Probing Sub-MeV Dark Matter with Neutron-Capture $\gamma$ Spectroscopy

We present a general, discovery-grade framework for searching for weakly coupled new particles emitted in nuclear de-excitation following neutron capture. Rather than relying on isolated spectral features, the method exploits correlated ``satellite-line combs’': multiple weak $\gamma$-ray lines appearing at a common energy offset $\mathrm{\Delta }$ below known capture transitions. By combining likelihood information across many parent lines and multiple target nuclei, the approach strongly suppresses nuclear-structure ambiguities and instrumental artifacts. We also discuss optimal target selection and practical experimental implementation with high-resolution HPGe detectors.