Hadronic weak decay Bb(12+)→B(12+, 32+)+V

Abstract

It is shown that for the effective Lagrangian with the factorization ansatz considered here, in the two-body hadronic decay ${\mathcal{B}}_{b}({\frac{1}{2}}^{+})\ensuremath{\rightarrow}\mathcal{B}({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})+V$, with ${\mathcal{B}}_{b}({\frac{1}{2}}^{+})$ belonging to the representation $\overline{3}$, the only allowed decay channel is ${\mathcal{B}}_{b}({\frac{1}{2}}^{+})\ensuremath{\rightarrow}\mathcal{B}({\frac{1}{2}}^{+})+V$, where $\mathcal{B}({\frac{1}{2}}^{+})$ belongs to the representation 8 of $SU(3)$. However, for ${\mathcal{B}}_{b}({\frac{1}{2}}^{+})$ belonging to the sextet representation 6, the allowed decay channels are ${\mathcal{B}}_{b}({\frac{1}{2}}^{+})\ensuremath{\rightarrow}\mathcal{B}({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})+V$, where $\mathcal{B}({\frac{1}{2}}^{+})$ and $\mathcal{B}({\frac{3}{2}}^{+})$ belong to the octet representation ${8}^{\ensuremath{'}}$ and the decuplet 10 of $SU(3)$, respectively. The decay channel ${\mathcal{B}}_{b}({\frac{1}{2}}^{+})\ensuremath{\rightarrow}\mathcal{B}({\frac{1}{2}}^{+})+V$ is analyzed in detail. The decay rate ($\mathrm{\ensuremath{\Gamma}}$) and the asymmetry parameters $\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}},\ensuremath{\beta},\ensuremath{\gamma}$, and ${\ensuremath{\gamma}}^{\ensuremath{'}}$ are expressed in terms of four amplitudes. In particular, for the decay ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}+J/\ensuremath{\psi}$ it is shown that within the factorization framework, using heavy quark spin symmetry, the decay rate and the asymmetry parameters can be expressed in terms of two form factors ${F}_{1}$ and ${F}_{2}/{F}_{1}$, which are to be evaluated in some model. By using the values of these form factors calculated in a quark model, the branching ratio and the asymmetry parameters $\ensuremath{\alpha}$ and ${\ensuremath{\alpha}}^{\ensuremath{'}}$ are calculated numerically. For other heavy quarks belonging to the triplet and sextet representations, the results can be easily obtained by using $SU(3)$ symmetry and a phase-space factor. Finally, the decay ${\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}+J/\ensuremath{\psi}$ is analyzed within the factorization framework. It is shown that the asymmetry parameter $\ensuremath{\alpha}$ in this particular decay is zero. The branching ratio obtained in the first approximation is compared with the experimental value.