Interactions between vector mesons and dynamically generated resonances

TL;DR

This paper revisits vector meson interactions, highlighting the need for improved unitarization methods to accurately identify dynamically generated resonances beyond near-threshold regions.

Contribution

It introduces an improved unitarization approach using the N/D method for covariant $ ho ho$ scattering, addressing issues with unphysical cuts in previous models.

Findings

Identification of unphysical left-hand cuts in on-shell Bethe-Salpeter approach.

Validation of the N/D method for reliable resonance predictions.

Comparison with nonrelativistic results supports the new approach.

Abstract

The $\rho\rho$ interaction and the corresponding dynamically generated bound states are revisited. We demonstrate that an improved unitarization method is necessary to study the pole structures of amplitudes outside the near-threshold region. In this work, we extend the study of the covariant $\rho\rho$ scattering in a unitarized chiral theory to the $S$-wave interactions for the whole vector-meson nonet. We demonstrate that there are unphysical left-hand cuts in the on-shell factorization approach of the Bethe-Salpeter equation. This is in conflict with the correct analytic behavior and makes the so-obtained poles, corresponding to possible bound states or resonances, unreliable. To avoid this difficulty, we employ the first iterated solution of the $N/D$ method and investigate the possible dynamically generated resonances from vector-vector interactions. A comparison with the results from the nonrelativistic calculation is provided as well.