The anomalous chiral Lagrangian at order p ⁸

We derive the order p ⁸ 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 N_f , 705 for N_f = 3 and 92 for N_f = 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 N_f = 2, instead yields 1210 operators for a general N_f , 892 for N_f = 3 and 211 for N_f = 2.