Chiral Perturbation Theory at NNNLO

TL;DR

This paper reviews the systematic construction of chiral perturbation theory at NNNLO, focusing on the Lagrangian, pion mass, and decay constant, and discusses the theory's predictivity given the large number of low energy constants.

Contribution

It provides a detailed construction of the NNNLO chiral Lagrangian and analyzes the implications for pion properties and the theory's predictability.

Findings

Constructed the NNNLO Lagrangian for chiral perturbation theory.

Analyzed pion mass and decay constant at NNNLO.

Discussed the challenges in the theory's predictivity due to many low energy constants.

Abstract

Chiral perturbation theory is a much successful effective field theory of quantum chromodynamics at low energies. The effective Lagrangian is constructed systematically order by order in powers of the momentum $p^2$, and until now the leading order (LO), next-to leading order (NLO), next-to-next-to leading order (NNLO) and next-to-next-to-next-to leading order (NNNLO) have been studied. In the following review we consider the construction of the Lagrangian and in particular focus on the NNNLO case. We in addition review and discuss the pion mass and decay constant at the same order, which are fundamental quantities to study for chiral perturbation theory. Due to the large number of terms in the Lagrangian and hence low energy constants arising at NNNLO, some remarks are made about the predictivity of this effective field theory.