Authors: P. Gonzalez, E. Oset, J. Vijande
Title: An explanation of the $\Delta_{D_{35}}(1930)$ as a $\rho \Delta $ bound state.
Keywords: baryon spectra, missing resonance
Abstract:
The nature of the $\Delta_{D_{35}}(1930)(***)$ \cite{PDG08} has been a matter of controversy since its discovery, from a partial wave analysis of elastic and charge exchange $\pi p$ scattering data, in 1976 \cite{Cut76}. From the theoretical point of view refined three-quark models for baryons, based on two-body (quark) interactions, have been developed \cite{Cap00}. In all these models the $\Delta _{D_{35}}(1930)$ (ground state of $\Delta (5/2^-))$ is out of the systematics: the predicted mass is significantly above (80-230 MeV) the tabulated average mass. This comes from quark Pauli blocking preventing the $\Delta (5/2^-)$ ground state to be in the first energy band of negative parity. Under this circumstance $4q1\bar q$ components may be energetically favorable (in spite of the extra $q\bar q)$ and contribute importantly to the formation of a bound structure. Thus for $\Delta_{D_{35}}(1930)$ a $\rho\Delta$ component could play an important role. By using a simplified model for the coupling of the valence quark-antiquark component with the $\rho\Delta$ one the probability for this has been estimated to be about the $80\%$ \cite{Gon08} pointing out to the possible description of $\Delta _{D_{35}}(1930)$ as a $\rho\Delta$ bound state. To analyze this possibility we have adressed the problem of finding the bound states from the $\rho\Delta$ interaction. A framework that makes the study of vector mesons interacting with baryons accurate and manageable is the hidden gauge formalism \cite{hidden1}. The combination of such an interaction with chiral unitary techniques leads to $\rho\Delta$ bound states \cite{Gon09} in fair agreement with known baryonic resonances, within experimental and theoretical uncertainties. In particular the $\Delta_{D_{35}}(1930)$ and also its almost degenerate partner resonances $\Delta (1900)S_{31}(**)$ and $\Delta(1940)D_{33}(*)$ appear as a dynamical feature of the theory. This makes us conclude that $\Delta_{D_{35}}(1930)$ can be quite confidently assigned to a $\rho\Delta$ bound state. |