Double chiral logarithms of generalized chiral perturbation theory for low-energy ππ scattering

We express the two-massless-flavor Gell-Mann–Oakes–Renner ratio in terms of low-energy ππ observables including the O(p6) double chiral logarithms of generalized chiral perturbation theory. Their contribution is sizeable and tends to compensate the one from the single chiral logarithms. However it is not large enough to spoil the convergence of the chiral expansion. As a signal of reduced theoretical uncertainty, we find that the scale dependence from the one-loop single logarithms is almost completely canceled by the one from the two-loop double logarithms.