Bethe–Salpeter studies of mesons beyond rainbow-ladder

Institute for Nuclear Physics, Darmstadt University of Technology, Schlossgartenstraße 9, 64289 Darmstadt, Germany

^a e-mail: richard.williams@physik.tu-darmstadt.de

Abstract

We investigate the masses of light mesons from a coupled system of Dyson–Schwinger and Bethe– Salpeter equations. We explicitly take into account dominant non-Abelian and sub-leading Abelian contributions to the dressed quark-gluon vertex. We also include unquenching effects in the form of hadronic resonance contributions via the back-reaction of pions. We construct the corresponding Bethe–Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity. Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane. This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the relative impact of different corrections beyond rainbow-ladder on the properties of mesons. We find that sub-leading Abelian corrections are further dynamically suppressed, and that our results supersede early qualitative predictions with significantly simpler truncation schemes.