In this work, we study $Lambda_{b}toLambda_{c}$ and $Sigma_{b}toSigma_{c}$ 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.
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