Anomalous chiral perturbation theory meson Lagrangian to orderp6reexamined

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, ${\mathcal{L}}_{6,\epsilon }.$ 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 $\mathrm{SU}\left(3\right),$ and 5 $\mathrm{SU}\left(2\right)\mathrm{}$ elements. Furthermore, we introduce 8 supplementary terms due to the extension of the chiral group to ${SU(N}_f{)}_L\times {SU(N}_f{)}_R\times {U\left(1\right)\mathrm{}}_V.$