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

Motivated by recent anomalies in FCNC $bto sell^+ell^-$, we study $B_1to B_2ell^+ell^-(ell=e,mu,tau)$ 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 $Lambda^0_bto Lambda^0 mu^+mu^-$. 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 $B(Lambda^+_cto pmu^+mu^-)$ and $B(Lambda^+_cto pe^+e^-)$, and find the experimental upper limit of $B(Lambda^+_cto pmu^+mu^-)$ giving effective bounds on the relevant SU(3) flavor symmetry parameters. The predictions of $B(Xi^0_c to Xi^0e^+e^-)$ and $B(Xi^0_c to Xi^0mu^+mu^-)$ will be different between the single-quark transition dominant contributions and the W-exchange dominant ones. (c) As for $T_{8}to T_8 ell^+ell^-$ decays, we analyze the single-quark transition contributions and the W-exchange contributions by using two measurements of $ B(Xi^0to Lambda^0 e^+e^-)$ and $ B(Sigma^+to pmu^+mu^-)$, and give the branching ratio predictions by assuming either single-quark transition dominant contributions or the W-exchange dominant ones.