Triangle mechanism in the decay process $J/\psi \to K^{-}{K}^{+}{a}_1(1260)$

Abstract

The role of 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 $K^{\ast }\varphi ,K^{\ast }\to K\pi$ and then $K^{\ast }\bar{K}$ fuses into the $a_1(1260)$ resonance. We find that this mechanism leads to a triangle singularity around $M_{\mathrm{inv}}(K^{-}{a}_1(1260))\approx 1920$ 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 $\text{Br}(J/\psi \to K^{-}{K}^{+}{a}_1(1260),a_1\to \pi \rho )=1.210\times 10^{-5}$ and $\text{Br}(J/\psi \to K^{-}{K}^{+}{a}_1(1260))=3.501\times 10^{-5}$. Such a effect from 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 $a_1(1260)$.

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