The role of the triangle mechanism in the decay process $J/\psi \to K^{-}{K}^{+}{a}_1(1260)$ is probed. In this mechanism, a close-up resonance with mass 1823 MeV and width 122 MeV decays into $K^{*}\varphi ,K^{*}\to K\pi$ and then $K^{*}\overline{K}$ fuses into the $a_1(1260)$ resonance. We find that this mechanism leads to a triangle singularity around $M_{\mathrm{inv}}(K^{-}{a}_1(1260))\approx 1920\mathrm{MeV}$, where the axial-vector meson $a_1(1260)$ is considered as a dynamically generated resonance. With the help of the triangle mechanism we find sizable branching ratios $\mathrm{Br}(J/\psi \to K^{-}{K}^{+}{a}_1(1260),a_1\to \pi \rho )=1.210\times {10}^{-5}$ and $\mathrm{Br}(J/\psi \to K^{-}{K}^{+}{a}_1(1260))=3.501\times {10}^{-5}$. Such an effect from the triangle mechanism of the decay process could be investigated by such as BESIII, LHCb and Belle-II experiments. This potential investigation can help us obtain the information of the axial-vector meson $a_1(1260)$.

中文翻译：

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衰变过程中的三角机制J/ψ→K−K+a1(1260)

三角机制在衰变过程中的作用 $J/\psi \to {钾}^{-}{钾}^{+}{\mathrm{一种}}_1(1260)$被探测。在这种机制中，质量为 1823 MeV、宽度为 122 MeV 的近距离共振衰减为${钾}^{*}\phi ,{钾}^{*}\to 钾\pi$ 进而 ${钾}^{*}\overline{钾}$ 熔断成 ${\mathrm{一种}}_1(1260)$谐振。我们发现这种机制导致了周围的三角形奇点${米}_{\mathrm{投资}}({钾}^{-}{\mathrm{一种}}_1(1260))\approx \mathrm{1920年}\mathrm{电动汽车}$，其中轴矢量介子 ${\mathrm{一种}}_1(1260)$被认为是动态产生的共振。在三角机制的帮助下，我们找到了相当大的分支率$溴(J/\psi \to {钾}^{-}{钾}^{+}{\mathrm{一种}}_1(1260),{\mathrm{一种}}_1\to \pi \rho )=1.210\times {10}^{-5}$ 和 $溴(J/\psi \to {钾}^{-}{钾}^{+}{\mathrm{一种}}_1(1260))=3.501\times {10}^{-5}$. 这种衰变过程三角机制的影响可以通过 BESIII、LHCb 和 Belle-II 等实验来研究。这种潜在的调查可以帮助我们获得轴矢量介子的信息${\mathrm{一种}}_1(1260)$.