An example of Dark Sector is Mirror Dark Matter. The idea that along with the ordinary matter may exist its exact mirror copy, introduced for the parity conservation, is not new. Accordingly, each ordinary particle of the SM has a corresponding mirror partner of exactly the same mass as the ordinary one. The mirror fields are all singlets under the SM SUc(3)⊗SUL(2)⊗U(1) gauge group. Mirror matter is dark in terms of the SM inter actions, and could be a good candidate for dark matter. In addition to gravity, the interaction between our and this type of dark matter could be transmitted by some gauge singlet particles interacting with both sectors. Any neutral, elementary or composite particle, in principle, can have mixing with its mirror duplicate. This results in several interesting phenomena, such, e.g. as Higgs, positronium, muonium, or neutron oscillations into their hidden partner, which have been or planned to be experimentally tested]. P348 plans to search for the K_L - mirror K_L oscillations, which would manifest themselves through the K_L → invisible decay. 

See, arXiv:1409.2288; 1503.01595.