The Mesonic Chiral Lagrangian of Order $p^6$

TL;DR

This paper constructs the mesonic chiral Lagrangian at order p^6, detailing the number of terms for different flavor cases and demonstrating methods to eliminate redundant terms through equations of motion and field redefinitions.

Contribution

It provides a comprehensive derivation of the order p^6 chiral Lagrangian, including the enumeration of terms and techniques for reducing redundancies.

Findings

Explicit enumeration of terms for different flavor cases

Demonstration of equivalence between equations of motion and field redefinitions

Implementation of methods to minimize the Lagrangian terms

Abstract

We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic even-intrinsic-parity sector at order $p^6$. The Lagrangian contains 112 in principle measurable + 3 contact terms for the general case of $n$ light flavours, 90+4 for three and 53+4 for two flavours. The equivalence between equations of motion and field redefinitions to remove spurious terms in the Lagrangians is shown to all orders in the chiral expansion. We also discuss and implement other methods for reducing the number of terms to a minimal set.