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

Abstract

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

Comments: 4 pages, 4 figures