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

Abstract

In this work, we study 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 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}^+), and analyze two specific cases of transitions: the weak decays of single heavy baryon Sigma _{b} rightarrow Sigma _{c}^* and the decays of double-charmed baryon Xi _{cc}rightarrow Sigma _{c}^*(Xi _{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}^+) lbar{nu }_l and non-leptonic {mathcal {B}}_i(frac{1}{2}^+)rightarrow {mathcal {B}}_f(frac{3}{2}^+)M. Previously we studied the transition Sigma _{b} rightarrow Sigma _{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}^* is induced by the brightarrow 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_1q_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.