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arxiv: 2305.15473 · v4 · submitted 2023-05-24 · ✦ hep-th · gr-qc· hep-ph

Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter

Arpan Bhattacharyya , Saptaswa Ghosh , Sounak Pal This is my paper

Pith reviewed 2026-05-24 08:51 UTC · model grok-4.3

classification ✦ hep-th gr-qchep-ph
keywords worldline effective field theoryblack hole binariesdark matteraxionsdark photonspost-Newtonian expansiongravitational radiation
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0 comments X

The pith

Binary black hole conservative dynamics receive corrections from dark photon kinetic mixing at 1PN order and from axion-photon coupling at 2.5PN order in a dark matter background.

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

This paper applies worldline effective field theory to inspiralling non-spinning black hole binaries in an environment of axion-like particles and dark photons. It derives the leading corrections to the two-body conservative potential from each field and coupling, together with the associated radiated power in gravitational, scalar, and vector channels. The kinetic mixing parameter enters the conservative sector at 1PN while the axion-photon coupling enters at 2.5PN; certain radiation contributions from the axion coupling vanish identically for planar orbits. These results supply explicit post-Newtonian corrections that can be folded into waveform models for binaries evolving inside dark matter halos.

Core claim

The conservative dynamics are computed up to 1PN for gravitational, electromagnetic, and Proca fields and up to 2PN for the scalar field. The axion-electromagnetic coupling g_aγγ first appears in the conservative dynamics at 2.5PN order and the kinetic mixing constant γ at 1PN order. Radiation calculations show that g_aγγ contributes to gravitational radiation at N(7)LO and to scalar radiation at N(5)LO; these contributions vanish for any orbit confined to a plane because of a binormal term in the effective radiative action but are nonzero for orbits that extend in three dimensions. The parameter γ contributes to gravitational radiation at N(2)LO and N(4)LO.

What carries the argument

The worldline effective field theory action that couples the binary worldlines to gravitational, scalar axion, Proca dark-photon, and electromagnetic fields together with their interaction vertices.

If this is right

  • The kinetic mixing constant γ modifies the conservative dynamics at 1PN order.
  • The axion-photon coupling g_aγγ modifies the conservative dynamics at 2.5PN order.
  • g_aγγ contributes to gravitational radiation at N(7)LO and to scalar radiation at N(5)LO.
  • The radiative corrections from g_aγγ vanish for planar orbits but remain for three-dimensional orbits.
  • γ contributes to gravitational radiation at N(2)LO and N(4)LO.

Where Pith is reading between the lines

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

  • Waveform templates that include these corrections could be used to search for dark-matter-induced phase shifts in LIGO-Virgo-KAGRA events.
  • The vanishing of certain axion contributions for planar orbits implies that orbital inclination or eccentricity may serve as an additional observable for constraining the axion-photon coupling.
  • The same worldline framework can be extended to spinning binaries or to higher post-Newtonian orders to generate further dark-matter signatures.

Load-bearing premise

The dark matter environment is treated as a uniform background that does not back-react on the binary at the post-Newtonian orders retained.

What would settle it

An explicit evaluation of the effective two-body action demonstrating that g_aγγ enters the conservative dynamics at an order lower than 2.5PN, or a direct computation of the radiative action showing nonzero g_aγγ contributions for strictly planar orbits.

read the original abstract

We investigate the correction to the potential that gives rise to the bound orbits and radiation from non-spinning inspiralling binary black holes in a dark matter environment consisting of axion-like particles and dark photons using the techniques of Worldline Effective Field Theory. We compute the conservative dynamics up to $1$PN order for gravitational, electromagnetic, and Proca fields and up to $2$PN order for the scalar field. The effect of axion-electromagnetic coupling ($g_{a\gamma\gamma}$) arises to the conservative dynamics at $2.5$PN order and the kinetic mixing constant ($\gamma$) at $1$PN order. Furthermore, we calculate the radiation due to the various fields present in our theory. We find that the contribution of $g_{a\gamma\gamma}$ to the gravitational radiation appears at $N^{(7)}LO$ and to the scalar radiation appears at $N^{(5)}LO$. We also find that these radiative corrections due to the coupling $g_{a\gamma\gamma}$ vanishes for any orbit confined to a plane because of the existence of a binormal like term in effective radiative action but give rise to non-zero contributions for any orbit that lies in three dimensions. Last but not the least, $\gamma$ contributes to the gravitational radiation at $N^{(2)}LO$ and $N^{(4)}LO$.

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

1 major / 0 minor

Summary. The paper applies worldline effective field theory to compute post-Newtonian corrections to the conservative dynamics and gravitational/scalar radiation of non-spinning inspiralling binary black holes embedded in a dark-matter environment consisting of axion-like particles and dark photons. It reports conservative dynamics to 1PN order for gravitational, electromagnetic, and Proca sectors and to 2PN for the scalar sector, with the axion-photon coupling g_aγγ entering conservative dynamics at 2.5PN and the kinetic mixing parameter γ at 1PN. Radiative contributions are also computed, including the claim that g_aγγ-induced corrections to gravitational radiation appear at N^(7)LO and to scalar radiation at N^(5)LO, with vanishing contributions for planar orbits due to a binormal-like term in the effective radiative action, while γ contributes at N^(2)LO and N^(4)LO.

Significance. If the central calculations and power-counting assumptions hold, the work supplies concrete PN-order predictions for how dark-photon and axion couplings modify binary dynamics and radiation, including a geometric mechanism that suppresses certain radiative effects in planar orbits. This could be relevant for interpreting gravitational-wave signals in the presence of ultralight dark matter. The explicit statement of PN orders and the identification of the binormal suppression constitute clear, falsifiable outputs.

major comments (1)
  1. [Setup and power counting (likely §2–3)] The treatment of the dark-matter fields as a fixed uniform background whose back-reaction on the binary can be neglected at the claimed orders is load-bearing for all reported corrections. The worldline EFT power counting does not automatically guarantee that binary-sourced perturbations to the scalar or Proca fields remain higher-order; the leading induced density or field fluctuations can enter the effective potential at the same 1–2PN level as the reported dark-matter corrections. An explicit power-counting argument or explicit computation of the back-reaction terms is required to justify the truncation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting this important point on power counting. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Setup and power counting (likely §2–3)] The treatment of the dark-matter fields as a fixed uniform background whose back-reaction on the binary can be neglected at the claimed orders is load-bearing for all reported corrections. The worldline EFT power counting does not automatically guarantee that binary-sourced perturbations to the scalar or Proca fields remain higher-order; the leading induced density or field fluctuations can enter the effective potential at the same 1–2PN level as the reported dark-matter corrections. An explicit power-counting argument or explicit computation of the back-reaction terms is required to justify the truncation.

    Authors: We agree that an explicit justification is required. In the revised manuscript we will add a dedicated paragraph (or short subsection) in §2 that supplies the missing power-counting argument. The argument will show that binary-induced fluctuations of the scalar and Proca fields are suppressed by the small DM density parameter ρ_DM / ρ_binary together with the weak couplings g_aγγ and γ; these factors push the back-reaction contributions to at least 3PN (scalar) and 2.5PN (Proca), safely above the orders we report. We will also clarify why the worldline EFT treats the DM background as external at the orders of interest. revision: yes

Circularity Check

0 steps flagged

Direct perturbative EFT calculation with no self-referential reductions

full rationale

The paper performs a standard post-Newtonian expansion using worldline effective field theory for the conservative dynamics and radiation in the presence of dark matter fields. The computations are direct perturbative calculations up to specified PN orders, with new couplings entering at specific orders as stated. No equations reduce the results to fitted parameters or self-citations that bear the load of the central claims. Self-citations to prior EFT works are standard and do not create circularity here. The derivation chain is self-contained against external benchmarks of EFT power counting.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The calculation rests on the standard worldline EFT axioms for point-particle sources coupled to gravity plus additional fields, plus the post-Newtonian velocity expansion. No new free parameters are introduced beyond the model couplings g_aγγ and γ, which are treated as external constants. No new entities are postulated.

free parameters (2)
  • g_aγγ
    Axion-photon coupling strength; treated as an external parameter whose effects are computed order by order.
  • γ
    Kinetic mixing parameter between dark and ordinary photons; enters at 1PN.
axioms (2)
  • domain assumption Worldline effective field theory is applicable to non-spinning black holes coupled to gravitational, electromagnetic, Proca, and scalar fields at the stated PN orders.
    Invoked throughout the abstract as the computational framework.
  • domain assumption Dark-matter background is uniform and does not back-react on the binary at the orders considered.
    Implicit in the setup of inspiralling binaries in a dark-matter environment.

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discussion (0)

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