Tetraquark candidate Zc(3900) from coupled-channel scattering -- how to extract hadronic interactions?
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 methods to extract the hadronic interactions were proposed; the Luscher's method and the HAL QCD method. These are known to be theoretically equivalent. In the first part of my talk, I will discuss baryon-baryon interactions using so-called the "direct method" in which the energy eigenvalues calculated from the temporal correlation of two baryons are used to extract the scattering phase shifts by the Luscher's method. I will demonstrate that energy eigenvalues in the direct method have serious contamination from 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 these issues. In the second part of my talk, I will proceed to discuss the structure of the tetraquark candidate Zc(3900) from the meson-meson coupled-channel scattering on the lattice with the HAL QCD method. The Zc(3900) is experimentally reported as a peak in the pi J/psi invariant mass in the Y(4260)-->pi pi J/psi decay. To understand the nature of the Zc(3900), it is most important to extract the coupled pi J/psi - rho eta_c - anti-D D interactions. For this purpose, we employ the coupled-channel HAL QCD method. The s-wave coupled-channel meson-meson potential relevant to the Zc(3900) is extracted, and scattering observables such as invariant mass spectra and the pole position of the S-matrix on the complex energy plane are calculated. Also, we calculate the decay rate of the Y(4260)-->pi pi J/psi reaction and compare the result with the experiments. All of our results show that the Zc(3900) is not a conventional resonance but a threshold cusp associated with the opening of the anti-D D threshold.
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Hadron Spectroscopy and Interactions