Photon--Dark Matter Elastic Scattering: An Effective-Operator Scan and First Operator-Resolved Sensitivity Estimates from the Galactic Halo

Elastic photon--dark matter scattering attenuates gamma-ray spectra along a line of sight, probing the same operators as dark matter annihilation to photons but at a rate linear, rather than quadratic, in dark matter density. We consider Standard Model gauge-invariant effective operators of mass-dimension 5 to 7, suppressed by a cutoff scale Λ, coupling scalar, Majorana or Dirac dark matter to the photon. The leading operators with non-vanishing real-photon amplitudes enter at dimension-5 for Dirac dark matter and dimension-7 for Majorana dark matter. In the electroweak-doublet dipole portal, the inelastic splitting invoked to evade direct detection also closes the CMB annihilation bound, leaving attenuation the only one of the three photon-sector probes that survives. Applying this to a pixel-level reanalysis of 17 years of Fermi--LAT Pass 8 data toward the Galactic centre, we derive the first operator-resolved sensitivity estimates for photon--dark matter scattering from the Galactic halo: Λ 0.32 GeV for the dimension-5 Dirac dipoles, 0.21 GeV for the dimension-6 scalar Rayleigh operator and 0.79 -- 1.06 GeV for the dimension-7 Rayleigh family. The reach is weak: it lies below the EFT-validity threshold across the cold dark matter mass range, and is superseded on the dipole plane by CMB and direct-detection constraints. The framework is calibrated against pseudo-experiments, and recomputes the sensitivity for any instrument that provides a per-bin spectrum with uncertainties and a line-of-sight column density.