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We make a detailed comparison between the direct method and the HAL QCDpotential method for the baryon-baryon interactions, taking the $\Xi\Xi$ systemat $m_\pi= 0.51$ GeV in 2+1 flavor QCD and using both smeared and wall quarksources. The energy shift $\Delta E_\mathrm{eff}(t)$ in the direct method showsthe strong dependence on the choice of quark source operators, which means thatthe results with either (or both) source are false. The time-dependent HAL QCDmethod, on the other hand, gives the quark source independent $\Xi\Xi$potential, thanks to the derivative expansion of the potential, which absorbsthe source dependence to the next leading order correction. The HAL QCDpotential predicts the absence of the bound state in the $\Xi\Xi$($^1$S$_0$)channel at $m_\pi= 0.51$ GeV, which is also confirmed by the volume dependenceof finite volume energy from the potential. We also demonstrate that the originof the fake plateau in the effective energy shift $\Delta E_\mathrm{eff}(t)$ at$t \sim 1$ fm can be clarified by a few low-lying eigenfunctions andeigenvalues on the finite volume derived from the HAL QCD potential, whichimplies that the ground state saturation of $\Xi\Xi$($^1$S$_0$) requires $t\sim 10$ fm in the direct method for the smeared source on $(4.3 \\mathrm{fm})^3$ lattice, while the HAL QCD method does not suffer from such aproblem.

Baryon interactions in lattice QCD: the direct method vs. the HAL QCD potential method