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arXiv · nucl-th/0510075

Sigma Terms of Light-Quark Hadrons

V. V. Flambaum·A. Hoell·P. Jaikumar·C. D. Roberts·S. V. Wright
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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 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 ~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 Delta, and thereby sigma_N and sigma_Delta. This "quark-core" piece is augmented by the "pion cloud" contribution, which is positive. The analysis yields sigma_N~60MeV and sigma_Delta~50MeV.

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V. V. Flambaum, A. Hoell, P. Jaikumar, C. D. Roberts, S. V. Wright. 2005-12-05. Sigma Terms of Light-Quark Hadrons. https://doi.org/10.1007/s00601-005-0123-1

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