6533b839fe1ef96bd12a59a2

RESEARCH PRODUCT

Description of thef2(1270),ρ3(1690),f4(2050),ρ5(2350), andf6(2510)resonances as multi-ρ(770)states

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In a previous work regarding the interaction of two $\ensuremath{\rho}(770)$ resonances, the ${f}_{2}(1270)$ (${J}^{PC}={2}^{++}$) resonance was obtained dynamically as a two-$\ensuremath{\rho}$ molecule with a very strong binding energy, 135 MeV per $\ensuremath{\rho}$ particle. In the present work we use the $\ensuremath{\rho}\ensuremath{\rho}$ interaction in spin 2 and isospin 0 channel to show that the resonances ${\ensuremath{\rho}}_{3}(1690)$ (${3}^{--}$), ${f}_{4}(2050)$ (${4}^{++}$), ${\ensuremath{\rho}}_{5}(2350)$ (${5}^{--}$), and ${f}_{6}(2510)$ (${6}^{++}$) are basically molecules of increasing number of $\ensuremath{\rho}(770)$ particles. We use the fixed center approximation of the Faddeev equations to write the multibody 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 $\ensuremath{\rho}$ as the number of $\ensuremath{\rho}$ mesons is increased.