The ρρinteraction in the hidden gauge formalism and the f_0(1370) and f_2(1270) resonances
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We have studied the interaction of vectors mesons within the hidden gauge formalism and applied it to the particular case of the $ρρ$ interaction. We find a strong attraction in the isospin, spin channels I,S=0,0 and 0,2, which is enough to bind the $ρρ$ 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 $ρ$ mass distribution is considered, and particularly when the $ππ$ 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 $ρρ$ interaction or, in simpler words, $ρρ$ molecular states.
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Version accepted for publication