Chiral expansion of baryon masses and $σ$-terms

TL;DR

This work analyzes the chiral expansion of octet baryon masses and σ-terms in heavy-baryon chiral perturbation theory up to ${\cal O}(m_q^2)$. It develops a complete ${\cal O}(q^4)$ effective Lagrangian and employs resonance saturation (decuplet, Roper octet, and scalar mesons) to fix fourteen LECs, finding all but one determined by octet masses and $\sigma_{\pi N}(0)$ with observables largely insensitive to the remaining parameter. The authors show two-loop corrections largely renormalize into one-loop parameters and report a chiral-limit baryon mass $m_0 = 770 \pm 110$ MeV, with nucleon mass corrections small and hyperon corrections sizeable, and a strangeness content $y = 0.21 \pm 0.20$. They also provide estimates for kaon-nucleon σ-terms and discuss theoretical uncertainties, concluding that three-flavor CHPT convergence is not yet established. Overall, the paper provides a systematic framework to connect baryon masses, σ-terms, and strangeness content within HBCHPT using resonance saturation, while highlighting remaining theoretical challenges and data needs.

Abstract

We analyze the octet baryon masses and the pion/kaon--nucleon $σ$--terms in the framework of heavy baryon chiral perturbation theory. We include {\it all} terms up-to-and-including quadratic order in the light quark masses, $m_q$. We develop a consistent scheme to estimate low--energy constants related to scalar--isoscalar operators in the framework of resonance exchange involving one--loop graphs. The pertinent low--energy constants can only be estimated up to some finite coefficients. Including contributions from loop graphs with intermediate spin--3/2 decuplet and spin--1/2 octet states and from tree graphs including scalar mesons, we use the octet baryon masses and the pion--nucleon $σ$--term to fix all but one of these coefficients. Physical results are insensitive to this remaining parameter. It is also demonstrated that two--loop corrections only modify some of the subleading low--energy constants. We find for the baryon mass in the chiral limit, $m_0 = 770 \pm 110$ MeV. While the corrections of order $m_q^2$ are small for the nucleon, they are still sizeable for the $Λ$, the $Σ$ and the $Ξ$. Therefore a definitive statement about the convergence of three--flavor baryon chiral perturbation can not yet be made. The strangeness content of the nucleon is $y = 0.21 \pm 0.20$. We also estimate the kaon--nucleon $σ$--terms and some two--loops contributions to the nucleon mass.