The anomalous Lagrangian in ChPT at NNLO

Abstract

The anomalous Lagrangian in mesonic Chiral Perturbation Theory, of odd intrinsic parity, is determined to next-to-next-to-leading order thereby completing the order $p^8$ Lagrangian. A schematic view of its construction with the MINIBAR package for Mathematica is presented and the final operator count is discussed for a general number of light quark flavours as well as for the physical cases $N_f=2,3$. The number of operators in our explicit construction of the Lagrangian basis is consistent with the number derived using the Hilbert series in the literature.