In this work, we investigate the exclusive decays of the fully-heavy tetraquark states $T_{4c,b}$ into light mesons, specifically $\pi$ and $K$, using the framework of nonrelativistic quantum chromodynamics (NRQCD) and collinear QCD factorization for hard exclusive processes. We estimate the decay widths to be ${10}^{-9}\mathrm{GeV}$ and ${10}^{-14}\mathrm{GeV}$ for the decays $T_{4c}\to {\pi }^{+}{\pi }^{-}$ and $T_{4b}\to {\pi }^{+}{\pi }^{-}$ (and similarly for $K^{+}{K}^{-}$), respectively. The branching ratio for $T_{4c}\to {\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ is on the order of ${10}^{-8}$, making it currently unobservable in existing experiments. The factorization of $T_{4c,b}$ into light hadrons shares similarities with the decay $J/\psi \to p\overline{p}$. However, unlike the latter process, the decay $T_{4c,b}\to {\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ exhibits unique features that arise only in processes involving multiple incoming or outgoing particles. One such feature is the necessity of maintaining the $iϵ$-prescription for the denominators or propagators due to the divergences in the kinematic region of interest. Employing the sector decomposition method, along with the aid of the Cheng-Wu theorem and the qhull program, we present a systematic approach to handle the convolutions and phase-space integrations. This method can also be extended to similar processes, such as $T_{4c,b}\to p\overline{p}$, as well as to phase-space integrations where each denominator is a linear combination of integration variables.

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