Subthreshold parameters of $\pi\pi$ scattering revisited

TL;DR

This paper refines the determination of subthreshold parameters in cc scattering by integrating experimental data, lattice QCD results, and dispersive analysis, highlighting the impact of theoretical correlations.

Contribution

It provides a comprehensive analysis of cc scattering subthreshold parameters using combined experimental, lattice, and dispersive methods, including the effect of theoretical correlations.

Findings

Refined values for cc subthreshold parameters.

Quantified uncertainties through Monte Carlo sampling.

Analyzed the influence of cc scattering length correlations.

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.