Analytic representations of $m_K$, $F_K$, $m_\eta$ and $F_\eta$ in two loop $SU(3)$ chiral perturbation theory

Understand

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in $SU(3)$ chiral perturbation theory.

• These involve sunset diagrams and their derivatives evaluated at $p^2=m_P^2$ ($P=\pi, K, \eta$).
• Recalling that there are three mass scales in this theory, $m_\pi$, $m_K$ and $m_\eta$, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past.
• In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for $m_\pi$ and $F_\pi$, the pion mass and decay constant.