$d^{\ast }(2380)$ dibaryon from lattice QCD

The $\mathrm{\Delta }\mathrm{\Delta }$ dibaryon resonance $d^{\ast }(2380)$ with $(J^P, I)=(3^+, 0)$ is studied theoretically on the basis of the 3-flavor lattice QCD simulation with heavy pion masses ($m_{\pi }=679,841$ and $1018$ MeV). By using the HAL QCD method, the central $\mathrm{\Delta }$-$\mathrm{\Delta }$ potential in the ${}^7{S}_3$ channel is obtained from the lattice data with the lattice spacing $a\simeq 0.121$fmandthelatticesize$L\simeq 3.87$ fm. The resultant potential shows a strong short-range attraction, so that a quasi-bound state corresponding to $d^{\ast }(2380)$ is formed with the binding energy $25$-$40$ MeV below the $\mathrm{\Delta }\mathrm{\Delta }$ threshold for the heavy pion masses. The tensor part of the transition potential from $\mathrm{\Delta }\mathrm{\Delta }$ to $NN$ is also extracted to investigate the coupling strength between the $S$-wave $\mathrm{\Delta }\mathrm{\Delta }$ system with $J^P=3^{+}$ and the $D$-wave $NN$ system. Although the transition potential is strong at short distances, the decay width of $d^{\ast }(2380)$ to $NN$ in the $D$-wave is kinematically suppressed, which justifies our single-channel analysis at the range of the pion mass explored in this study.