Schwinger functions and light-quark bound states, and sigma terms

Abstract

We explore the viability of using solely spacelike information about a Schwinger function to extract properties of bound states. In a concrete example it is not possible to determine properties of states with masses \gsim 1.2 GeV. Modern Dyson-Schwinger equation methods supply a well-constrained tool that provide access to hadron masses and σ-terms. We report values of the latter for a range of hadrons. Of interest is analysis relating to a u,d scalar meson, which is compatible with a picture of the lightest 0^{++} as a bound state of a dressed-quark and -antiquark supplemented by a material pion cloud. A constituent-quark σ-term is defined, which affords a means for assessing the flavour-dependence of dynamical chiral symmetry breaking.