A prediction of $D^*$-multi-$ρ$ states

Abstract

We present a study of the many-body interaction between a $D^*$ and multi-$ρ$. We use an extrapolation to SU(4) of the hidden gauge formalism, which produced dynamically the resonances $f_2(1270)$ in the $ρρ$ interaction and $D^*_2(2460)$ in the $ρD^*$ interaction. Then let a third particle, $ρ$, $D^*$, or a resonance collide with them, evaluating the scattering amplitudes in terms of the Fixed Center Approximation of the Faddeev equations. We find several clear resonant structures above $2800\mev$ in the multibody scattering amplitudes. They would correspond to new charmed resonances, $D^*_3$, $D^*_4$, $D^*_5$ and $D^*_6$, which are not yet listed in the PDG, which would be analogous to the $ρ_3(1690)$, $f_4(2050)$, $ρ_5(2350)$, $f_6(2510)$ and $K^*_3(1780)$, $K^*_4(2045)$, $K^*_5(2380)$ described before as multi-$ρ$ and $K^*$-multi-$ρ$ states respectively.