$ππ$ Scattering in Three Flavour ChPT

Abstract

We present the scattering lengths for the $ππ$ processes in the three flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading order. We then combine this calculation with the determination of the parameters from $K_{e4}$ and the masses and decay constants and compare with the results of a dispersive analysis of $ππ$ scattering. The comparison indicates a small but nonzero value for the $1/N_c$ suppressed NLO low energy constants $L_4^r$ and $L_6^r$.