Nucleon sigma term and strange quark content from lattice QCD with exact chiral symmetry

TL;DR

This work determines the nucleon sigma term $\sigma_{\pi N}$ and the strange-quark content in two-flavor QCD using lattice QCD with exact chiral symmetry via overlap fermions. The authors implement the Feynman-Hellman approach to relate derivatives of the nucleon mass $M_N$ with respect to valence and sea-quark masses to connected and disconnected scalar matrix elements, enabling a separation of valence and sea contributions. They analyze unitary data with baryon chiral perturbation theory (BChPT) and partially quenched ChPT (PQChPT), including finite-volume corrections, to extract $\sigma_{\pi N}$ and to estimate the strange content $y$. Their key finding is a relatively small strange content, $y\approx 0.03$, and a sigma term around $\sigma_{\pi N} \sim 53$ MeV, supporting a valence-dominated origin of the sigma term and resolving some prior lattice artifacts associated with Wilson fermions. The results establish a reliable framework for future 2+1 flavor calculations and have implications for neutralino dark matter-nucleon interactions and nucleon structure studies.

Abstract

We calculate the nucleon sigma term in two-flavor lattice QCD utilizing the Feynman-Hellman theorem. Both sea and valence quarks are described by the overlap fermion formulation, which preserves exact chiral and flavor symmetries on the lattice. We analyse the lattice data for the nucleon mass using the analytical formulae derived from the baryon chiral perturbation theory. From the data at valence quark mass set different from sea quark mass, we may extract the sea quark contribution to the sigma term, which corresponds to the strange quark content. We find that the strange quark content is much smaller than the previous lattice calculations and phenomenological estimates.

Figures (8)

• Figure 1: Effective mass of the smeared-local nucleon correlator. Data are shown for various degenerate valence quark masses $m_{\mathrm{val}}$ at a fixed sea quark mass $am_{\mathrm{sea}}=0.035$.
• Figure 2: BChPT fit of the nucleon mass for unitary points. The solid, dot, dashed, dot-dashed curves represent the Fit 0a, Ia, II, and III, respectively.
• Figure 3: Chiral fit of the corrected data (diamonds). Solid and dashed curves represent the fits using 5 and 6 heaviest data points, respectively. For a reference, we also show the raw data (circles).
• Figure 4: Chiral fit with the $\mathcal{O}(p^4)$ formula plus the finite volume effect $\Delta_a+\Delta_b$. Dashed, solid and dotted curves represent the fit results in the infinite volume from the Fit Ia, II and III, respectively. For a reference, we show the finite volume corrected data points (diamonds).
• Figure 5: Partially quenched nucleon masses and fit curves (Fit PQ-b).