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

TL;DR

This paper investigates whether the broad enhancement X(1576) observed in certain decay channels can be explained by final state interactions involving $ ho(1450,1700)$ decays, considering dispersive effects and their implications.

Contribution

It introduces a detailed analysis of dispersive contributions from $ ho(1450,1700)$ decays to explain the X(1576) enhancement, linking FSI effects to observed spectral features.

Findings

Dispersive effects from $ ho(1450,1700)$ decays can produce enhancements near 1576 MeV.

Similar mechanisms predict an enhancement around 1580 MeV in the $ ho^+ ho^-$ spectrum.

The results suggest X(1576) may be explained without invoking new resonances.

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 $\rho(1450,1700)\to \rho^+\rho^-$.