Decoding spin-parity quantum numbers and decay widths of double $J\mathrm{/}\psi$ exotic states

We derive helicity amplitudes for the fully charmed tetraquark states decays into vector meson pair under two types of models, where the one is from quark model and the other one is from diquark model. The decay angular distributions have been given by the cascade decays $T_{4c}\to J\mathrm{/}\psi (D_{(s)}^{\ast })+J\mathrm{/}\psi ({\bar{D}}_{(s)}^{\ast })$ along with $J\mathrm{/}\psi \to {\mu }^{+}+{\mu }^{-}$ or $D_{(s)}^{\ast }\to D_{(s)}+\pi$, showing that spin-0 and spin-2 states can be distinguished. We also find that the spin-0 state decay to $J\mathrm{/}\psi$-pair exhibits a higher degree of quantum entanglement than that in spin-2 state decays. These findings will assist in experimentally differentiating various spin-parity states, determining decay widths and unveiling undiscovered hadronic states within existing structures, thereby shedding light on the internal properties of double $J\mathrm{/}\psi$ exotic states.