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

Abstract

In this work, we study the weak decay between two heavy baryons ${\mathcal{B}}_i({\frac{1}{2}}^{+})\to {\mathcal{B}}_f({\frac{3}{2}}^{+})$ in the light-front quark model where three-quark picture is employed for baryon. We derive general form of transition amplitude of ${\mathcal{B}}_i({\frac{1}{2}}^{+})\to {\mathcal{B}}_f({\frac{3}{2}}^{+})$, and analyze two specific cases of transitions: the weak decays of single heavy baryon ${\Sigma }_b\to {\Sigma }_c^{\ast }$ and the decays of double-charmed baryon ${\Xi }_{cc}\to {\Sigma }_c^{\ast }({\Xi }_c^{\ast })$. We compute the hadronic form factors for the transitions and apply them to study the decay widths of the semi-leptonic ${\mathcal{B}}_i({\frac{1}{2}}^{+})\to {\mathcal{B}}_f({\frac{3}{2}}^{+})l{\bar{\nu }}_l$ and non-leptonic ${\mathcal{B}}_i({\frac{1}{2}}^{+})\to {\mathcal{B}}_f({\frac{3}{2}}^{+})M$. Previously we studied the transition ${\Sigma }_b\to {\Sigma }_c^{\ast }$ 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 ${\Sigma }_b\to {\Sigma }_c^{\ast }$ is induced by the $b\to c$ 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 $c{q}_2$ 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.

arXiv comment20 pages, 6 figures and 10 tables

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• Angular distribution of the FCNC process $B_c\to D_s^{\ast }(\to D_s\pi ){\ell }^{+}{\ell }^{-}$
• Baryonic heavy-to-light form factors induced by tensor current in light-front approach
• Analysis of the semileptonic decays of ${\Xi }_{cc}$ and ${\Omega }_{cc}$ baryons in QCD sum rules