Tetraquark candidate Zc(3900) from coupled-channel scattering - how to extract hadronic interactions? -

We present recent progress of lattice QCD studies on hadronic interactions which play a crucial role to understand the properties of atomic nuclei and hadron resonances. There are two methods, the plateau method (or the direct method) and the HAL QCD method, to study the hadronic interactions. In the plateau method, the determination of a ground state energy from the temporal correlation functions of multi-hadron systems is a key to reliably extract the physical observables. It turns out that, due to the contamination of excited elastic scattering states nearby, one can easily be misled by a fake plateau into extracting the ground state energy. We introduce a consistency check (sanity check) which can rule out obviously false results obtained from a fake plateau, and find that none of the results obtained at the moment for two-baryon systems in the plateau method pass the test. On the other hand, the HAL QCD method is free from the fake-plateau problem. We investigate the systematic uncertainties of the HAL QCD method, which are found to be well controlled.On the basis of the HAL QCD method, the structure of the tetraquark candidate Z c (3900), which was experimentally reported in e + e - collisions, is studied by the s-wave two-meson coupled-channel scattering. The results show that the Z c (3900) is not a conventional resonance but a threshold cusp. A semi-phenomenological analysis with the coupled-channel interaction to the experimentally observed decay mode is also presented to confirm the conclusion.