The dispersive contribution of $ρ(1450,1700)$ decays and X(1576)

Abstract

We study whether the broad enhancement X(1576) arises from the final state interaction (FSI) of $ρ(1450,1700)\to ρ^+ρ^-\to K^{+}K^{-}$ decays. We consider both the absorptive and dispersive contribution of the above amplitudes since the intermediate states are very close to $ρ(1450,1700)$. The same mechanism leads to a similar enhancement around 1580 MeV in the $π^{+}π^-$ spectrum in the $J/ψ\to π^{0}π^{+}π^{-}$ channel, which can be used to test whether X(1576) can be ascribed to the FSI effect of $ρ(1450,1700)\to ρ^+ρ^-$.