Study on the weak decay between two heavy baryons $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)$$ in the light-front quark model

AbstractIn this work, we study the weak decay between two heavy baryons $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)$$ B i ( 1 2 + ) → B f ( 3 2 + ) in the light-front quark model where three-quark picture is employed for baryon. We derive general form of transition amplitude of $$ {\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)$$ B i ( 1 2 + ) → B f ( 3 2 + ) , and analyze two specific cases of transitions: the weak decays of single heavy baryon $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$ Σ b → Σ c ∗ and the decays of double-charmed baryon $$\Xi _{cc}\rightarrow \Sigma _{c}^*(\Xi _{c}^*)$$ Ξ cc → Σ c ∗ ( Ξ c ∗ ) . We compute the hadronic form factors for the transitions and apply them to study the decay widths of the semi-leptonic $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+) l\bar{\nu }_l$$ B i ( 1 2 + ) → B f ( 3 2 + ) l ν ¯ l and non-leptonic $${\mathcal {B}}_i(\frac{1}{2}^+)\rightarrow {\mathcal {B}}_f(\frac{3}{2}^+)M$$ B i ( 1 2 + ) → B f ( 3 2 + ) M . Previously we studied the transition $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$ Σ b → Σ c ∗ 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 $$\Sigma _{b} \rightarrow \Sigma _{c}^*$$ Σ b → Σ c ∗ is induced by the $$b\rightarrow c$$ 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 $$\Xi _{cc}$$ Ξ cc , a c quark decays to a light quark $$q_1$$ q 1 , so both the initial state cc and final state $$q_1q_2$$ q 1 q 2 ($$q_1$$ q 1 and the original $$q_2$$ 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 $$cq_2$$ c q 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.