The anomalous chiral Lagrangian at order p8

Abstract

We derive the order p8 Lagrangian of odd intrinsic parity for mesonic chiral perturbation theory, and provide the resulting operator basis in the supplementary material. Neglecting the non-zero singlet trace, we find 999 operators for a general number of quark flavours Nf , 705 for Nf = 3 and 92 for Nf = 2. Our numbers agree with those obtained through the Hilbert series approach in the literature. Including a singlet trace, as needed for the physical case of Nf = 2, instead yields 1210 operators for a general Nf , 892 for Nf = 3 and 211 for Nf = 2.