Forward-backward asymmetries in $\Lambda_b \rightarrow \Lambda l^+ l^-$ in Bethe-Salpeter equation approach

TL;DR

This paper uses the Bethe-Salpeter equation in a quark-diquark model to calculate form factors and analyze forward-backward asymmetries in the rare decay $ ext{Lambda}_b ightarrow ext{Lambda} l^+ l^-$, providing precise predictions for various asymmetries and polarization fractions.

Contribution

It introduces a Bethe-Salpeter equation approach to compute decay form factors and asymmetries, offering an alternative to QCD sum rules with more precise predictions.

Findings

Calculated integrated forward-backward asymmetries for different leptons.

Predicted specific values for hadron-side and lepton-hadron side asymmetries.

Determined the longitudinal polarization fraction in the decay.

Abstract

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