Untangling the spin of a dark boson in decays

We analyze the Z-boson decay Z ->gamma X into a photon (gamma) plus a hypothetical light boson (X) belonging to a dark or secluded sector. Because of its feeble interactions with Standard Model fields, this dark boson behaves as missing energy in the detector. We consider for X the cases of spin-1 (massless dark-photon), spin-0 (axionlike), and spin-2 (gravitonlike) particles and explore the way to untangle its spin origin. All these scenarios predict a universal signature for this decay, characterized by a single monochromatic photon in the Z center of mass, with energy about half of the Z mass, plus a neutrinolike missing energy associated with the X boson. We show that if the Z -> gamma X signal should be discovered at e(+)e(-) colliders, the angular distribution of the monochromatic photon in e(+)e(-) -> Z -> gamma X can provide a clean probe to discriminate between the J = 1 and alternative J = 0/2 spin nature of the dark boson.