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 p2, 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.
Highlights
The strong force of nature is described by Quantum Chromodynamics (QCD), a quantum field theory whose degrees of freedom are the fundamental quarks and gluons
In the following we shall review the current status of chiral perturbation theory (ChPT) at next-to-next-to-next-to leading order (NNNLO), but due to the scarce literature this review will focus on the construction of the Lagrangian and the pion mass and decay constant at NNNLO
Chiral perturbation theory has been very successful in describing the low energy sector of QCD in terms of mesonic degrees of freedom
Summary
The strong force of nature is described by Quantum Chromodynamics (QCD), a quantum field theory whose degrees of freedom are the fundamental quarks and gluons. Each order introduces new LECs and in order to make numerical predictions one needs to know these coefficients Not until recently that the next-to-next-to-next-to leading order (NNNLO) Lagrangian was derived [6] and calculations at this order were started [7] These references only consider the non-anomalous sector. In the following we shall review the current status of ChPT at NNNLO, but due to the scarce literature this review will focus on the construction of the Lagrangian and the pion mass and decay constant at NNNLO. Minor remarks about the prospect for future NNNLO calculations are made
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