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 $K^* \phi, K^* \to K \pi$ and then $K^* \bar{K}$ fuses into the $a_1(1260)$ resonance. We find that this mechanism leads to a triangle singularity around $M_{\rm inv}(K^- a_1(1260))\approx 1920$ 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 $a_1(1260)$.
Highlights
Researchers have shown an increased interest in triangle singularities which were first researched by Landau [1,2] in the 1960s
A considerable amount of literature [3,4,5,6,7] has been published on triangle singularities which are essentially brought about triangle loop Feynman diagrams where an external particle 1 decays into A and B particles, internal particle B decays into particle C and an external particle 2, and particles A and C fuse into an external particle 3
Particle B has a finite width since it can decay to particle C and 2, which leads to a finite peak in the invariant mass distributions
Summary
Researchers have shown an increased interest in triangle singularities which were first researched by Landau [1,2] in the 1960s. Soon the peak was explained as a triangle singularity corresponding to the πf0ð980Þ decay mode of a1ð1260Þ resonance [11,12,13] Another consideration of the triangle mechanism lies in the abnormally enhanced isospin violating process ηð1405Þ → πf0ð980Þ compared to the process ηð1405Þ → πa0ð980Þ [14]. We reach a peak of the invariant mass MinvðKþa1Þ at around 1920 MeV by applying the triangle mechanism, where a close-up dynamically generated resonance decays into KÃφ, KÃ → Kπ and KÃKfuses into the a1ð1260Þ resonance. For the a1K−KÃþ vertex inside the triangle loop of the decay process, we apply the chiral unitary approach by viewing the a1ð1260Þ as a dynamically generated hadron state.
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