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Resonance pole positions of the f₀ (500) alias (500) meson are computed and plotted as a continuous function of pion mass in the framework of a unitary and analytic coupled-channel model for scalar mesons as dynamical qq states. The is described with a light and a strange qq seed, mixing with each other mainly through the common, KK, and meson-meson channels. The few model parameters are fitted to experimental S-wave phase shifts up to 1 GeV, yielding, in the case of the physical pion mass, resonance poles at (460-i222) MeV for the (500) and (978-i37) MeV for the f₀ (980). Resonance, bound-state, and virtual-state pole trajectories are shown as a function of m_ running from 139. 57 MeV to 1 GeV. These are compared to recent lattice QCD computations that use interpolating fields corresponding to the model's channels, i. e. , for a few discrete m_ values.
George Rupp (Mon,) studied this question.