We constructed all possible kinematically allowed three-point interactions of two massless Dirac spinors with massive higher-spin bosons. In any D spacetime, the interactions have been constructed using the projections of the higher spin irreducible representations of Spin(D − 1) over the product of two irreducible spinor representations of Spin(D − 2). Based on this analysis, we have further classified the space of theories involving two massless Dirac spinors and a single (or multiple) massive higher spin(s) based on the discrete symmetries: C, R, and T. We found that in any D = 2m + 1/2m, the interacting theories of a single massive higher spin have a “m” mod 2 (or D mod 4) classification.
