Chiral extrapolation of the sigma resonance

We analyze results on isoscalar ππ scattering from a $N_f=2+1$ lattice QCD calculation by the HadronSpectrum collaboration by re-summing the two-flavor chiral scattering amplitude of the next-to-leading order in the so-called inverse amplitude method. The lattice data can be well extrapolated to the physical pion mass. We also find that both $I=0$ and $I=1$ lattice data can be described simultaneously for pion masses up to $M_{\pi }=236$ MeV. Our analysis of the lattice data suggests that the $f_0\left(500\right)$ or σ resonance becomes a bound state at $M_{\pi }\approx 320$ MeV. A future lattice simulation at this pion mass can, therefore, be of large value for insight into properties of the isoscalar resonance.