${\mathrm{\Sigma }}_b\to {\mathrm{\Sigma }}_c^{\ast }$ weak decays in the light-front quark model with two schemes to deal with the polarization of diquark

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 ${\mathrm{\Sigma }}_c^{(\ast )}$ and ${\mathrm{\Sigma }}_b$, 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 (${ϵ}_{\mu }$) 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.