Hadronic bound states in SU(2) from Dyson–Schwinger equations

Abstract

By using the Dyson–Schwinger/Bethe–Salpeter formalism in Euclidean spacetime, we calculate the ground state spectrum of J≤1 hadrons in an SU(2) gauge theory with two fundamental fermions. We show that the rainbow-ladder truncation, commonly employed in QCD studies, is unsuitable for a description of an SU(2) theory. This we remedy by truncating at the level of the quark–gluon vertex Dyson–Schwinger equation in a diagrammatic expansion. Results obtained within this novel approach show good agreement with lattice studies. These findings emphasize the need to use techniques more sophisticated than rainbow-ladder when investigating generic strongly interacting gauge theories.