Three point interaction of Dirac fermions with higher spin particles and discrete symmetries

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 $D=2m+1\mathrm{/}2m$, the interacting theories of a single massive higher spin have a \enquote{$m$} mod $2$ (or $D$ mod $4$) classification.