Low-Energy Constants of Chiral Perturbation Theory from Pion Scalar Form Factors in N_{f}=2+1-Flavor Lattice QCD with Controlled Errors

We determine the low-energy constants f_{0}, L_{4}^{r} and L_{5}^{r} of SU(3) chiral perturbation theory from a lattice QCD calculation of the scalar form factors of the pion with fully controlled systematics. Lattice results are computed on a large set of N_{f}=2+1 gauge ensembles covering four lattice spacings a∈[0.049,0.086]  fm, pion masses M_{π}∈[130,350]  MeV, and various large physical volumes. By determining the notorious quark-disconnected contributions with unprecedented precision and using a large range of source-sink separations t_{sep}∈[1.0,3.25]  fm, we are able for the first time to obtain the scalar radii from a z-expansion parametrization of the form factors rather than a simple linear approximation at small momentum transfer. The low-energy constants are obtained from the physical extrapolation of the radii using next-to-leading-order SU(3) next-to-leading-order chiral perturbation theory to parametrize the quark mass dependence. Systematic uncertainties are estimated via model averages based on the Akaike information criterion. Our determination of L_{4}^{r} is the first lattice determination to obtain a result not compatible with zero.