Studying ${\mathcal{B}}_1({\frac{1}{2}}^{+})\to {\mathcal{B}}_2({\frac{1}{2}}^{+}){\ell }^{+}{\ell }^{-}$ Semi-leptonic Weak Baryon Decays with the SU(3) Flavor Symmetry

Abstract

Motivated by recent anomalies in FCNC $b\to s{\ell }^{+}{\ell }^{-}$, we study $B_1\to B_2{\ell }^{+}{\ell }^{-}(\ell =e,\mu ,\tau )$ semi-leptonic weak decays with the SU(3) flavor symmetry, where $B_{1,2}$ are the spin-1/2 baryons of single bottomed anti-triplet $T_{b3}$, single charmed anti-triplet $T_{c3}$ or light baryon octet $T_8$. Using the SU(3) irreducible representation approach, we first obtain the amplitude relations among different decays, and then predict the relevant not-yet measured observables of these decays. (a) We calculate the branching ratios of the $T_{b3}\to T_8{\mu }^{+}{\mu }^{-}$ and $T_{b3}\to T_8{\tau }^{+}{\tau }^{-}$ in the whole $q^2$ region and in the different $q^2$ bins by the measurement of ${\Lambda }_b^0\to {\Lambda }^0{\mu }^{+}{\mu }^{-}$. Many of them are obtained for the first time. In addition, the longitudinal polarization fractions and the leptonic forward-backward asymmetries of all $T_{b3}\to T_8{\ell }^{+}{\ell }^{-}$ decays are very similar to each other in certain $q^2$ bin due to the SU(3) flavor symmetry. (b) We analyze the upper limits of $B(T_{c3}\to T_8{\ell }^{+}{\ell }^{-})$ by using the experimental upper limits of $B({\Lambda }_c^{+}\to p{\mu }^{+}{\mu }^{-})$ and $B({\Lambda }_c^{+}\to p{e}^{+}{e}^{-})$, and find the experimental upper limit of $B({\Lambda }_c^{+}\to p{\mu }^{+}{\mu }^{-})$ giving effective bounds on the relevant SU(3) flavor symmetry parameters. The predictions of $B({\Xi }_c^0\to {\Xi }^0{e}^{+}{e}^{-})$ and $B({\Xi }_c^0\to {\Xi }^0{\mu }^{+}{\mu }^{-})$ will be different between the single-quark transition dominant contributions and the W-exchange dominant ones. (c) As for $T_8\to T_8^{\prime }{\ell }^{+}{\ell }^{-}$ decays, we analyze the single-quark transition contributions and the W-exchange contributions by using two measurements of $B({\Xi }^0\to {\Lambda }^0{e}^{+}{e}^{-})$ and $B({\Sigma }^{+}\to p{\mu }^{+}{\mu }^{-})$, and give the branching ratio predictions by assuming either single-quark transition dominant contributions or the W-exchange dominant ones.

Comments: 17 pages