2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/47656In the absence of nucleons, we use partial wave unitarity, to show that the chiral expansion parameter must be close to $p^2/4πf_π^2$ rather than $p^2/16π^2 f_π^2$ as previously suggested, where $p$ is a typical pion momentum and $f_π$ the pion decay constant. When nucleons are included, we apply the Tani-Foldy-Wouthuysen (TFW) transformation to the pion-nucleon effective Lagrangian to obtain an expansion in powers of $1/m_N$ (inverse nucleon mass). The results are presented up to order ${\cal O} (1/m_N^3)$, corresponding to ${\cal O} (p^4)$ in the momentum. In this case partial wave-unitarity is also lost in about the same range of momenta.7 pagesHigh Energy Physics - Phenomenologytext