An a$_{0}$ resonance in strongly coupled πη, K$\bar K$ scattering from lattice QCD

Abstract

We present the first calculation of coupled-channel meson-meson scattering in the isospin =1, G-parity negative sector, with channels πη, K$\bar K$ and πη′, in a first-principles approach to QCD. From the discrete spectrum of eigenstates in three volumes extracted from lattice QCD correlation functions we determine the energy dependence of the S-matrix, and find that the S-wave features a prominent cusplike structure in πη→πη close to the K$\bar K$ threshold coupled with a rapid turn-on of amplitudes leading to the K$\bar K$ final state. This behavior is traced to an a$_{0}$(980)-like resonance, strongly coupled to both πη and K$\bar K$, which is identified with a pole in the complex energy plane, appearing on only a single unphysical Riemann sheet. Consideration of D-wave scattering suggests a narrow tensor resonance at higher energy.