Dispersive Contribution of ρ(1450,1700) Decays and X(1576)

We study whether the broad enhancement X(1576) arises from the final
state interaction (FSI) of ρ(1450,1700)→ρ⁺ρ^-→K⁺K^- decays. Both the absorptive and dispersive contributions of the above amplitudes are considered since the intermediate states are very close to ρ(1450,1700). The same mechanism leads to a similar enhancement around 1580MeV in the π⁺π^- spectrum in the J/ψ→π⁰π⁺π^- channel, which can be used to test whether X(1576) can be ascribed to the FSI effect of ρ(1450,1700)→ρ⁺ρ^-.