On the interpretation of a possible ~ 750 GeV particle decaying into ??

We consider interpretations of the recent ~ 3s reports by the CMS and ATLAS collaborations of a possible X (~750 GeV) state decaying into ?? final states. We focus on the possibilities that this is a scalar or pseudoscalar electroweak isoscalar state produced by gluon-gluon fusion mediated by loops of heavy fermions. We consider several models for these fermions, including a single vector-like charge 2/3 T quark, a doublet of vector-like quarks (T, B), and a vector-like generation of quarks, with or without leptons that also contribute to the X ? ?? decay amplitude. We also consider the possibility that X (750) is a dark matter mediator, with a neutral vector-like dark matter particle. These scenarios are compatible with the present and prospective direct limits on vector-like fermions from LHC Runs 1 and 2, as well as indirect constraints from electroweak precision measurements, and we show that the required Yukawa-like couplings between the X particle and the heavy vector-like fermions are small enough to be perturbative so long as the X particle has dominant decay modes into gg and ??. The decays X ? ZZ, Z? and W+W- are interesting prospective signatures that may help distinguish between different vector-like fermion scenarios.