σ(500) resonance pole positions as function of m_π: analysis with a unitary coupled-channel model

Resonance pole positions of the f₀(500) alias σ(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 qq̄ states. The σ is described with a light and a strange qq̄ seed, mixing with each other mainly through the common ππ, KK̄, and ηη meson-meson channels. The few model parameters are fitted to experimental S-wave ππ phase shifts up to 1 GeV, yielding, in the case of the physical pion mass, resonance poles at $(460-i222)$ MeV for the σ(500) and $(978-i37)$ MeV for the f₀(980). Resonance, bound-state, and virtual-state pole trajectories are shown as a function of m_π 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_πvalues.