Triangle mechanism in the decay process J/ψ→K−K+a1(1260)

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 $122$ decays into $K^* \phi, K^* K \pi$ then \bar{K}$ fuses $a_1(1260)$ resonance. We find that leads to singularity around $M_{\rm inv}(K^- a_1(1260))\approx 1920$ MeV, where axial-vector meson considered as dynamically generated With help we sizable branching ratios $\text{Br}(J/\psi a_1(1260),a_1 \pi \rho)=1.210 \times 10^{-5}$ a_1(1260))=3.501 10^{-5}$. Such effect from could be investigated by such BESIII, LHCb Belle-II experiments. This potential investigation can us obtain information $a_1(1260)$.