An a0 resonance in strongly coupled π η , K K ¯ scattering from lattice QCD

We present the first calculation of coupled-channel meson-meson scattering in the isospin =1 , G -parity negative sector, with channels π η , K K ¯ and π η^', 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 π η →π η close to the K K ¯ threshold coupled with a rapid turn-on of amplitudes leading to the K K ¯ final state. This behavior is traced to an a₀(980 )-like resonance, strongly coupled to both π η and K 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.