Nonlocal Portal to the Dark Sector

We propose a nonlocal realization of the Stueckelberg portal between the Standard Model and Dark Sector, which decouple in the local limit. This implies that the mediator, $U(1{)}_D$ Dark Photon $A^{\mathrm{\prime }}$ with a Stueckelberg mass, interacts nonlocally with the Standard Model quarks and leptons. We study phenomenological implications of this scenario for the meson decays into semi-invisible and invisible channels. We discuss the experimental limitations on the model parameters, including the nonlocality scale.