Lattice QCD studies on baryon interactions from Luschers finite volume method and HAL QCD method

A comparative study between the Luschers finite volume method and the time-dependent HAL QCD method is given for the $XiXi$($^1mathrm{S}_0$) interaction as an illustrative example. By employing the smeared source and the wall source for the interpolating operators, we show that the effective energy shifts $Delta E_{rm eff} (t)$ in Luschers method do not agree between different sources, yet both exhibit fake plateaux. On the other hand, the interaction kernels $V(vec{r})$ obtained from the two sources in the HAL QCD method agree with each other already for modest values of $t$. We show that the energy eigenvalues $Delta E(L)$ in finite lattice volumes ($L^3$) calculated by $V(vec{r})$ indicate that there is no bound state in the $XiXi(^1mathrm{S}_0)$ channel at $m_{pi}=0.51$ GeV in 2+1 flavor QCD.