The form factors of transition process ${\mathcal{B}}_{Q_1{Q}_2}({\frac{1}{2}}^{+})\to {\mathcal{B}}_{Q_1}^{\ast }({\frac{3}{2}}^{+})$ and their applications to semileptonic decays

Abstract

In the framework of QCD sum rules, we obtain the form factors of the weak transition process ${\mathcal{B}}_{Q_1{Q}_2}({\frac{1}{2}}^{+})\to {\mathcal{B}}_{Q_1}^{\ast }({\frac{3}{2}}^{+})$. In this analysis, we eliminate the interferences of the low spin states and negative parity states to final results by employing 16 different dirac structures. As an application, these form factors are finally used to analyze the semileptonic decays of ${\mathcal{B}}_{Q_1{Q}_2}({\frac{1}{2}}^{+})\to {\mathcal{B}}_{Q_1}^{\ast }({\frac{3}{2}}^{+})l\nu$, where these decays are driven by the transition processes $c\to d/s+l^{+}+{\nu }_l$ and $b\to u+l^{-}+{\overline{\nu }}_l$. The predicted physical quantities include not only the partial widths, ratios of ${\Gamma }_L/{\Gamma }_T$ and the branching fractions, but also some observables such as the forward-backward asymmetry parameter $A_{FB}^l$ of lepton, the $P_z^F$ component of the polarization vector for daughter baryon and the longitudinal polarization of the lepton $P_z^l$. We hope all of these theoretical predictions about the weak decays will be helpful for studying the properties of doubly heavy baryons in experiments in the future.