  Up to now, the excited charmed and bottom baryon states are still not well
studied both experimentally and theoretically. In the present paper, we predict
the mass of $\Omega_b^*$, the only $L = 0$ baryon state which has not been
observed, to be 6069.2 MeV. The spectra of charmed and bottom baryons with the
orbital angular momentum $L = 1$ are studied in two popular constituent quark
models, the Goldstone boson exchange (GBE) and the one gluon exchange (OGE)
hyperfine interaction models, respectively. Inserting the latest experimental
data from the "Review of Particle Physics", we find that in the GBE model,
there exist some multiplets ($\Sigma_{c(b)}$, $\Xi'_{c(b)}$ and
$\Omega_{c(b)}$) which total spins of three quarks in their lowest energy
states are 3/2, but in the OGE model there is no such phenomenon. This is the
most important difference between the GBE and OGE models. These results can be
tested in the near future. We suggest more efforts to study the excited charmed
and bottom baryons both theoretically and experimentally, not only for the
abundance of baryon spectra, but also for determining which hyperfine
interaction model is realized in nature.
