Sigma Terms of Light-Quark Hadrons

Abstract.A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature’s fundamental parameters. A hadron’s σ-term is a measure of this dependence. The connection between a hadron’s σ-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit σπ = mπ/2. This truncation also provides a decent estimate of σρ because the two dominant self-energy corrections to the ρ-meson’s mass largely cancel in their contribution to σρ. The truncation is less accurate for the ω, however, because there is little to compete with an ω → ρπ self-energy contribution that magnifies the value of σω by ≲25%. A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Δ, and thereby σN and σΔ. This “quark-core” piece is augmented by the “pion cloud” contribution, which is positive. The analysis yields σN ≃ 60 MeV and σΔ ≃ 50 MeV.