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

Abstract

The $\Delta \Delta$ 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 $\Delta$-$\Delta$ potential in the ${}^7{S}_3$ channel is obtained from the lattice data with the lattice spacing $a\simeq 0.121$ fm and the lattice size $L\simeq 3.87$ 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 $\Delta \Delta$ threshold for the heavy pion masses. The tensor part of the transition potential from $\Delta \Delta$ to $NN$ is also extracted to investigate the coupling strength between the $S$-wave $\Delta \Delta$ 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.

Comments: 8 pages, 6 figures