Systematics of the HAL QCD Potential at Low Energies in Lattice QCD

7 May 2018Takumi IritaniSinya AokiTakumi DoiShinya GongyoTetsuo HatsudaYoichi IkedaTakashi InoueNoriyoshi IshiiHidekatsu NemuraKenji Sasaki

The $\Xi\Xi$ interaction in the $^1$S$_0$ channel is studied to examine the convergence of the derivative expansion of the non-local HAL QCD potential at the next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order potential from the N$^2$LO analysis gives the scattering phase shifts accurately at low energies, (ii) the full N$^2$LO potential gives only small correction to the phase shifts even at higher energies below the inelastic threshold, and (iii) the potential determined from the wall quark source at the leading order analysis agrees with the one at the N$^2$LO analysis except at short distances, and thus, it gives correct phase shifts at low energies... (read more)

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