  In recent years, detailed studies of three-pion systems have become possible
in lattice QCD. This has in turn led to interest in 3-to-3 scattering of pions
in the chiral perturbation theory framework. In addition to being an
interesting study of multi-meson dynamics in its own right, it provides a
valuable handle on finite-volume effects and the pion mass dependence, thus
complementing the lattice results. I present our derivation of the
next-to-leading order amplitude for this process, as well as its conversion
into the three-particle K-matrix, which enables direct comparison to the
lattice. Our results significantly improve the agreement between theory and
lattice, which was poor when only leading-order effects were taken into
account.
