Survey of heavy-meson observables

We employ a Dyson-Schwinger equation model to effect a unified and uniformly accurate description of light- and heavy-meson observables, which we characterize by heavy-meson leptonic decays, semileptonic heavy-to-heavy and heavy-to-light transitions, $\overrightarrow{B}{D}^{*},$ D, $\rho ,$ $\pi ;$ $\overrightarrow{D}{K}^{*},$ K, $\pi$, radiative and strong decays, $B_{\mathrm{}\left(s\right)\mathrm{}}^{*}\to B_{\mathrm{}\left(s\right)\mathrm{}}\gamma ;$ $D_{\mathrm{}\left(s\right)\mathrm{}}^{*}\to D_{\mathrm{}\left(s\right)\mathrm{}}\gamma ,$ $D\pi$, and the rare $\overrightarrow{B}{K}^{*}\gamma$ flavor-changing neutral-current process. We elucidate the heavy-quark limit of these processes and, using a model-independent mass formula valid for all nonsinglet pseudoscalar mesons, demonstrate that their mass rises linearly with the mass of their heaviest constituent. In our numerical calculations we eschew a heavy-quark expansion and rely instead on the observation that the dressed $c,b$-quark mass functions are well approximated by a constant, interpreted as their constituent mass: we find $M_c=1.32\mathrm{}\hspace{0.5em}\mathrm{GeV}$ and $M_b=4.65\mathrm{}\hspace{0.5em}\mathrm{GeV}$. The calculated heavy-meson leptonic decay constants and transition form factors are a necessary element in the experimental determination of CKM matrix elements. The results also show that this framework, as employed hitherto, is able to describe vector meson polarization observables well.