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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 $b\to s\ell^+\ell^-$, we study $B_1\to B_2\ell^+\ell^-(\ell=e,μ,τ)$ 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 $T_{b3}\to T_8 μ^+μ^-$ and $T_{b3}\to T_8 τ^+τ^-$ in the whole $q^2$ region and in the different $q^2$ bins by the measurement of $Λ^0_b\to Λ^0 μ^+μ^-$. 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 $B(Λ^+_c\to pμ^+μ^-)$ and $B(Λ^+_c\to pe^+e^-)$, and find the experimental upper limit of $B(Λ^+_c\to pμ^+μ^-)$ giving effective bounds on the relevant SU(3) flavor symmetry parameters. The predictions of $B(Ξ^0_c \to Ξ^0e^+e^-)$ and $B(Ξ^0_c \to Ξ^0μ^+μ^-)$ 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(Ξ^0\to Λ^0 e^+e^-)$ and $ B(Σ^+\to pμ^+μ^-)$, and give the branching ratio predictions by assuming either single-quark transition dominant contributions or the W-exchange dominant ones.