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

Motivated by recent anomalies in FCNC $b\to s{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$, 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 $T_{b3}\to T_8 \tau^+\tau^-$inthewhole$q^2$regionandinthedifferent$q^2$ bins by the measurement of ${\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}^0{\mu }^{+}{\mu }^{-}$. Many of them are obtained for the first time. In addition, the longitudinal polarization fractions and the leptonic forward-backward asymmetries of all $T_{b3}\to T_8{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ 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 $B(T_{c3}\to T_{8}\ell^+\ell^-)$byusingtheexperimentalupperlimitsof$B(\Lambda^+_c\to p\mu^+\mu^-)$and$B(\Lambda^+_c\to pe^+e^-)$, and find the experimental upper limit of $B({\mathrm{\Lambda }}_c^{+}\to p{\mu }^{+}{\mu }^{-})$ giving effective bounds on the relevant SU(3) flavor symmetry parameters. The predictions of $B(\Xi^0_c \to \Xi^0e^+e^-)$and$B(\Xi^0_c \to \Xi^0\mu^+\mu^-)$ will be different between the single-quark transition dominant contributions and the W-exchange dominant ones. © As for $T_8\to T_8^{\mathrm{\prime }}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ decays, we analyze the single-quark transition contributions and the W-exchange contributions by using two measurements of $B({\mathrm{\Xi }}^0\to {\mathrm{\Lambda }}^0{e}^{+}{e}^{-})$ 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.