The order $p^8$ mesonic chiral Lagrangian

Understand

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.