Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory

TL;DR

This paper computes vector and axial-vector two-point functions, meson masses, and decay constants at two-loop order in three-flavour Chiral Perturbation Theory, providing detailed theoretical expressions and numerical estimates.

Contribution

It extends Chiral Perturbation Theory calculations to next-to-next-to-leading order for three light flavours, including new ${ m O}(p^6)$ constants and numerical estimates.

Findings

Derived expressions for two-point functions at two loops

Provided numerical estimates for meson masses and decay constants

Estimated some ${ m O}(p^6)$ constants using resonance models

Abstract

The vector and axial-vector two-point functions are calculated to next-to-next-to-leading order in Chiral Perturbation Theory for three light flavours. We also obtain expressions at the same order for the masses, $m_\pi^2$, $m_K^2$ and $m_\eta^2$, and the decay constants, $F_\pi$, $F_K$ and $F_\eta$. We present some numerical results after a simple resonance estimate of some of the new ${\cal O}(p^6)$ constants.