  In this work, we study $\Lambda_{b}\to\Lambda_{c}$ and
$\Sigma_{b}\to\Sigma_{c}$ weak decays in the light-front quark model. As is
well known, the key point for such calculations is properly evaluating the
hadronic transition matrix elements which are dominated by the non-perturbative
QCD effect. In our calculation, we employ the light-front quark model and
rather than the traditional diquark picture, we account the two spectator light
quarks as individual ones. Namely during the transition, they retain their
color indices, momenta and spin polarizations unchanged. Definitely, the
subsystem composed of the two light quarks is still in a color-anti-triplet and
possesses a definite spin, but we do not priori assume the two light quarks to
be in a bound system-diquark. Our purpose is probing the diquark picture, via
comparing the results with the available data, we test the validity and
applicability of the diquark structure which turns a three-body problem into a
two-body one, so greatly simplifies the calculation. It is indicated that the
two approaches (diquark and a subsystem within which the two light quarks are
free) lead to similar numerical results even though the model parameters in the
two schemes might deviate slightly. Thus, the diquark approach seems
sufficiently reasonable.
