Probing a minimal dark gauge sector via microlensing of compact dark objects

Abstract: We introduce a minimal Dark Standard Model (DSM) consisting of a single spin-0 particle with dark $U(1)$ gauge symmetry, and completely decoupled from the visible sector. Characterized only by the scalar mass $μ$ and the dark charge $q$, this framework naturally gives rise to a rich phenomenology, including stable solitonic configurations that behave as dark "mini-MACHOs". We numerically build and evolve these gauged scalar-field solitons, derive their mass-radius relations, and identify a critical charge beyond which no gravitationally bound configurations exist. By combining these results with microlensing surveys that exclude compact objects heavier than the asteroid-mass scale ($M\lesssim 10^{-11}M_\odot$), we obtain the constraint $μ\gtrsim 10\,\rm eV$ for viable configurations, depending on $q$. Our results represent a step forward in showing that purely gravitational observations can constrain the internal parameters of a dark gauge sector, and provide a framework for exploring broader DSM scenarios through future probes such as gravitational wave detections.