Exclusive Decays of the Fully Heavy Tetraquarks into Light Mesons

In this work, we investigate the exclusive decays of the fully heavy tetraquark states $T_{4c,b}$ into light mesons, specifically $π$ and $K$, using the framework of Non-Relativistic QCD (NRQCD) and collinear QCD factorization for hard exclusive processes. We estimate the decay widths to be $10^{-9}$ GeV and $10^{-14}$ GeV for the decays $T_{4c} \to π^+π^-$ and $T_{4b} \to π^+π^-$ (and similarly for $K^+K^-$), respectively. The branching ratio for $T_{4c} \to π^+π^-(K^+K^-)$ 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 $J/ψ\to p\bar{p}$. However, unlike the latter process, the decay $T_{4c,b} \to π^+π^-(K^+K^-)$ exhibits unique features that arise only in processes involving multiple incoming or outgoing particles. One such feature is the necessity of maintaining the $i\varepsilon$-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 {\tt 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 $T_{4c,b} \to p\bar{p}$, as well as to phase-space integrations where each denominator is a linear combination of integration variables.

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