A chiral covariant approach to $\rho\rho$ scattering

TL;DR

This paper employs a unitarized chiral covariant approach to vector meson scattering, successfully generating the scalar meson $f_0(1370)$ dynamically, but not the tensor meson $f_2(1270)$, highlighting the importance of relativistic effects.

Contribution

It introduces a covariant framework for vector meson scattering that clarifies the dynamical generation of certain resonances, correcting previous non-relativistic artifacts.

Findings

The scalar meson $f_0(1370)$ can be dynamically generated from $ ho ho$ interactions.

The tensor meson $f_2(1270)$ generation is not supported in this covariant approach.

Relativistic effects are crucial for accurate resonance generation in vector-vector interactions.

Abstract

We analyze vector meson - vector meson scattering in a unitarized chiral theory based on a chiral covariant framework. We show that a pole assigned to the the scalar meson $f_0(1370)$ can be dynamically generated from the $\rho\rho$ interaction, while this is not the case for the tensor meson $f_2(1270)$ as found in earlier works. We show that the generation of the tensor state is untenable due to an artefact of the extreme non-relativistic kinematics used before. We further consider the effects arising from the coupling of channels with different orbital angular momenta. We suggest to use the formalism outlined here to obtain more reliable results for the dynamical generation of resonances in the vector-vector interaction.