### Speaker

### Description

Chiral perturbation theory (ChPT) and the $1/N_c$ expansion provide systematic frameworks in investigating the strong interactions at low energy. A combined framework of both approaches has been developed and applied for baryons with three light-quark-flavors. The small scale expansion of the combined approach is identified as the $\xi$-expansion, in which the power counting of $1/N_c$ and chiral expansions are linked as $\cal{O}({p})=\cal{O}({1/N_c})=\cal{O}({\xi})$. Experimentally observed baryon masses as well as the lattice QCD baryon masses are analyzed to $\cal{O}({\xi^3})$ in the combined framework, with explicit inclution of the decuplet intermediate-baryon states. The connection between the deviation of the Gell-Mann-Okubo relation and the $\sigma$ term associated with the scalar density $\bar u u+\bar d d-2\bar s s$ is identified. In particular, the deviation from the mass combination $\hat{m}\frac{\partial}{\partial \hat{m}}m_N= \frac{\hat{m}}{m_s-\hat{m}}\left(m_\Sigma + m_\Xi - 2 m_N \right)$ which gives rise to the so called $\sigma$-term puzzle is studied in the $\xi$-expansion. The application of this present framework allows one to identify the large higher order non-analytic inquark masses contributions to that mass combination. The final result on the nucleon $\sigma_{\pi N}$ obtained by combined fits to experimental and lattice QCD baryon masses, will be presented.