Poincar\'e-covariant analysis of heavy-quark baryons

We use a symmetry-preserving truncation of meson and baryon bound-state equations in quantum field theory in order to develop a unified description of systems constituted from light- and heavy-quarks. In particular, we compute the spectrum and leptonic decay constants of ground-state pseudoscalar- and vector-mesons: $q^\prime \bar q$, $Q^\prime \bar Q$, with $q^\prime,q=u,d,s$ and $Q^\prime,Q = c,b$; and the masses of $J^P=3/2^+$ baryons and their first positive-parity excitations, including those containing one or more heavy quarks. This Poincar\'e-covariant analysis predicts that such baryons have a complicated angular momentum structure. For instance, the ground states are all primarily $S$-wave in character, but each possesses $P$-, $D$- and $F$-wave components, with the $P$-wave fraction being large in the $qqq$ states; and the first positive-parity excitation in each channel has a large $D$-wave component, which grows with increasing current-quark mass, but also exhibits features consistent with a radial excitation. The configuration space extent of all such baryons decreases as the mass of the valence-quark constituents increases.