Sigma terms of light-quark hadrons

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 sigma-term is a measure of this dependence. The connection between a hadron's sigma-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 sigma(pi) = m(pi)/2. This truncation also provides a decent estimate of sigma(rho) because the two dominant self-energy corrections to the rho-meson's mass largely cancel in their contribution to sigma(rho). The truncation is less accurate for the omega, however, because there is little to compete with an omega -> rho pi self-energy contribution that magnifies the value of sigma(omega) by less than or similar to 25%. A Poincare-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 triangle, and thereby sigma(N) and sigma(triangle). This quark-core piece is augmented by the pion cloud contribution, which is positive. The analysis yields sigma(N) similar or equal to 60 MeV and sigma(Delta) similar or equal to 50 MeV.