Six-quark structure of $d^{\ast }(2380)$ in chiral constituent quark model

Abstract

The structure of $d^{\ast }(2380)$ is re-studied with the single cluster structure in the chiral SU(3) quark model which has successfully been employed to explain the $N-N$ scattering data and the binding energy of deuteron. The binding behavior of such a six quark system is solved by using a variational method. The trial wave function is chosen to be a combination of a basic spherical symmetric component of $[(0s{)}^6{]}_{orb}$ in the orbital space with $0\hslash \omega$ excitation and an inner structural deformation component of $[(0s{)}^5(1s){]}_{orb}$ and $[(0s{)}^4(0p{)}^2{]}_{orb}$ in the orbital space with $2\hslash \omega$ excitation, both of which are in the spatial [6] symmetry. It is shown that the mass of the system is about $2356$ MeV, which is qualitative consistent with the result both from the two-cluster configuration calculation and from the data measured by the WASA Collaborations. This result tells us that as long as the medium-range interaction due to the chiral symmetry consideration is properly introduced, the mass of system will be reduced in a rather large extent. It also implies that the observed $d^{\ast }$ is a six-quark bound state with respect to the $\Delta \Delta$ threshold, which again supports the conclusion that $d^{\ast }$ is a hexaquark dominant state.

Comments: 6 pages, 3 figures.