The \rho\rho interaction in the hidden gauge formalism and the f_0(1370) and f_2(1270) resonances

TL;DR

This paper investigates the interaction of rho mesons using the hidden gauge formalism, demonstrating that certain isospin and spin channels form bound states that correspond to the f_0(1370) and f_2(1270) resonances, supporting a molecular interpretation.

Contribution

The study provides a novel dynamical generation mechanism for the f_0(1370) and f_2(1270) resonances as rho-rho molecular states within the hidden gauge approach.

Findings

Strong attraction in I,S=0,0 and 0,2 channels leads to bound rho-rho states.

Results align with experimental masses and widths of f_0(1370) and f_2(1270).

Tensor state (f_2(1270)) is more strongly bound than the scalar (f_0(1370)).

Abstract

We have studied the interaction of vectors mesons within the hidden gauge formalism and applied it to the particular case of the $\rho \rho$ interaction. We find a strong attraction in the isospin, spin channels I,S=0,0 and 0,2, which is enough to bind the $\rho \rho$ system. We also find that the attraction in the I,S=0,2 channel is much stronger than in the 0,0 case. The states develop a width when the $\rho$ mass distribution is considered, and particularly when the $\pi \pi$ decay channel is turned on. Using a regularization scheme with cut offs of natural size, we obtain results in fair agreement with the mass and the width of the $f_0(1370)$ and $f_2(1270)$ meson states, providing a natural explanation of why the tensor state is more bound than the scalar and offering a new picture for these states, which would be dynamically generated from the $\rho \rho$ interaction or, in simpler words, $\rho \rho$ molecular states.