The anomalous chiral Lagrangian of order $p^6$

Abstract

We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$ . The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavors, 23 terms for three and 5 for two flavors. In the two flavor case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.