The order $p^8$ mesonic chiral Lagrangian

Abstract

We derive the chiral Lagrangian at next-to-next-to-next-to-leading order (NNNLO) for a general number $N_f$ of light quark flavours as well as for $N_f=2,3$. We enumerate the contact terms separately. We also discuss the cases where some of the external fields are not included. An example of a choice of Lagrangian is given in the supplementary material.

Comments: 23 pages, The file basis.pdf contains the full basis. Misprints in Lorentz indices in basis corrected w.r.t. v2