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Forward-backward asymmetries in $Λ_b \rightarrow Λl^+ l^-$ in Bethe-Salpeter equation approach

Using the Bethe-Salpeter equation (BSE) we investigate the forward-backward asymmetries $( A_{FB}) $ in $Λ_b \rightarrow Λl^+ l^-(l=e,μ,τ)$ in the quark-diquark model. This approach provides precise form factors that are different from those of QCD sum rules. We calculate the rare decay form factors for $Λ_b \rightarrow Λl^+ l^-$ and investigate the (integrated) forward-backward asymmetries in these decay channels. We find that the integrated $A^l_{FB}$, $\bar{A}^l_{FB}(Λ_b \rightarrow Λe^+ e^-) \simeq -0.1371 $, $\bar{A}^l_{FB}(Λ_b \rightarrow Λμ^+ μ^- ) \simeq -0.1376 $, $\bar{A}^l_{FB}(Λ_b \rightarrow Λτ^+ τ^-) \simeq -0.1053 $, the hadron side asymmetries $\bar{A}^h_{FB}(Λ_b \rightarrow Λμ^+ μ^-)\simeq -0.2315$, the lepton-hadron side asymmetries $\bar{A}^{lh}_{FB}(Λ_b \rightarrow Λμ^+ μ^-)\simeq 0.0827$, the longitudinal polarization fractions $\bar{F}_L(Λ_b \rightarrow Λμ^+ μ^-)\simeq 0.5681$.