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Lattice QCD studies on baryon interactions from Lüscher's finite volume method and HAL QCD method

A comparative study between the Lüscher's finite volume method and the time-dependent HAL QCD method is given for the $ΞΞ$($^1\mathrm{S}_0$) 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 $ΔE_{\rm eff} (t)$ in Lüscher's 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 $ΔE(L)$ in finite lattice volumes ($L^3$) calculated by $V(\vec{r})$ indicate that there is no bound state in the $ΞΞ(^1\mathrm{S}_0)$ channel at $m_π=0.51$ GeV in 2+1 flavor QCD.