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

Thanks to the remarkable achievements of the LHC, a large database on baryons has been accumulated. There is therefore now the opportunity to precisely study baryons, particularly heavy baryons. By analyzing the data, the quark–diquark structure, which has been the subject of intensive discussions, can be tested. In this work the decay widths of weak transitions ${\Sigma }_b\to {\Sigma }_c^{\ast }+X$ are calculated in terms of the light-front quark model. 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 processes concerned. The first step of this work is to construct the vertex functions for ${\Sigma }_c^{(\ast )}$ and Σ_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, the question of how to properly depict the polarization (ϵ _μ) 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 future experiments. (paper)