The anomalous chiral perturbation theory meson Lagrangian to order $p^6$ revisited

Abstract

We present a revised and extended construction of the mesonic Lagrangian density in chiral perturbation theory (ChPT) at order $p^6$ in the anomalous (or epsilon) sector, ${\mathcal{L}}_{6,\hat{I}\mu }$. After improving several aspects of the strategy we used originally, i.e., a more efficient application of partial integration, the implementation of so-called Bianchi identities, and additional trace relations, we find the new monomial sets to include 24 $SU(N_f)$, 23 SU(3), and 5 SU(2) elements. Furthermore, we introduce 8 supplementary terms due to the extension of the chiral group to $SU(N_f{)}_L\times SU(N_f{)}_R\times U(1{)}_V$.

21 pages, Latex, using RevTeX