  Thanks to the remarkable achievements of LHC, a large database on baryons has
been accumulated, so it is believed that the time for precisely studying
baryons especially heavy baryons, has come. By analyzing the data, the
quark-diquark structure which has been under intensive discussions, can be
tested. In this work the decay widths of weak transitions $\Sigma_b\to
\Sigma^*_c+X$ are calculated in terms of the light front quark model (LFQM). To
carry out the calculations, the quark-diquark picture is employed where an
axial-vector diquark composed of two light quarks serves as a spectator in the
concerned processes. The first step of this work is to construct the vertex
functions for $\Sigma^{(*)}_c$ and $\Sigma_b$, then the relevant form factors
are derived. It is shown that under the heavy quark limit the Isgur-Wise
functions for the transition are re-deduced. Indeed, how to properly depict the
polarization ($\epsilon_{\mu}$) of the diquark is slightly tricky. In this
work, we apply two schemes to explicitly determine the momentum-dependence of
the diquark. The corresponding numerical results are presented which will be
testified by the future experiments.
