Spin identification of dark sector mediators through angular distributions

A variety of experiments are operating or planned to search for displaced decays of light long-lived dark sector particles. In case such a state is discovered, the next step is determining its quantum numbers. We identify an angular observable, reconstructible solely from the decay products' four-momenta, that exhibits an anisotropic distribution for vector bosons from light meson decays and an isotropic distribution for scalars. We demonstrate that searches at DUNE, SHiP and FASER2 will be able to identify the mediator spin in sizable regions of yet unconstrained parameter space.