Disentangling Dark Gauge Symmetries with Deep Learning on the Lund Jet Plane
While dark sectors with new confining gauge symmetries are compelling candidates for resolving the dark matter mystery, discerning the underlying dark gauge group structure remains a significant phenomenological challenge. In this work, we systematically investigate the distinct radiation patterns of dark quarks and gluons by developing a novel Monte Carlo parton shower simulation framework applicable to arbitrary gauge groups. To handle generalized color topologies and the momentum recoil scheme, our algorithm constructs color dipoles using a group-theoretic tagging procedure. Furthermore, our simulation framework employs an exact three-body phase-space parameterization by analytically solving the cubic kinematic equation for each branching. This enables capturing full mass effects for both dark quarks and dark gluons, naturally yielding precise boundaries including mass-induced gaps and dead-cone thresholds. To decode these complex emission topologies, we utilize the Lund Jet Plane representation alongside a dedicated Neural Sorter Mamba Network. We demonstrate that our framework can successfully disentangle the perturbative footprints of different gauge symmetries. Finally, we show that our discrimination power remains robust against the unknown non-perturbative details of dark hadronization by maintaining high classification efficiencies even under stringent infrared $k_T$ cutoffs, and we explicitly quantify the impact of massive dark gauge bosons on the classification sensitivity.