Sigma term and strangeness content of octet baryons

TL;DR

This study computes the sigma terms and strangeness content for all octet baryons from lattice QCD using the Hellmann-Feynman theorem, relating mass derivatives to quark masses. It combines regular mass-expansion fits with covariant SU(3) baryon χPT extrapolations to reach physical light-quark masses, and performs a thorough, multi-faceted uncertainty analysis across 864 extrapolation procedures. The nucleon results favor a low $\sigma_{\pi N}$ around the canonical value, but uncertainties remain sizable, particularly for the strangeness content $y_N$, which shows model dependence when invoked with χPT alone. Overall, the work provides a principled, first-principles determination of octet sigma terms and strangeness contents, while highlighting the need for lighter pion masses and broader strange-quark mass coverage to reduce systematic uncertainties and strengthen conclusions for dark-matter phenomenology and hadron structure.

Abstract

By using lattice QCD computations we determine the sigma terms and strangeness content of all octet baryons by means of an application of the Hellmann-Feynman theorem. In addition to polynomial and rational expressions for the quark mass dependence of octet members, we use SU(3) covariant baryon chiral perturbation theory to perform the extrapolation to the physical up and down quark masses. Our N_f=2+1 lattice ensembles include pion masses down to about 190 MeV in large volumes (M_πL > 4), and three values of the lattice spacing. Our main results are the nucleon sigma term σ_{πN} = 39(4)(^{+18}_{-7}) and the strangeness content y_{N} = 0.20(7)(^{+13}_{-17}). Under the assumption of validity of covariant baryon χPT in our range of masses one finds y_{N} = 0.276(77)(^{+90}_{-62}).

Figures (3)

• Figure 1: Overview of our simulation points in terms of $M_\pi$ and $\sqrt{2M_K^2 - M_\pi^2}$. The former gives a measure of the isospin averaged up and down quark mass while the latter determines the strange quark mass. The symbols refer to the three lattice spacings, and the physical point is marked with a cross. Error bars are statistical only.
• Figure 2: Example of a $\chi$PT fit corresponding to a particular choice of fitting interval for the correlators. In this particular case we choose to fit $g_A$ and $\xi$, and not to include higher-order terms. We have only used data with $M_\pi < 410$ MeV. The correlated $\chi^2 = 38.5$ for 34 degrees of freedom, yields a fit quality of $\sim 0.27$.
• Figure 3: Distribution of values for $\sigma_{\pi N}$ in background (yellow), and how different pion mass cuts (left) and functional forms (right) shape it.