A study of hidden-color channel on the strangeness $-1$ dibaryon

Abstract

In theoretical studies of the baryon baryon interaction, dibaryons states are obtained some times. A WASA-at-COSY experiment suggests that one such state might have been observed in the $p n \rightarrow d \pi ^0 \pi ^0$ fusion reaction, although there are alternative explanations for this peak. We predicted prior to that experiment a possible Delta Delta bound state, that could play a role in that reaction. Also we found that the hidden-color (CC) channel plays an important role in the binding behavior of the Delta Delta system. In the present work, we will extend the theoretical investigation to another interesting dibaryon candidate $\Sigma ^{*}\Delta$ with strangeness $\mathcal{{S}}=-1$ for further understanding the role of the hidden-color channel. The $\Sigma ^{*}\Delta$ state with isospin $T=\frac{1}{2}$ and spin $S=3$ is dynamically investigated within the framework of chiral SU(3) quark model by solving a resonating group method (RGM) equation. The results show that the $\Sigma ^{*}\Delta$ can become bound state with a binding energy of about $35\text { MeV}$ and the corresponding root-mean-square (RMS) $0.89\text { fm}$ in the single-channel ($\Sigma ^{*}\Delta$) calculation, and would become $52\text { MeV}$ and $0.84\text { fm}$ in the coupled-channel ($\Sigma ^{*}\Delta$-CC) calculation, respectively. The hidden-color channel makes an increment of about $17\text { MeV}$ to the binding energy and the RMS decreases from $0.89\text { fm}$ to $0.84\text { fm}$, it clearly shows that $\Sigma ^* \Delta$ is a $\Sigma ^* \Delta$-CC deeply bound and compact state, where the coupling to the CC channel plays a significant role. The present work is significant for our further understanding the effect of the hidden-color channel on some other interesting dibaryon candidates with strangeness.