On the minimality of the order p^6 chiral Lagrangian

TL;DR

This paper introduces a method to determine the minimal set of independent operators in the order p^6 mesonic chiral Lagrangian, exemplified by identifying 27 operators in the two-flavour case without scalar or pseudo-scalar sources.

Contribution

A new procedure is developed to establish the minimal basis of operators in the mesonic Lagrangian at order p^6 in Chiral Perturbation Theory.

Findings

The minimal Lagrangian for two-flavour case has 27 independent operators.

The method can verify the minimality of operator bases in chiral Lagrangians.

Application of the method confirms the operator count in a specific scenario.

Abstract

A method to find relations between the operators in the mesonic Lagrangian of Chiral Perturbation Theory at order p^6 is presented. The procedure can be used to establish if the basis of operators in the Lagrangian is minimal. As an example, we apply the method to the two-flavour case in the absence of scalar and pseudo-scalar sources (s=p=0), and conclude that the minimal Lagrangian contains 27 independent operators.