Unitary model analysis of f 0(500) pole positions by continuously varying m: Comparison with discrete lattice predictions

Resonance, bound -state, and virtual -state pole positions of the f0(500) scalar meson are computed as a continuous function of pion mass in the framework of a unitarized and analytic coupled -channel model for scalar mesons, described as dynamical quark-antiquark states. The f0(500) is modeled with both light and strange qq over bar seeds, mixing with each other through the common S -wave pi pi, K over bar K, and eta eta meson -meson decay channels. The few model parameters are fitted to experimental S -wave pi pi phase shifts up to 1 GeV. In the case of the physical pi +/- mass of 139.57 MeV, resonance poles at (460 - i222) MeV and (978 - i37.2) MeV are found for the f0(500) and f0(980), respectively. Resonance, bound -state, and virtual -state pole trajectories are computed and plotted as a function of pion masses up to 500 MeV, both in the complex -energy and complex -momentum planes. The results are discussed and compared to the most advanced lattice QCD computations employing interpolators that correspond to the qq over bar and meson -meson channels in the present model, that is, for a few discrete values of the unphysical pion mass in those lattice calculations.