Hadron interactions from lattice QCD - application to hadron resonances

I will present recent progresses of LQCD on hadronic interactions which play a crucial role to understand hadron resonances and the properties of atomic nuclei. So far, two theoretically equivalent methods, the L\"{u}scher's method and the HAL QCD method, to extract the hadronic interactions were proposed.
First, I will discuss hadron interactions using so-called the ``plateau method'' in which the energy eigenvalues calculated from the temporal correlation of two hadrons are used to extract the scattering phase shifts by the L\"{u}scher's method. I will demonstrate that energy eigenvalues in the plateau method have a serious contamination of the mixing with different states, so that the results obtained are inconsistent with the effective range expansion.
I then demonstrate how the HAL QCD method solves this issue.
I then proceed to discussions of coupled-channel hadron interactions on the lattice with the HAL QCD method, which are important to study the nature of hadron resonances.