Subthreshold parameters of $\pi\pi$ scattering revisited

Abstract

Using a variety of experimental results and lattice QCD calculations of $\pi\pi$ scattering lengths, while employing dispersive representations of the amplitude based on Roy equations, we compute the subthreshold parameters of this process. We use Monte Carlo sampling to numerically model the probability distribution of the results based on all uncertainties in the inputs. We also investigate the dependence of the results on a theoretical correlation between the $\pi\pi$ scattering lengths $a^0_0$ and $a^2_0$, which was previously established in the framework of two-flavor chiral perturbation theory.