We present a study of the many-body interaction between a $D^{*}$ and multi-$\rho$. We use an extrapolation to SU(4) of the hidden gauge formalism, which produced dynamically the resonances $f_2(1270)$ in the $\rho \rho$ interaction and $D_2^{*}(2460)$ in the $\rho D^{*}$ interaction. We then let a third particle, $\rho$, $D^{*}$, 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 Particle Data Group, which would be analogous to the ${\rho }_3(1690)$, $f_4(2050)$, ${\rho }_5(2350)$, $f_6(2510)$ and $K_3^{*}(1780)$, $K_4^{*}(2045)$, $K_5^{*}(2380)$ described before as multi-$\rho$ and $K^{*}$-multi-$\rho$ states, respectively.

• Received 23 July 2012

DOI:https://doi.org/10.1103/PhysRevD.86.094019