section limit to a parameter fitted from the same data or to a self-citation chain. The claim that NLO EM interactions arise inevitably is presented as a derivation from the EFT structure rather than an assumption that loops back to the target result. The derivation remains self-contained against external benchmarks (BBN, meson lifetimes) without self-definitional or fitted-input reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of chiral effective theory for sub-GeV momentum transfers and the assumption that dark matter has no direct leading-order coupling to photons or electrons.

axioms (1)

domain assumption Chiral effective theory accurately captures low-energy hadronic interactions independent of UV completion
Invoked to derive bounds that do not depend on high-energy details

pith-pipeline@v0.9.0 · 5472 in / 1304 out tokens · 34223 ms · 2026-05-16T19:52:17.869562+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Working exclusively within the low-energy chiral effective theory... DM that interacts only hadronically at leading order also inevitably interacts with photons or electrons at next-to-leading-order.
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The leading order DM-meson interactions are given by the CV-dependent terms... at O(p4) via L10 + 2H1 and WZW

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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DM interacts only hadronically at leading order. 1

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The mediator(s) between the DM and SM have mass greater than 2 O(100) MeV

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(Motivated by aU(1) orZ 2 stabilising symmetry.)

DM interacts with the SM via an operator that is bilinear in the DM fieldχ. (Motivated by aU(1) orZ 2 stabilising symmetry.)

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The DM fieldχis a singlet underSU(3) c ×U(1) Q. Schematically, we consider DM interactions of the form L ⊃ cαβ Λn Oα SMOβ χ ,(1) whereO α SM are local, gauge-singlet operators consisting of quark and/or gluon fields and the operatorsO β χ are bi- linear inχand can be non-local. Thec αβ are dimension- less coefficients and Λ parametrises the scale of the U...

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Big Bang Nucleosynthesis The success of SM BBN tightly constraints the abun- dances of any additional relativistic degrees of freedom during neutrino decoupling and nucleosynthesis. In fact, sub-MeV mass states that were in equilibrium at any time after the QCD phase transition but before the end of BBN are essentially excluded. More specifically, an elec...

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In particular, the decay rates ofπ,K, andBmesons to final states with miss- ing energy are all tightly constrained

Meson decays Meson decays can provide strong constraints on the hadronic interactions of DM. In particular, the decay rates ofπ,K, andBmesons to final states with miss- ing energy are all tightly constrained. This is espe- cially true for the FCNC decaysK→π+ invisible, B→K+ invisible, andB→π+ invisible. In this work, we do not consider bounds from invisib...

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Other constraints There are many other observables that can be used to constrain the DM parameter space, but which we do not consider here. First, there are those observables 5 that require the specification of a Lagrangian valid at higher energies, beyond a few hundred MeV. These in- clude searches for missing energy at the Large Hadron Collider, direct ...

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Vector operator For the vector operator, DM interacts with the SM plasma atT≲10 MeV via the processese +e− →χ¯χand/or γγ→γχ¯χ. The former process generally dominates, since the latter is suppressed by an additional factor ofαand the three-body phase space. However,γγ→γχ¯χbecomes the dominant process for the case of universal couplings, C V =1. In the foll...

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Pseudoscalar operator For DM interactions with the quark pseudoscalar operator,γγ→χ¯χis the leading process for DM thermalisation and freeze-in production atT≲10 MeV. This process proceeds via the Feynman diagram shown in the left panel of fig. 4 and its amplitude can be readily obtained from the leading order Chiral Lagrangian in eq. (19): iMγγ→χ¯χ= iα π...

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