Effects of a dressed quark-gluon vertex in vector heavy-light mesons and theory average of theBc*meson mass

Abstract

We extend earlier investigations of heavy-light pseudoscalar mesons to the vector case, using a simple model in the context of the Dyson-Schwinger-Bethe-Salpeter approach. We investigate the effects of a dressed quark-gluon vertex in a systematic fashion and illustrate and attempt to quantify corrections beyond the phenomenologically very useful and successful rainbow-ladder truncation. In particular we investigate the dressed quark-photon vertex in such a setup and make a prediction for the experimentally as yet unknown mass of the ${B}_{c}^{*}$, which we obtain at 6.334 GeV well in line with predictions from other approaches. Furthermore, we combine a comprehensive set of results from the theoretical literature. The theoretical average for the mass of the ${B}_{c}^{*}$ meson is $6.336\ifmmode\pm\else\textpm\fi{}0.002\text{ }\text{ }\mathrm{GeV}$.