First Look at Heavy–Light Mesons with a Dressed Quark–Gluon Vertex

Following up on earlier work, we investigate possible effects of a dressed quark–gluon vertex in heavy–light mesons. In particular, we study corrections to the popular rainbow-ladder truncation of the Dyson–Schwinger–Bethe–Salpeter equation system. We adopt a simple interaction kernel which reduces the resulting set of coupled integral equations to a set of coupled algebraic equations, which are solved numerically. In this way, we extend previous studies to quark–antiquark systems with unequal current-quark masses, at first for the pseudoscalar case, and investigate the resulting set of problems and solutions. We attempt to find patterns in—as well as to quantify corrections to—the rainbow-ladder truncation. In addition, we open this approach to phenomenological predictions of the heavy quark symmetry.