Unitary model analysis of f0(500 ) pole positions by continuously varying mπ: 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 q q ¯ seeds, mixing with each other through the common S -wave π π , K K ¯, and η η meson-meson decay channels. The few model parameters are fitted to experimental S -wave π π phase shifts up to 1 GeV. In the case of the physical π^± mass of 139.57 MeV, resonance poles at (460 -i 222 ) MeV and (978 -i 37.2 ) 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 q q ¯ and meson-meson channels in the present model, that is, for a few discrete values of the unphysical pion mass in those lattice calculations.