Bethe–Salpeter studies of mesons beyond rainbow-ladder
Institute for Nuclear Physics, Darmstadt University of
Technology, Schlossgartenstraße 9, 64289 Darmstadt,
a e-mail: firstname.lastname@example.org
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.
© Owned by the authors, published by EDP Sciences, 2010