Forward-backward asymmetries in ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ in Bethe-Salpeter equation approach

Abstract

Using the Bethe-Salpeter equation (BSE) we investigate the forward-backward asymmetries $(A_{FB})$ in ${\Lambda }_b\to \Lambda l^{+}{l}^{-}(l=e,\mu ,\tau )$ 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 ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ and investigate the (integrated) forward-backward asymmetries in these decay channels. We find that the integrated $A_{FB}^l$, ${\bar{A}}_{FB}^l({\Lambda }_b\to \Lambda e^{+}{e}^{-})\simeq -0.1371$, ${\bar{A}}_{FB}^l({\Lambda }_b\to \Lambda {\mu }^{+}{\mu }^{-})\simeq -0.1376$, ${\bar{A}}_{FB}^l({\Lambda }_b\to \Lambda {\tau }^{+}{\tau }^{-})\simeq -0.1053$, the hadron side asymmetries ${\bar{A}}_{FB}^h({\Lambda }_b\to \Lambda {\mu }^{+}{\mu }^{-})\simeq -0.2315$, the lepton-hadron side asymmetries ${\bar{A}}_{FB}^{lh}({\Lambda }_b\to \Lambda {\mu }^{+}{\mu }^{-})\simeq 0.0827$, the longitudinal polarization fractions ${\bar{F}}_L({\Lambda }_b\to \Lambda {\mu }^{+}{\mu }^{-})\simeq 0.5681$.