Possible existence of a dibaryon candidate $N\Delta$ ($D_{21}$)

TL;DR

This study investigates the potential existence of the $N\Delta$ dibaryon candidate $D_{21}$, concluding that current models and phase shift analyses do not support its bound state formation, making it less likely than the $D_{12}$ candidate.

Contribution

The paper provides a dynamical calculation and mass analysis indicating the unlikelihood of the $D_{21}$ dibaryon existing as a bound state.

Findings

Dynamical models do not produce a bound $D_{21}$ state.

Low-energy scattering phase shifts support the non-existence of $D_{21}$.

Mass estimates suggest $D_{21}$ is heavier than $D_{12}$, reducing its bound state probability.

Abstract

Inspired by the experimental report by WASA-at-COSY Collaboration, we investigate the possibile existence of the dibaryon candidate $N\Delta$ with quantum numbers $IJ^P=21^+$ ($D_{21}$). The dynamical calculation shows that we cannot obtain the bound $D_{21}$ state in the models which can obtain the experimental $d^{*}$. %although the $D_{21}$ state can bound in the range of parameters in quark models. The low-energy scattering phase shifts of the $N-\Delta$ scattering give the same conclusion. Besides, the mass calculation by using the Gursey-Radicati mass formula and the analysis of the matrix elements of the color magnetic interaction show that the mass of $D_{21}$ is larger than that of $D_{12}$ ($N\Delta$ with $IJ^P=12^+$), which indicate that it is less possible for the $D_{21}$ than the $D_{12}$ to form bound state.