Baryon sigma terms in SU(3) BChPT x 1/Nc

Abstract

ChPT and the $1/N_c$ expansion provide systematic frameworks for the strong interactions at low energy. A combined framework of both expansions has been developed and applied for baryons with three light-quark-flavors. The small scale expansion of the combined approach is identified as the $ξ$-expansion, in which the power counting of the expansions is linked according to $O(p)=O(1/N_c)=O(ξ)$. The physical baryon masses as well as lattice QCD baryon masses for different quark mass masses are analyzed to $O(ξ^3)$ in that framework. $σ$ terms are addressed using the Feynman Hellmann theorem. For the nucleon, a useful connection between the deviation of the Gell-Mann-Okubo relation and the $σ$ term $σ_{8N}$ associated with the scalar density $\bar u u+\bar d d-2\bar s s$ is identified. In particular, the deviation from the tree level relation $σ_{8N}=\frac 13(2 m_N-m_Σ-m_Ξ)$, which gives rise to the so called $σ$-term puzzle, is studied in the $ξ$-expansion. A large correction non-analytic in $ξ$ results for that relation, making plausible the resolution of the puzzle. Issues with the determination of the strangeness $σ$ terms are discussed, emphasizing the need for lattice calculations at smaller $m_s$ for better understanding the range of validity of the effective theory. The analysis presented here leads to $σ_{πN}=69(10)$~MeV and $σ_{πΔ}=60(10)$~MeV.