Study on the weak decay between two heavy baryons $B_i$(${\frac{1}{2}}^{+}$) → $B_f$(${\frac{3}{2}}^{+}$) in the light-front quark model

In this work, we study the weak decay between two heavy baryons $B_i$(${\frac{1}{2}}^{+}$) → $B_f$(${\frac{3}{2}}^{+}$) in the light-front quark model where three-quark picture is employed for baryon. We derive general form of transition amplitude of $B_i$(${\frac{1}{2}}^{+}$) → $B_f$(${\frac{3}{2}}^{+}$), and analyze two specific cases of transitions: the weak decays of single heavy baryon ${\Sigma }_b$ → ${\Sigma }_c^{\ast }$ and the decays of double-charmed baryon ${\Xi }_{cc}$ → ${\Sigma }_c^{\ast }$(${\Xi }_c^{\ast }$). We compute the hadronic form factors for the transitions and apply them to study the decay widths of the semi-leptonic $B_i$(${\frac{1}{2}}^{+}$) → $B_f$(${\frac{3}{2}}^{+}$)l${\overline{\nu }}_l$ and non-leptonic $B_i$(${\frac{1}{2}}^{+}$) → $B_f$(${\frac{3}{2}}^{+}$)M. Previously we studied the transition ${\Sigma }_b$ → ${\Sigma }_c^{\ast }$ with the quark-diquark picture of baryon in the light-front quark model. Here we revisit this transition with three-quark picture of baryon. At the quark level, the transition ${\Sigma }_b$ → ${\Sigma }_c^{\ast }$ is induced by the b → c transition.The subsystem of the two unchanged light quarks which possesses definite and same spin in initial and final state can be viewed as a spectator, so the spectator approximation can be applied directly. For the weak decay of doubly charmed baryon ${\Xi }_{cc}$, a c quark decays to a light quark q${}_1$, so both the initial state cc and final state q${}_1$q${}_2$ (q${}_1$ and the original q${}_2$ in initial state may be the same flavor quarks) which possess definite spin are no longer spectators. A rearrangement of quarks for initial and final states is adopted to isolate the unchanged subsystem cq${}_2$ which can be viewed as the spectator approximately. Future measurements on these channels will constrain the nonperturbative parameter in the wavefunctions and test the model predictions.