ϕ(2170) Decaying to ϕππ and ϕKK

Within the framework of dispersion theory, we study the the processes e+e−→ϕ(2170)→ϕππ(KK¯). The strong pion–pion final-state interactions, especially the KK¯ coupled channel in the S wave, are taken into account in a model-independent way using the Omnès function solution. Through fitting the experimental data of the ππ and ϕπ invariant mass distributions of the e+e−→ϕ(2170)→ϕπ+π− process, the low-energy constants in the chiral Lagrangian are determined. The theoretical prediction for the cross sections’ ratio σ(e+e−→ϕ(2170)→ϕK+K−)/σ(e+e−→ϕ(2170)→ϕπ+π−) is given, which could be useful for selecting the physical solution, when the fit to the e+e−→ϕK+K− cross-section distribution is available in the future. Our results suggest that above the kinematical threshold of ϕKK¯, the mechanism e+e−→ϕK+K−, with the kaons rescattering to a pion pair, plays an important role in the e+e−→ϕπ+π− transition.