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

Understand

We make a detailed comparison between the direct method and the HAL QCD potential method for the baryon-baryon interactions, taking the $\Xi\Xi$ system at $m_\pi= 0.51$ GeV in 2+1 flavor QCD and using both smeared and wall quark sources.

• The energy shift $\Delta E_\mathrm{eff}(t)$ in the direct method shows the strong dependence on the choice of quark source operators, which means that the results with either (or both) source are false.
• The time-dependent HAL QCD method, on the other hand, gives the quark source independent $\Xi\Xi$ potential, thanks to the derivative expansion of the potential, which absorbs the source dependence to the next leading order correction.
• The HAL QCD potential 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 dependence of finite volume energy from the potential.