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.

中文翻译：

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NNNLO 的手性微扰理论

手性微扰理论是一种非常成功的低能量子色动力学场论。有效拉格朗日函数是按动量 $p^2$ 的幂按顺序系统地构造的，到目前为止，领先顺序 (LO)、次领先 (NLO)、次到次领先 (NNLO) ) 和 next-to-next-to-next-to-lead order (NNNLO) 已经被研究过。在下面的回顾中，我们考虑拉格朗日函数的构造，特别关注 NNNLO 情况。此外，我们还回顾和讨论了相同数量级的介子质量和衰变常数，它们是手性微扰理论研究的基本量。由于拉格朗日项中的大量项以及因此在 NNNLO 处出现的低能量常数，对这种有效场理论的预测性进行了一些评论。