A description of the f2(1270), rho3(1690), f4(2050), rho5(2350) and f6(2510) resonances as multi-rho(770) states
In a previous work regarding the interaction of two $\rho(770)$ resonances, the $f_2(1270)$ ($J^{PC}=2^{++}$) resonance was obtained dynamically as a two-$\rho$ molecule with a very strong binding energy, 135~MeV per $\rho$ particle. In the present work we use the $\rho\rho$ interaction in spin 2 and isospin 0 channel to show that the resonances $\rho_3(1690)$ ($3^{--}$), $f_4(2050)$ ($4^{++}$), $\rho_5(2350)$ ($5^{--}$) and $f_6(2510)$ ($6^{++}$) are basically molecules of increasing number of $\rho(770)$ particles. We use the fixed center approximation of the Faddeev equations to write the multi-body interaction in terms of the two-body scattering amplitudes. We find the masses of the states very close to the experimental values and we get an increasing value of the binding energy per $\rho$ as the number of $\rho$ mesons is increased.