Composite asymmetric dark matter scenarios naturally explain why the dark matter mass density is comparable with the visible matter mass density. Such scenarios generically require some entropy transfer mechanism below the composite scale; otherwise, their late-time cosmology is incompatible with observations. A tiny kinetic mixing between a dark photon and the visible photon is a promising example of the low-energy portal. In this paper, we demonstrate that grand unifications in the dark and the visible sectors explain the origin of the tiny kinetic mixing. We particularly consider an ultraviolet completion of a simple composite asymmetric dark matter model, where asymmetric dark matter carries a $B-L$ charge. In this setup, the longevity of asymmetric dark matter is explained by the $B-L$ symmetry, while the dark matter asymmetry originates from the $B-L$ asymmetry generated by thermal leptogenesis. In our minimal setup, the Standard Model sector and the dark sector are unified into $SU(5)_mathrm{GUT} times SU(4)_mathrm{DGUT}$ gauge theories, respectively. This model generates required $B-L$ portal operators while suppressing unwanted higher-dimensional operators that could wash out the generated $B-L$ asymmetry.
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