A description of the f2(1270), rho3(1690), f4(2050), rho5(2350) and f6(2510) resonances as multi-rho(770) states

TL;DR

This paper models several high-spin meson resonances as multi-rho states, showing they can be understood as molecules of rho(770) particles with masses matching experimental data.

Contribution

It demonstrates that high-spin meson resonances are dynamically generated as multi-rho molecules using the fixed center approximation of Faddeev equations.

Findings

Resonance masses closely match experimental values

Binding energy per rho increases with number of rho mesons

Resonances are effectively described as multi-rho molecular states

Abstract

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.