Extension of the chiral perturbation theory meson Lagrangian to orderp6

We have constructed the most general chirally invariant Lagrangian ${\mathit{scrL}}_6$ for the meson sector at order ${\mathit{p}}^6$. The result provides an extension of the standard Gasser-Leutwyler Lagrangian ${\mathit{scrL}}_4$ to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the construction was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The claim to have obtained the most general Lagrangian relies on this systematic construction and on the elimination of redundant quantities using relations of which we are aware, rather than on a general formal proof of either completeness or independence. The ‘‘equation-of-motion’’ terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating ${\mathit{p}}^6$ contributions to simple processes. © 1995 The American Physical Society.