$d^ast (2380)$ dibaryon from lattice QCD

The $DeltaDelta$ 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 ${}^7S_3$ channel is obtained from the lattice data with the lattice spacing $asimeq 0.121$ fm and the lattice size $Lsimeq 3.87$ 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 $DeltaDelta$ threshold for the heavy pion masses. The tensor part of the transition potential from $DeltaDelta$ to $NN$ is also extracted to investigate the coupling strength between the $S$-wave $DeltaDelta$ 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.

Partial wave decomposition on the lattice and its applications to the HAL QCD method

The approximated partial wave decomposition method to the discrete data on a cubic lattice, developed by C. W. Misner, is applied to the calculation of $S$-wave hadron-hadron scatterings by the HAL QCD method in lattice QCD. We consider the Nambu-Bethe-Salpeter (NBS) wave function for the spin-singlet $Lambda_c N$ system calculated in the $(2+1)$-flavor QCD on a $(32a~mathrm{fm})^3$ lattice at the lattice spacing $asimeq0.0907$ fm and $m_pi simeq 700$ MeV. We find that the $l=0$ component can be successfully extracted by Misners method from the NBS wave function projected to $A_1^+$ representation of the cubic group, which contains small $lge 4$ components. Furthermore, while the higher partial wave components are enhanced so as to produce significant comb-like structures in the conventional HAL QCD potential if the Laplacian approximated by the usual second order difference is applied to the NBS wave function, such structures are found to be absent in the potential extracted by Misners method, where the Laplacian can be evaluated analytically for each partial wave component. Despite the difference in the potentials, two methods give almost identical results on the central values and on the magnitude of statistical errors for the fits of the potentials, and consequently on the scattering phase shifts. This indicates not only that Misners method works well in lattice QCD with the HAL QCD method but also that the contaminations from higher partial waves in the study of $S$-wave scatterings are well under control even in the conventional HAL QCD method. It will be of interest to study interactions in higher partial wave channels in the HAL QCD method with Misners decomposition, where the utility of this new technique may become clearer.