Decoupling-limit consistency of the generalized SU(2) Proca theory

We study the consistency of decoupling limit generalized SU(2) Proca theory (GSU2P). Namely, we healthiness those terms whose analysis in scalar was not originally established reconstruction full (see work by Gallego Cadavid et al. [Phys. Rev. D 102, 104066 (2020)]). Those are parity-violating ${\stackrel{\texttildelow{}}{\mathcal{L}}}_{4,2}^{1}$ and parity-conserving beyond ${\mathcal{L}}_{4,2}^{3}$ ${\mathcal{L}}_{4,2}^{4}$. Using $3+1$ Arnowitt-Deser-Misner formalism, write down kinetic Lagrangian these show that their corresponding matrices degenerate. This degeneracy is a necessary condition for propagation right number degrees freedom, as required primary constraint-enforcing relation. Interestingly, term, which purely non-Abelian, does contribute to theory, so its contribution trivially Similarly, but cases, contributions ${\mathcal{L}}_{4,2}^{4}$ turn out be degenerate well. The results presented this paper represent progress construction fully healthy GSU2P.